DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP217^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Feb 28 09:05:10 AM UTC 2026

% Result   : Theorem 25.35s 7.41s
% Output   : Refutation 25.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   58 (  28 unt;   0 typ;   0 def)
%            Number of atoms       :  756 (  94 equ;   0 cnn)
%            Maximal formula atoms :    5 (  13 avg)
%            Number of connectives : 1128 (  44   ~;  19   |;  17   &;1024   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :   55 (  54 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  774 ( 771 usr;  43 con; 0-8 aty)
%            Number of variables   :  111 (  20   ^;  84   !;   7   ?; 111   :)

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

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

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

thf(type_def_9,type,
    heap_T5660665574680485309rray_o: $tType ).

thf(type_def_10,type,
    heap_T1346037964561226099ay_int: $tType ).

thf(type_def_11,type,
    heap_T3836121109492952855ay_nat: $tType ).

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

thf(type_def_13,type,
    heap_T5738788834812785303t_unit: $tType ).

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

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

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

thf(type_def_17,type,
    set_Pr1261947904930325089at_nat: $tType ).

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

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

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

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

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

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

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

thf(type_def_25,type,
    produc6271795597528267376eger_o: $tType ).

thf(type_def_26,type,
    produc8923325533196201883nteger: $tType ).

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

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

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

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

thf(type_def_31,type,
    filter1242075044329608583at_nat: $tType ).

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

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

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

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

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

thf(type_def_37,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(type_def_38,type,
    heap_e7401611519738050253t_unit: $tType ).

thf(type_def_39,type,
    option8956607266484857688it_nat: $tType ).

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

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

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

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

thf(type_def_44,type,
    set_Pr958786334691620121nt_int: $tType ).

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

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

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

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

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

thf(type_def_50,type,
    produc8664842809031399944it_nat: $tType ).

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

thf(type_def_52,type,
    produc7822875418678951345atural: $tType ).

thf(type_def_53,type,
    produc5835291356934675326atural: $tType ).

thf(type_def_54,type,
    produc6653097349344004940it_nat: $tType ).

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

thf(type_def_56,type,
    produc6756470014200349799atural: $tType ).

thf(type_def_57,type,
    produc859450856879609959at_nat: $tType ).

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

thf(type_def_59,type,
    set_se6260736226359567993nt_int: $tType ).

thf(func_def_0,type,
    produc6756470014200349799atural: $tType ).

thf(func_def_1,type,
    option8956607266484857688it_nat: $tType ).

thf(func_def_2,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(func_def_3,type,
    produc8664842809031399944it_nat: $tType ).

thf(func_def_4,type,
    produc5835291356934675326atural: $tType ).

thf(func_def_5,type,
    produc859450856879609959at_nat: $tType ).

thf(func_def_6,type,
    produc6653097349344004940it_nat: $tType ).

thf(func_def_7,type,
    set_se6260736226359567993nt_int: $tType ).

thf(func_def_8,type,
    produc7822875418678951345atural: $tType ).

thf(func_def_9,type,
    produc8923325533196201883nteger: $tType ).

thf(func_def_10,type,
    filter1242075044329608583at_nat: $tType ).

thf(func_def_11,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(func_def_12,type,
    set_Pr958786334691620121nt_int: $tType ).

thf(func_def_13,type,
    heap_T3836121109492952855ay_nat: $tType ).

thf(func_def_14,type,
    heap_T1346037964561226099ay_int: $tType ).

thf(func_def_15,type,
    produc6271795597528267376eger_o: $tType ).

thf(func_def_16,type,
    heap_T5738788834812785303t_unit: $tType ).

thf(func_def_17,type,
    heap_T5660665574680485309rray_o: $tType ).

thf(func_def_18,type,
    heap_e7401611519738050253t_unit: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_54,type,
    archim2889992004027027881ng_rat: rat > int ).

thf(func_def_55,type,
    archim3151403230148437115or_rat: rat > int ).

thf(func_def_56,type,
    archimedean_frac_rat: rat > rat ).

thf(func_def_57,type,
    array_make_o: nat > ( nat > $o ) > heap_T5660665574680485309rray_o ).

thf(func_def_58,type,
    array_make_int: nat > ( nat > int ) > heap_T1346037964561226099ay_int ).

thf(func_def_59,type,
    array_make_nat: nat > ( nat > nat ) > heap_T3836121109492952855ay_nat ).

thf(func_def_60,type,
    array_7872002506669749220t_unit: array_Product_unit > nat > heap_T5738788834812785303t_unit ).

thf(func_def_61,type,
    array_of_list_o: list_o > heap_T5660665574680485309rray_o ).

thf(func_def_62,type,
    array_of_list_int: list_int > heap_T1346037964561226099ay_int ).

thf(func_def_63,type,
    array_of_list_nat: list_nat > heap_T3836121109492952855ay_nat ).

thf(func_def_64,type,
    bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).

thf(func_def_65,type,
    bNF_re6321650412969554871eger_o: ( int > code_integer > $o ) > ( ( int > $o ) > ( code_integer > $o ) > $o ) > ( int > int > $o ) > ( code_integer > code_integer > $o ) > $o ).

thf(func_def_66,type,
    bNF_re398004352372739002nteger: ( int > code_integer > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( int > int > int ) > ( code_integer > code_integer > code_integer ) > $o ).

thf(func_def_67,type,
    bNF_re4711666741709854504_nat_o: ( int > code_integer > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( code_integer > nat > $o ) > $o ).

thf(func_def_68,type,
    bNF_re6574881592172037608er_o_o: ( int > code_integer > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( code_integer > $o ) > $o ).

thf(func_def_69,type,
    bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).

thf(func_def_70,type,
    bNF_re3804157879324367682nt_int: ( int > code_integer > $o ) > ( int > int > $o ) > ( int > int ) > ( code_integer > int ) > $o ).

thf(func_def_71,type,
    bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).

thf(func_def_72,type,
    bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).

thf(func_def_73,type,
    bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).

thf(func_def_74,type,
    bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).

thf(func_def_75,type,
    bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).

thf(func_def_76,type,
    bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).

thf(func_def_77,type,
    bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).

thf(func_def_78,type,
    bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_79,type,
    bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).

thf(func_def_80,type,
    bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).

thf(func_def_81,type,
    bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).

thf(func_def_82,type,
    bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).

thf(func_def_83,type,
    bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).

thf(func_def_84,type,
    bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).

thf(func_def_85,type,
    bNF_re4935368626670024657nteger: ( nat > nat > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( nat > int > int ) > ( nat > code_integer > code_integer ) > $o ).

thf(func_def_86,type,
    bNF_re4785983289428654063nt_int: ( nat > nat > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( nat > int > int ) > ( nat > int > int ) > $o ).

thf(func_def_87,type,
    bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_88,type,
    bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).

thf(func_def_89,type,
    bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_90,type,
    bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).

thf(func_def_91,type,
    bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).

thf(func_def_92,type,
    bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).

thf(func_def_93,type,
    bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).

thf(func_def_94,type,
    bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).

thf(func_def_95,type,
    bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).

thf(func_def_96,type,
    bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).

thf(func_def_97,type,
    bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).

thf(func_def_98,type,
    bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).

thf(func_def_99,type,
    bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).

thf(func_def_100,type,
    bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).

thf(func_def_101,type,
    bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).

thf(func_def_102,type,
    bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).

thf(func_def_103,type,
    bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).

thf(func_def_104,type,
    bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).

thf(func_def_105,type,
    bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).

thf(func_def_106,type,
    bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).

thf(func_def_107,type,
    bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).

thf(func_def_108,type,
    bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).

thf(func_def_109,type,
    bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).

thf(func_def_110,type,
    bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).

thf(func_def_111,type,
    bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).

thf(func_def_112,type,
    bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).

thf(func_def_113,type,
    bNF_re7934895593101944656at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > $o ).

thf(func_def_114,type,
    bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).

thf(func_def_115,type,
    basic_1567116559311922317nt_int: ( int > $o ) > ( int > $o ) > product_prod_int_int > $o ).

thf(func_def_116,type,
    basic_570253317919918037at_nat: ( nat > $o ) > ( nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_117,type,
    basic_4387203522000727145nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_118,type,
    basic_5328504652464829177at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

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

thf(func_def_120,type,
    gbinom8545251970709558553nteger: code_integer > nat > code_integer ).

thf(func_def_121,type,
    gbinom7368847122466276068atural: code_natural > nat > code_natural ).

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

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

thf(func_def_124,type,
    gbinomial_rat: rat > nat > rat ).

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

thf(func_def_126,type,
    bit_and_not_num: num > num > option_num ).

thf(func_def_127,type,
    bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).

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

thf(func_def_129,type,
    bit_or_not_num_neg: num > num > num ).

thf(func_def_130,type,
    bit_ri7632146776885996613nteger: code_integer > code_integer ).

thf(func_def_131,type,
    bit_ri7919022796975470100ot_int: int > int ).

thf(func_def_132,type,
    bit_ri631733984087533419it_int: nat > int > int ).

thf(func_def_133,type,
    bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).

thf(func_def_134,type,
    bit_se2773287842338716102atural: code_natural > code_natural > code_natural ).

thf(func_def_135,type,
    bit_se725231765392027082nd_int: int > int > int ).

thf(func_def_136,type,
    bit_se727722235901077358nd_nat: nat > nat > nat ).

thf(func_def_137,type,
    bit_se3928097537394005634nteger: nat > code_integer > code_integer ).

thf(func_def_138,type,
    bit_se2751692689150723149atural: nat > code_natural > code_natural ).

thf(func_def_139,type,
    bit_se8568078237143864401it_int: nat > int > int ).

thf(func_def_140,type,
    bit_se8570568707652914677it_nat: nat > nat > nat ).

thf(func_def_141,type,
    bit_se1345352211410354436nteger: nat > code_integer > code_integer ).

thf(func_def_142,type,
    bit_se168947363167071951atural: nat > code_natural > code_natural ).

thf(func_def_143,type,
    bit_se2159334234014336723it_int: nat > int > int ).

thf(func_def_144,type,
    bit_se2161824704523386999it_nat: nat > nat > nat ).

thf(func_def_145,type,
    bit_se2119862282449309892nteger: nat > code_integer ).

thf(func_def_146,type,
    bit_se943457434206027407atural: nat > code_natural ).

thf(func_def_147,type,
    bit_se2000444600071755411sk_int: nat > int ).

thf(func_def_148,type,
    bit_se2002935070580805687sk_nat: nat > nat ).

thf(func_def_149,type,
    bit_se1080825931792720795nteger: code_integer > code_integer > code_integer ).

thf(func_def_150,type,
    bit_se9127793120404214118atural: code_natural > code_natural > code_natural ).

thf(func_def_151,type,
    bit_se1409905431419307370or_int: int > int > int ).

thf(func_def_152,type,
    bit_se1412395901928357646or_nat: nat > nat > nat ).

thf(func_def_153,type,
    bit_se7788150548672797655nteger: nat > code_integer > code_integer ).

thf(func_def_154,type,
    bit_se6611745700429515170atural: nat > code_natural > code_natural ).

thf(func_def_155,type,
    bit_se545348938243370406it_int: nat > int > int ).

thf(func_def_156,type,
    bit_se547839408752420682it_nat: nat > nat > nat ).

thf(func_def_157,type,
    bit_se2793503036327961859nteger: nat > code_integer > code_integer ).

thf(func_def_158,type,
    bit_se1617098188084679374atural: nat > code_natural > code_natural ).

thf(func_def_159,type,
    bit_se7879613467334960850it_int: nat > int > int ).

thf(func_def_160,type,
    bit_se7882103937844011126it_nat: nat > nat > nat ).

thf(func_def_161,type,
    bit_se1745604003318907178nteger: nat > code_integer > code_integer ).

thf(func_def_162,type,
    bit_se569199155075624693atural: nat > code_natural > code_natural ).

thf(func_def_163,type,
    bit_se2923211474154528505it_int: nat > int > int ).

thf(func_def_164,type,
    bit_se2925701944663578781it_nat: nat > nat > nat ).

thf(func_def_165,type,
    bit_se8260200283734997820nteger: nat > code_integer > code_integer ).

thf(func_def_166,type,
    bit_se7083795435491715335atural: nat > code_natural > code_natural ).

thf(func_def_167,type,
    bit_se4203085406695923979it_int: nat > int > int ).

thf(func_def_168,type,
    bit_se4205575877204974255it_nat: nat > nat > nat ).

thf(func_def_169,type,
    bit_se3222712562003087583nteger: code_integer > code_integer > code_integer ).

thf(func_def_170,type,
    bit_se2046307713759805098atural: code_natural > code_natural > code_natural ).

thf(func_def_171,type,
    bit_se6526347334894502574or_int: int > int > int ).

thf(func_def_172,type,
    bit_se6528837805403552850or_nat: nat > nat > nat ).

thf(func_def_173,type,
    bit_se9216721137139052372nteger: code_integer > nat > $o ).

thf(func_def_174,type,
    bit_se8040316288895769887atural: code_natural > nat > $o ).

thf(func_def_175,type,
    bit_se1146084159140164899it_int: int > nat > $o ).

thf(func_def_176,type,
    bit_se1148574629649215175it_nat: nat > nat > $o ).

thf(func_def_177,type,
    bit_take_bit_num: nat > num > option_num ).

thf(func_def_178,type,
    bit_un7362597486090784418nd_num: num > num > option_num ).

thf(func_def_179,type,
    bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_180,type,
    code_Nat: code_integer > code_natural ).

thf(func_def_181,type,
    code_Neg: num > code_integer ).

thf(func_def_182,type,
    code_Suc: code_natural > code_natural ).

thf(func_def_183,type,
    code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).

thf(func_def_184,type,
    code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_185,type,
    code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_186,type,
    code_dup: code_integer > code_integer ).

thf(func_def_187,type,
    code_int_of_integer: code_integer > int ).

thf(func_def_188,type,
    code_integer_of_int: int > code_integer ).

thf(func_def_189,type,
    code_integer_of_nat: nat > code_integer ).

thf(func_def_190,type,
    code_i5400310926305786745atural: code_natural > code_integer ).

thf(func_def_191,type,
    code_integer_of_num: num > code_integer ).

thf(func_def_192,type,
    code_nat_of_integer: code_integer > nat ).

thf(func_def_193,type,
    code_nat_of_natural: code_natural > nat ).

thf(func_def_194,type,
    code_natural_of_nat: nat > code_natural ).

thf(func_def_195,type,
    code_n4118661773612635043nteger: code_integer > code_natural ).

thf(func_def_196,type,
    code_negative: num > code_integer ).

thf(func_def_197,type,
    code_num_of_integer: code_integer > num ).

thf(func_def_198,type,
    code_pcr_integer: int > code_integer > $o ).

thf(func_def_199,type,
    code_positive: num > code_integer ).

thf(func_def_200,type,
    code_size_nat: code_natural > nat ).

thf(func_def_201,type,
    code_sub: num > num > code_integer ).

thf(func_def_202,type,
    complete_Inf_Inf_nat: set_nat > nat ).

thf(func_def_203,type,
    comple7806235888213564991et_nat: set_set_nat > set_nat ).

thf(func_def_204,type,
    complete_Sup_Sup_int: set_int > int ).

thf(func_def_205,type,
    complete_Sup_Sup_nat: set_nat > nat ).

thf(func_def_206,type,
    comple7399068483239264473et_nat: set_set_nat > set_nat ).

thf(func_def_207,type,
    adjust_div: product_prod_int_int > int ).

thf(func_def_208,type,
    adjust_mod: int > int > int ).

thf(func_def_209,type,
    divmod_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_210,type,
    eucl_rel_int: int > int > product_prod_int_int > $o ).

thf(func_def_211,type,
    unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).

thf(func_def_212,type,
    unique5052692396658037445od_int: num > num > product_prod_int_int ).

thf(func_def_213,type,
    unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).

thf(func_def_214,type,
    unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_215,type,
    unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).

thf(func_def_216,type,
    unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_217,type,
    euclid6377331345833325938nteger: code_integer > nat ).

thf(func_def_218,type,
    euclid5200926497590043453atural: code_natural > nat ).

thf(func_def_219,type,
    euclid4774559944035922753ze_int: int > nat ).

thf(func_def_220,type,
    euclid4777050414544973029ze_nat: nat > nat ).

thf(func_def_221,type,
    euclid6289375185220004616nteger: code_integer > code_integer ).

thf(func_def_222,type,
    euclid5112970336976722131atural: code_natural > code_natural ).

thf(func_def_223,type,
    euclid3395696857347342551nt_int: int > int ).

thf(func_def_224,type,
    euclid3398187327856392827nt_nat: nat > nat ).

thf(func_def_225,type,
    comm_s8582702949713902594nteger: code_integer > nat > code_integer ).

thf(func_def_226,type,
    comm_s7406298101470620109atural: code_natural > nat > code_natural ).

thf(func_def_227,type,
    comm_s4660882817536571857er_int: int > nat > int ).

thf(func_def_228,type,
    comm_s4663373288045622133er_nat: nat > nat > nat ).

thf(func_def_229,type,
    comm_s4028243227959126397er_rat: rat > nat > rat ).

thf(func_def_230,type,
    semiri3624122377584611663nteger: nat > code_integer ).

thf(func_def_231,type,
    semiri2447717529341329178atural: nat > code_natural ).

thf(func_def_232,type,
    semiri1406184849735516958ct_int: nat > int ).

thf(func_def_233,type,
    semiri1408675320244567234ct_nat: nat > nat ).

thf(func_def_234,type,
    semiri773545260158071498ct_rat: nat > rat ).

thf(func_def_235,type,
    inverse_inverse_rat: rat > rat ).

thf(func_def_236,type,
    at_top_nat: filter_nat ).

thf(func_def_237,type,
    eventually_nat: ( nat > $o ) > filter_nat > $o ).

thf(func_def_238,type,
    eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).

thf(func_def_239,type,
    filter3212408913953519116et_nat: ( nat > set_nat ) > filter_set_nat > filter_nat > $o ).

thf(func_def_240,type,
    finite3254316476582989077op_nat: set_nat > filter_set_nat ).

thf(func_def_241,type,
    prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).

thf(func_def_242,type,
    finite_card_int: set_int > nat ).

thf(func_def_243,type,
    finite_card_list_nat: set_list_nat > nat ).

thf(func_def_244,type,
    finite_card_nat: set_nat > nat ).

thf(func_def_245,type,
    finite410649719033368117t_unit: set_Product_unit > nat ).

thf(func_def_246,type,
    finite_card_set_nat: set_set_nat > nat ).

thf(func_def_247,type,
    finite6017078050557962740nteger: set_Code_integer > $o ).

thf(func_def_248,type,
    finite_finite_int: set_int > $o ).

thf(func_def_249,type,
    finite_finite_nat: set_nat > $o ).

thf(func_def_250,type,
    bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).

thf(func_def_251,type,
    comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_252,type,
    comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_253,type,
    comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).

thf(func_def_254,type,
    comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).

thf(func_def_255,type,
    comp_nat_num_int: ( nat > num ) > ( int > nat ) > int > num ).

thf(func_def_256,type,
    id_nat_o: ( nat > $o ) > nat > $o ).

thf(func_def_257,type,
    id_o: $o > $o ).

thf(func_def_258,type,
    id_int: int > int ).

thf(func_def_259,type,
    id_nat: nat > nat ).

thf(func_def_260,type,
    id_num: num > num ).

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

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

thf(func_def_263,type,
    map_fu2496120808607739376eger_o: ( code_integer > int ) > ( ( int > $o ) > code_integer > $o ) > ( int > int > $o ) > code_integer > code_integer > $o ).

thf(func_def_264,type,
    map_fu8272188784021352819nteger: ( code_integer > int ) > ( ( int > int ) > code_integer > code_integer ) > ( int > int > int ) > code_integer > code_integer > code_integer ).

thf(func_def_265,type,
    map_fu186220595405829473_nat_o: ( code_integer > int ) > ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > code_integer > nat > $o ).

thf(func_def_266,type,
    map_fu6957801986076833569nt_o_o: ( code_integer > int ) > ( $o > $o ) > ( int > $o ) > code_integer > $o ).

thf(func_def_267,type,
    map_fu2599414010547811884nteger: ( code_integer > int ) > ( int > code_integer ) > ( int > int ) > code_integer > code_integer ).

thf(func_def_268,type,
    map_fu1051355602067684763atural: ( code_integer > int ) > ( nat > code_natural ) > ( int > nat ) > code_integer > code_natural ).

thf(func_def_269,type,
    map_fu6539832666145259331at_nat: ( code_integer > int ) > ( nat > nat ) > ( int > nat ) > code_integer > nat ).

thf(func_def_270,type,
    map_fu1227494855608507351um_num: ( code_integer > int ) > ( num > num ) > ( int > num ) > code_integer > num ).

thf(func_def_271,type,
    map_fu6256889081107267320ural_o: ( code_natural > nat ) > ( ( nat > $o ) > code_natural > $o ) > ( nat > nat > $o ) > code_natural > code_natural > $o ).

thf(func_def_272,type,
    map_fu6244533035418998608_nat_o: ( code_natural > nat ) > ( ( nat > $o ) > nat > $o ) > ( nat > nat > $o ) > code_natural > nat > $o ).

thf(func_def_273,type,
    map_fu6549440983881763648atural: ( code_natural > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > code_natural > code_natural > code_natural ).

thf(func_def_274,type,
    map_fu4892316939951275536at_o_o: ( code_natural > nat ) > ( $o > $o ) > ( nat > $o ) > code_natural > $o ).

thf(func_def_275,type,
    map_fu2787874002554666395nteger: ( code_natural > nat ) > ( int > code_integer ) > ( nat > int ) > code_natural > code_integer ).

thf(func_def_276,type,
    map_fu1239815594074539274atural: ( code_natural > nat ) > ( nat > code_natural ) > ( nat > nat ) > code_natural > code_natural ).

thf(func_def_277,type,
    map_fu226235371393106610at_nat: ( code_natural > nat ) > ( nat > nat ) > ( nat > nat ) > code_natural > nat ).

thf(func_def_278,type,
    map_fu7831380289885515383nt_rat: ( int > int ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).

thf(func_def_279,type,
    map_fu3424225382358772769nt_rat: ( int > int ) > ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).

thf(func_def_280,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_281,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_282,type,
    map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).

thf(func_def_283,type,
    map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).

thf(func_def_284,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_285,type,
    map_fu8224359078269604234nteger: ( nat > nat ) > ( ( int > int ) > code_integer > code_integer ) > ( nat > int > int ) > nat > code_integer > code_integer ).

thf(func_def_286,type,
    map_fu6981160461238011112atural: ( nat > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > nat > code_natural > code_natural ).

thf(func_def_287,type,
    map_fu6290471996055670595nteger: ( nat > nat ) > ( int > code_integer ) > ( nat > int ) > nat > code_integer ).

thf(func_def_288,type,
    map_fu4742413587575543474atural: ( nat > nat ) > ( nat > code_natural ) > ( nat > nat ) > nat > code_natural ).

thf(func_def_289,type,
    map_fu6891787308814931657nteger: ( num > num ) > ( ( num > int ) > num > code_integer ) > ( num > num > int ) > num > num > code_integer ).

thf(func_def_290,type,
    map_fu8638147718074629079nteger: ( num > num ) > ( int > code_integer ) > ( num > int ) > num > code_integer ).

thf(func_def_291,type,
    map_fu4333342158222067775at_rat: ( rat > product_prod_int_int ) > ( ( product_prod_int_int > product_prod_int_int ) > rat > rat ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > rat > rat > rat ).

thf(func_def_292,type,
    map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).

thf(func_def_293,type,
    map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).

thf(func_def_294,type,
    fun_is_measure_int: ( int > nat ) > $o ).

thf(func_def_295,type,
    fun_pair_leq: set_Pr8693737435421807431at_nat ).

thf(func_def_296,type,
    fun_pair_less: set_Pr8693737435421807431at_nat ).

thf(func_def_297,type,
    gcd_Gcd_int: set_int > int ).

thf(func_def_298,type,
    gcd_Gcd_nat: set_nat > nat ).

thf(func_def_299,type,
    bezw: nat > nat > product_prod_int_int ).

thf(func_def_300,type,
    bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_301,type,
    gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_302,type,
    gcd_gcd_int: int > int > int ).

thf(func_def_303,type,
    gcd_gcd_nat: nat > nat > nat ).

thf(func_def_304,type,
    gcd_lcm_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_305,type,
    gcd_lcm_int: int > int > int ).

thf(func_def_306,type,
    gcd_lcm_nat: nat > nat > nat ).

thf(func_def_307,type,
    gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_308,type,
    abs_abs_Code_integer: code_integer > code_integer ).

thf(func_def_309,type,
    abs_abs_int: int > int ).

thf(func_def_310,type,
    abs_abs_rat: rat > rat ).

thf(func_def_311,type,
    minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).

thf(func_def_312,type,
    minus_7197305767214868737atural: code_natural > code_natural > code_natural ).

thf(func_def_313,type,
    minus_minus_int: int > int > int ).

thf(func_def_314,type,
    minus_minus_nat: nat > nat > nat ).

thf(func_def_315,type,
    minus_minus_rat: rat > rat > rat ).

thf(func_def_316,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_317,type,
    one_one_Code_integer: code_integer ).

thf(func_def_318,type,
    one_one_Code_natural: code_natural ).

thf(func_def_319,type,
    one_one_int: int ).

thf(func_def_320,type,
    one_one_nat: nat ).

thf(func_def_321,type,
    one_one_rat: rat ).

thf(func_def_322,type,
    plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).

thf(func_def_323,type,
    plus_p4538020629002901425atural: code_natural > code_natural > code_natural ).

thf(func_def_324,type,
    plus_plus_int: int > int > int ).

thf(func_def_325,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_326,type,
    plus_plus_num: num > num > num ).

thf(func_def_327,type,
    plus_plus_rat: rat > rat > rat ).

thf(func_def_328,type,
    sgn_sgn_Code_integer: code_integer > code_integer ).

thf(func_def_329,type,
    sgn_sgn_int: int > int ).

thf(func_def_330,type,
    sgn_sgn_rat: rat > rat ).

thf(func_def_331,type,
    times_3573771949741848930nteger: code_integer > code_integer > code_integer ).

thf(func_def_332,type,
    times_2397367101498566445atural: code_natural > code_natural > code_natural ).

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

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

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

thf(func_def_336,type,
    times_times_rat: rat > rat > rat ).

thf(func_def_337,type,
    uminus1351360451143612070nteger: code_integer > code_integer ).

thf(func_def_338,type,
    uminus_uminus_int: int > int ).

thf(func_def_339,type,
    uminus_uminus_rat: rat > rat ).

thf(func_def_340,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

thf(func_def_341,type,
    zero_z3403309356797280102nteger: code_integer ).

thf(func_def_342,type,
    zero_z2226904508553997617atural: code_natural ).

thf(func_def_343,type,
    zero_zero_int: int ).

thf(func_def_344,type,
    zero_zero_nat: nat ).

thf(func_def_345,type,
    zero_zero_rat: rat ).

thf(func_def_346,type,
    groups4538972089207619220nt_int: ( int > int ) > set_int > int ).

thf(func_def_347,type,
    groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_348,type,
    groups1705073143266064639nt_int: ( int > int ) > set_int > int ).

thf(func_def_349,type,
    groups705719431365010083at_int: ( nat > int ) > set_nat > int ).

thf(func_def_350,type,
    groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_351,type,
    groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).

thf(func_def_352,type,
    groups4561878855575611511st_nat: list_nat > nat ).

thf(func_def_353,type,
    nO_MAT8252062027627875367nteger: code_integer > code_integer > $o ).

thf(func_def_354,type,
    nO_MAT7795273704451493282er_rat: code_integer > rat > $o ).

thf(func_def_355,type,
    nO_MAT9066612773553876470nteger: int > code_integer > $o ).

thf(func_def_356,type,
    nO_MATCH_int_int: int > int > $o ).

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

thf(func_def_358,type,
    nO_MATCH_int_rat: int > rat > $o ).

thf(func_def_359,type,
    nO_MAT8694959213317031834nteger: nat > code_integer > $o ).

thf(func_def_360,type,
    nO_MATCH_nat_int: nat > int > $o ).

thf(func_def_361,type,
    nO_MATCH_nat_nat: nat > nat > $o ).

thf(func_def_362,type,
    nO_MATCH_nat_rat: nat > rat > $o ).

thf(func_def_363,type,
    nO_MATCH_rat_rat: rat > rat > $o ).

thf(func_def_364,type,
    the_int: ( int > $o ) > int ).

thf(func_def_365,type,
    the_Pr4378521158711661632nt_int: ( product_prod_int_int > $o ) > product_prod_int_int ).

thf(func_def_366,type,
    heap_T6183433275982383450t_unit: ( heap_e7401611519738050253t_unit > option8956607266484857688it_nat ) > heap_T5738788834812785303t_unit ).

thf(func_def_367,type,
    heap_T2633723481742716231t_unit: heap_T5738788834812785303t_unit > ( product_unit > heap_T5738788834812785303t_unit ) > heap_T5738788834812785303t_unit ).

thf(func_def_368,type,
    heap_T757603679106148408unit_a: heap_T5738788834812785303t_unit > ( product_unit > heap_Time_Heap_a ) > heap_Time_Heap_a ).

thf(func_def_369,type,
    heap_T8685611227969916822t_unit: heap_Time_Heap_a > ( a > heap_T5738788834812785303t_unit ) > heap_T5738788834812785303t_unit ).

thf(func_def_370,type,
    heap_Time_bind_a_a: heap_Time_Heap_a > ( a > heap_Time_Heap_a ) > heap_Time_Heap_a ).

thf(func_def_371,type,
    heap_T875086893843062177t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > option8956607266484857688it_nat ).

thf(func_def_372,type,
    heap_T7011250591035762645t_unit: ( product_unit > product_unit ) > product_unit > heap_T5738788834812785303t_unit ).

thf(func_def_373,type,
    heap_T6901581777565460678unit_a: ( product_unit > a ) > product_unit > heap_Time_Heap_a ).

thf(func_def_374,type,
    heap_Time_lift_a_a: ( a > a ) > a > heap_Time_Heap_a ).

thf(func_def_375,type,
    heap_T2927564422264180874t_unit: list_char > heap_T5738788834812785303t_unit ).

thf(func_def_376,type,
    heap_Time_raise_a: list_char > heap_Time_Heap_a ).

thf(func_def_377,type,
    heap_T7507251653302230130t_unit: product_unit > heap_T5738788834812785303t_unit ).

thf(func_def_378,type,
    heap_Time_return_a: a > heap_Time_Heap_a ).

thf(func_def_379,type,
    heap_T4284346855313245393t_unit: product_unit > heap_T5738788834812785303t_unit ).

thf(func_def_380,type,
    heap_Time_ureturn_a: a > heap_Time_Heap_a ).

thf(func_def_381,type,
    heap_Time_wait: nat > heap_T5738788834812785303t_unit ).

thf(func_def_382,type,
    if_Code_integer: $o > code_integer > code_integer > code_integer ).

thf(func_def_383,type,
    if_Code_natural: $o > code_natural > code_natural > code_natural ).

thf(func_def_384,type,
    if_Hea8138950348631371857t_unit: $o > heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit ).

thf(func_def_385,type,
    if_Heap_Time_Heap_a: $o > heap_Time_Heap_a > heap_Time_Heap_a > heap_Time_Heap_a ).

thf(func_def_386,type,
    if_int: $o > int > int > int ).

thf(func_def_387,type,
    if_list_int: $o > list_int > list_int > list_int ).

thf(func_def_388,type,
    if_nat: $o > nat > nat > nat ).

thf(func_def_389,type,
    if_num: $o > num > num > num ).

thf(func_def_390,type,
    if_option_num: $o > option_num > option_num > option_num ).

thf(func_def_391,type,
    if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).

thf(func_def_392,type,
    if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_393,type,
    if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).

thf(func_def_394,type,
    if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_395,type,
    if_rat: $o > rat > rat > rat ).

thf(func_def_396,type,
    if_set_int: $o > set_int > set_int > set_int ).

thf(func_def_397,type,
    infini8530281810654367211te_nat: set_nat > nat > nat ).

thf(func_def_398,type,
    abs_Integ: product_prod_nat_nat > int ).

thf(func_def_399,type,
    rep_Integ: int > product_prod_nat_nat ).

thf(func_def_400,type,
    cr_int: product_prod_nat_nat > int > $o ).

thf(func_def_401,type,
    int_ge_less_than: int > set_Pr958786334691620121nt_int ).

thf(func_def_402,type,
    int_ge_less_than2: int > set_Pr958786334691620121nt_int ).

thf(func_def_403,type,
    intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_404,type,
    nat2: int > nat ).

thf(func_def_405,type,
    pcr_int: product_prod_nat_nat > int > $o ).

thf(func_def_406,type,
    power_int_rat: rat > int > rat ).

thf(func_def_407,type,
    ring_11222124179247155820nteger: set_Code_integer ).

thf(func_def_408,type,
    ring_1_Ints_int: set_int ).

thf(func_def_409,type,
    ring_1_Ints_rat: set_rat ).

thf(func_def_410,type,
    ring_18347121197199848620nteger: int > code_integer ).

thf(func_def_411,type,
    ring_1_of_int_int: int > int ).

thf(func_def_412,type,
    ring_1_of_int_rat: int > rat ).

thf(func_def_413,type,
    inf_in3604695632404883862_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).

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

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

thf(func_def_416,type,
    semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_417,type,
    sup_sup_int: int > int > int ).

thf(func_def_418,type,
    sup_sup_nat: nat > nat > nat ).

thf(func_def_419,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_420,type,
    lattic8263393255366662781ax_int: set_int > int ).

thf(func_def_421,type,
    lattic8265883725875713057ax_nat: set_nat > nat ).

thf(func_def_422,type,
    quotie1194848508323700631at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int > $o ) > $o ).

thf(func_def_423,type,
    append_int: list_int > list_int > list_int ).

thf(func_def_424,type,
    append_nat: list_nat > list_nat > list_nat ).

thf(func_def_425,type,
    butlast_nat: list_nat > list_nat ).

thf(func_def_426,type,
    drop_nat: nat > list_nat > list_nat ).

thf(func_def_427,type,
    filter_nat2: ( nat > $o ) > list_nat > list_nat ).

thf(func_def_428,type,
    fold_int_int: ( int > int > int ) > list_int > int > int ).

thf(func_def_429,type,
    fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).

thf(func_def_430,type,
    foldr_o_nat: ( $o > nat > nat ) > list_o > nat > nat ).

thf(func_def_431,type,
    foldr_int_nat: ( int > nat > nat ) > list_int > nat > nat ).

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

thf(func_def_433,type,
    gen_length_o: nat > list_o > nat ).

thf(func_def_434,type,
    gen_length_int: nat > list_int > nat ).

thf(func_def_435,type,
    gen_length_nat: nat > list_nat > nat ).

thf(func_def_436,type,
    last_nat: list_nat > nat ).

thf(func_def_437,type,
    linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).

thf(func_def_438,type,
    linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_439,type,
    linord2614967742042102400et_nat: set_nat > list_nat ).

thf(func_def_440,type,
    cons_o: $o > list_o > list_o ).

thf(func_def_441,type,
    cons_int: int > list_int > list_int ).

thf(func_def_442,type,
    cons_nat: nat > list_nat > list_nat ).

thf(func_def_443,type,
    cons_num: num > list_num > list_num ).

thf(func_def_444,type,
    cons_rat: rat > list_rat > list_rat ).

thf(func_def_445,type,
    cons_char: char > list_char > list_char ).

thf(func_def_446,type,
    nil_o: list_o ).

thf(func_def_447,type,
    nil_int: list_int ).

thf(func_def_448,type,
    nil_nat: list_nat ).

thf(func_def_449,type,
    nil_num: list_num ).

thf(func_def_450,type,
    nil_rat: list_rat ).

thf(func_def_451,type,
    nil_char: list_char ).

thf(func_def_452,type,
    map_nat_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_453,type,
    set_int2: list_int > set_int ).

thf(func_def_454,type,
    set_nat2: list_nat > set_nat ).

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

thf(func_def_456,type,
    nth_Code_integer: list_Code_integer > nat > code_integer ).

thf(func_def_457,type,
    nth_int: list_int > nat > int ).

thf(func_def_458,type,
    nth_nat: list_nat > nat > nat ).

thf(func_def_459,type,
    nth_num: list_num > nat > num ).

thf(func_def_460,type,
    nth_rat: list_rat > nat > rat ).

thf(func_def_461,type,
    nth_char: list_char > nat > char ).

thf(func_def_462,type,
    rotate1_o: list_o > list_o ).

thf(func_def_463,type,
    rotate1_int: list_int > list_int ).

thf(func_def_464,type,
    rotate1_nat: list_nat > list_nat ).

thf(func_def_465,type,
    rotate_o: nat > list_o > list_o ).

thf(func_def_466,type,
    rotate_int: nat > list_int > list_int ).

thf(func_def_467,type,
    rotate_nat: nat > list_nat > list_nat ).

thf(func_def_468,type,
    sorted_wrt_o: ( $o > $o > $o ) > list_o > $o ).

thf(func_def_469,type,
    sorted710888440204495920nteger: ( code_integer > code_integer > $o ) > list_Code_integer > $o ).

thf(func_def_470,type,
    sorted_wrt_int: ( int > int > $o ) > list_int > $o ).

thf(func_def_471,type,
    sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).

thf(func_def_472,type,
    sorted_wrt_num: ( num > num > $o ) > list_num > $o ).

thf(func_def_473,type,
    sorted_wrt_rat: ( rat > rat > $o ) > list_rat > $o ).

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

thf(func_def_475,type,
    upt: nat > nat > list_nat ).

thf(func_def_476,type,
    upto: int > int > list_int ).

thf(func_def_477,type,
    upto_aux: int > int > list_int > list_int ).

thf(func_def_478,type,
    upto_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_479,type,
    slice_o: nat > nat > list_o > list_o ).

thf(func_def_480,type,
    slice_int: nat > nat > list_int > list_int ).

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

thf(func_def_482,type,
    slice_char: nat > nat > list_char > list_char ).

thf(func_def_483,type,
    mset_nat: list_nat > multiset_nat ).

thf(func_def_484,type,
    mset_set_nat: set_nat > multiset_nat ).

thf(func_def_485,type,
    suc: nat > nat ).

thf(func_def_486,type,
    compow_nat_nat: nat > ( nat > nat ) > nat > nat ).

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

thf(func_def_488,type,
    case_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_489,type,
    case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).

thf(func_def_490,type,
    pred: nat > nat ).

thf(func_def_491,type,
    semiring_1_Nats_int: set_int ).

thf(func_def_492,type,
    semiri4939895301339042750nteger: nat > code_integer ).

thf(func_def_493,type,
    semiri3763490453095760265atural: nat > code_natural ).

thf(func_def_494,type,
    semiri1314217659103216013at_int: nat > int ).

thf(func_def_495,type,
    semiri1316708129612266289at_nat: nat > nat ).

thf(func_def_496,type,
    semiri681578069525770553at_rat: nat > rat ).

thf(func_def_497,type,
    semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).

thf(func_def_498,type,
    semiri2879080225315754349atural: ( code_natural > code_natural ) > nat > code_natural > code_natural ).

thf(func_def_499,type,
    semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).

thf(func_def_500,type,
    semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).

thf(func_def_501,type,
    semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).

thf(func_def_502,type,
    size_size_list_o: list_o > nat ).

thf(func_def_503,type,
    size_s3445333598471063425nteger: list_Code_integer > nat ).

thf(func_def_504,type,
    size_size_list_int: list_int > nat ).

thf(func_def_505,type,
    size_size_list_nat: list_nat > nat ).

thf(func_def_506,type,
    size_size_list_num: list_num > nat ).

thf(func_def_507,type,
    size_size_list_rat: list_rat > nat ).

thf(func_def_508,type,
    size_size_list_char: list_char > nat ).

thf(func_def_509,type,
    size_size_num: num > nat ).

thf(func_def_510,type,
    size_size_char: char > nat ).

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

thf(func_def_512,type,
    nat_list_decode_rel: nat > nat > $o ).

thf(func_def_513,type,
    nat_list_encode: list_nat > nat ).

thf(func_def_514,type,
    nat_list_encode_rel: list_nat > list_nat > $o ).

thf(func_def_515,type,
    nat_prod_decode: nat > product_prod_nat_nat ).

thf(func_def_516,type,
    nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).

thf(func_def_517,type,
    nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_518,type,
    nat_prod_encode: product_prod_nat_nat > nat ).

thf(func_def_519,type,
    nat_set_decode: nat > set_nat ).

thf(func_def_520,type,
    nat_set_encode: set_nat > nat ).

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

thf(func_def_522,type,
    bitM: num > num ).

thf(func_def_523,type,
    inc: num > num ).

thf(func_def_524,type,
    neg_nu8804712462038260780nteger: code_integer > code_integer ).

thf(func_def_525,type,
    neg_numeral_dbl_int: int > int ).

thf(func_def_526,type,
    neg_numeral_dbl_rat: rat > rat ).

thf(func_def_527,type,
    neg_nu7757733837767384882nteger: code_integer > code_integer ).

thf(func_def_528,type,
    neg_nu3811975205180677377ec_int: int > int ).

thf(func_def_529,type,
    neg_nu3179335615603231917ec_rat: rat > rat ).

thf(func_def_530,type,
    neg_nu5831290666863070958nteger: code_integer > code_integer ).

thf(func_def_531,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(func_def_532,type,
    neg_nu5219082963157363817nc_rat: rat > rat ).

thf(func_def_533,type,
    neg_nu5755505904847501662nteger: num > num > code_integer ).

thf(func_def_534,type,
    neg_numeral_sub_int: num > num > int ).

thf(func_def_535,type,
    bit0: num > num ).

thf(func_def_536,type,
    bit1: num > num ).

thf(func_def_537,type,
    one: num ).

thf(func_def_538,type,
    case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).

thf(func_def_539,type,
    size_num: num > nat ).

thf(func_def_540,type,
    num_of_nat: nat > num ).

thf(func_def_541,type,
    numera6620942414471956472nteger: num > code_integer ).

thf(func_def_542,type,
    numera5444537566228673987atural: num > code_natural ).

thf(func_def_543,type,
    numeral_numeral_int: num > int ).

thf(func_def_544,type,
    numeral_numeral_nat: num > nat ).

thf(func_def_545,type,
    numeral_numeral_rat: num > rat ).

thf(func_def_546,type,
    pow: num > num > num ).

thf(func_def_547,type,
    pred_numeral: num > nat ).

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

thf(func_def_549,type,
    none_num: option_num ).

thf(func_def_550,type,
    none_P9117596204409417319it_nat: option8956607266484857688it_nat ).

thf(func_def_551,type,
    some_num: num > option_num ).

thf(func_def_552,type,
    some_P1914260805536162275it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat ).

thf(func_def_553,type,
    case_option_int_num: int > ( num > int ) > option_num > int ).

thf(func_def_554,type,
    case_option_num_num: num > ( num > num ) > option_num > num ).

thf(func_def_555,type,
    case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).

thf(func_def_556,type,
    map_option_num_num: ( num > num ) > option_num > option_num ).

thf(func_def_557,type,
    bot_bot_nat: nat ).

thf(func_def_558,type,
    bot_bot_set_int: set_int ).

thf(func_def_559,type,
    bot_bot_set_nat: set_nat ).

thf(func_def_560,type,
    ord_Least_nat: ( nat > $o ) > nat ).

thf(func_def_561,type,
    ord_less_o: $o > $o > $o ).

thf(func_def_562,type,
    ord_le6747313008572928689nteger: code_integer > code_integer > $o ).

thf(func_def_563,type,
    ord_le5570908160329646204atural: code_natural > code_natural > $o ).

thf(func_def_564,type,
    ord_less_int: int > int > $o ).

thf(func_def_565,type,
    ord_less_nat: nat > nat > $o ).

thf(func_def_566,type,
    ord_less_num: num > num > $o ).

thf(func_def_567,type,
    ord_less_rat: rat > rat > $o ).

thf(func_def_568,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(func_def_569,type,
    ord_less_eq_o_int: ( $o > int ) > ( $o > int ) > $o ).

thf(func_def_570,type,
    ord_less_eq_o_nat: ( $o > nat ) > ( $o > nat ) > $o ).

thf(func_def_571,type,
    ord_less_eq_o_num: ( $o > num ) > ( $o > num ) > $o ).

thf(func_def_572,type,
    ord_less_eq_o_rat: ( $o > rat ) > ( $o > rat ) > $o ).

thf(func_def_573,type,
    ord_le7022414076629706543et_nat: ( $o > set_nat ) > ( $o > set_nat ) > $o ).

thf(func_def_574,type,
    ord_less_eq_o: $o > $o > $o ).

thf(func_def_575,type,
    ord_le3102999989581377725nteger: code_integer > code_integer > $o ).

thf(func_def_576,type,
    ord_le1926595141338095240atural: code_natural > code_natural > $o ).

thf(func_def_577,type,
    ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).

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

thf(func_def_579,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(func_def_580,type,
    ord_less_eq_num: num > num > $o ).

thf(func_def_581,type,
    ord_less_eq_rat: rat > rat > $o ).

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

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

thf(func_def_584,type,
    ord_max_Code_natural: code_natural > code_natural > code_natural ).

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

thf(func_def_586,type,
    ord_max_nat: nat > nat > nat ).

thf(func_def_587,type,
    ord_min_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_588,type,
    ord_min_Code_natural: code_natural > code_natural > code_natural ).

thf(func_def_589,type,
    ord_min_int: int > int > int ).

thf(func_def_590,type,
    ord_min_nat: nat > nat > nat ).

thf(func_def_591,type,
    order_Greatest_int: ( int > $o ) > int ).

thf(func_def_592,type,
    order_Greatest_nat: ( nat > $o ) > nat ).

thf(func_def_593,type,
    order_Greatest_num: ( num > $o ) > num ).

thf(func_def_594,type,
    order_Greatest_rat: ( rat > $o ) > rat ).

thf(func_def_595,type,
    order_5724808138429204845et_nat: ( set_nat > $o ) > set_nat ).

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

thf(func_def_597,type,
    ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).

thf(func_def_598,type,
    top_top_set_int: set_int ).

thf(func_def_599,type,
    top_top_set_nat: set_nat ).

thf(func_def_600,type,
    top_to1996260823553986621t_unit: set_Product_unit ).

thf(func_def_601,type,
    top_top_set_char: set_char ).

thf(func_def_602,type,
    power_8256067586552552935nteger: code_integer > nat > code_integer ).

thf(func_def_603,type,
    power_7079662738309270450atural: code_natural > nat > code_natural ).

thf(func_def_604,type,
    power_power_int: int > nat > int ).

thf(func_def_605,type,
    power_power_nat: nat > nat > nat ).

thf(func_def_606,type,
    power_power_rat: rat > nat > rat ).

thf(func_def_607,type,
    produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).

thf(func_def_608,type,
    produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_609,type,
    produc3574140220909816553atural: code_natural > code_natural > produc7822875418678951345atural ).

thf(func_def_610,type,
    produc6639722614265839536atural: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_611,type,
    produc584006145561248582it_nat: heap_e7401611519738050253t_unit > nat > produc6653097349344004940it_nat ).

thf(func_def_612,type,
    product_Pair_int_int: int > int > product_prod_int_int ).

thf(func_def_613,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_614,type,
    product_Pair_nat_num: nat > num > product_prod_nat_num ).

thf(func_def_615,type,
    product_Pair_num_num: num > num > product_prod_num_num ).

thf(func_def_616,type,
    produc4480994950612372183atural: produc7822875418678951345atural > produc7822875418678951345atural > produc6756470014200349799atural ).

thf(func_def_617,type,
    produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).

thf(func_def_618,type,
    produc7133225469290080770it_nat: product_unit > produc6653097349344004940it_nat > produc8664842809031399944it_nat ).

thf(func_def_619,type,
    product_Unity: product_unit ).

thf(func_def_620,type,
    produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_621,type,
    produc4188289175737317920o_char: ( code_integer > $o > char ) > produc6271795597528267376eger_o > char ).

thf(func_def_622,type,
    produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).

thf(func_def_623,type,
    produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).

thf(func_def_624,type,
    produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).

thf(func_def_625,type,
    produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).

thf(func_def_626,type,
    produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_627,type,
    produc8282080750456430313atural: ( code_natural > code_natural > produc6756470014200349799atural ) > produc7822875418678951345atural > produc6756470014200349799atural ).

thf(func_def_628,type,
    produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).

thf(func_def_629,type,
    produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).

thf(func_def_630,type,
    produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).

thf(func_def_631,type,
    produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_632,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_633,type,
    produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_634,type,
    produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).

thf(func_def_635,type,
    produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).

thf(func_def_636,type,
    produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_637,type,
    produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).

thf(func_def_638,type,
    produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer ).

thf(func_def_639,type,
    product_fst_int_int: product_prod_int_int > int ).

thf(func_def_640,type,
    product_fst_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_641,type,
    produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).

thf(func_def_642,type,
    produc6591912806276919810atural: produc5835291356934675326atural > produc7822875418678951345atural ).

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

thf(func_def_644,type,
    product_snd_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_645,type,
    produc5538323210962509403atural: ( produc7822875418678951345atural > produc5835291356934675326atural ) > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_646,type,
    inc_shift: code_natural > code_natural > code_natural ).

thf(func_def_647,type,
    iterat8892046348760725948atural: code_natural > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_648,type,
    log: code_natural > code_natural > code_natural ).

thf(func_def_649,type,
    log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o ).

thf(func_def_650,type,
    minus_shift: code_natural > code_natural > code_natural > code_natural ).

thf(func_def_651,type,
    next: produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_652,type,
    range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_653,type,
    split_seed: produc7822875418678951345atural > produc6756470014200349799atural ).

thf(func_def_654,type,
    abs_Rat: product_prod_int_int > rat ).

thf(func_def_655,type,
    fract: int > int > rat ).

thf(func_def_656,type,
    frct: product_prod_int_int > rat ).

thf(func_def_657,type,
    rep_Rat: rat > product_prod_int_int ).

thf(func_def_658,type,
    cr_rat: product_prod_int_int > rat > $o ).

thf(func_def_659,type,
    normalize: product_prod_int_int > product_prod_int_int ).

thf(func_def_660,type,
    of_int: int > rat ).

thf(func_def_661,type,
    pcr_rat: product_prod_int_int > rat > $o ).

thf(func_def_662,type,
    positive: rat > $o ).

thf(func_def_663,type,
    quotient_of: rat > product_prod_int_int ).

thf(func_def_664,type,
    abs_rat: set_Pr958786334691620121nt_int > rat ).

thf(func_def_665,type,
    rep_rat: rat > set_Pr958786334691620121nt_int ).

thf(func_def_666,type,
    ratrel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_667,type,
    ref_ch7259622376331601608t_unit: ( product_unit > product_unit ) > ref_Product_unit > heap_T5738788834812785303t_unit ).

thf(func_def_668,type,
    ref_lo7930775386976318366t_unit: ref_Product_unit > heap_T5738788834812785303t_unit ).

thf(func_def_669,type,
    ref_up627237114476368303t_unit: ref_Product_unit > product_unit > heap_T5738788834812785303t_unit ).

thf(func_def_670,type,
    refine_Imp_assert: $o > heap_T5738788834812785303t_unit ).

thf(func_def_671,type,
    refine451278484176762712t_unit: heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit > $o ).

thf(func_def_672,type,
    refine_Imp_refines_a: heap_Time_Heap_a > heap_Time_Heap_a > $o ).

thf(func_def_673,type,
    domain452967906960104687nteger: ( int > code_integer > $o ) > int > $o ).

thf(func_def_674,type,
    domainp_int_int: ( int > int > $o ) > int > $o ).

thf(func_def_675,type,
    domainp_nat_nat: ( nat > nat > $o ) > nat > $o ).

thf(func_def_676,type,
    domain9213661015745956397nt_rat: ( product_prod_int_int > rat > $o ) > product_prod_int_int > $o ).

thf(func_def_677,type,
    domain7287725470393535433at_int: ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > $o ).

thf(func_def_678,type,
    relcom8911704206367525917at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > product_prod_nat_nat > int > $o ).

thf(func_def_679,type,
    algebr932160517623751201me_int: int > int > $o ).

thf(func_def_680,type,
    algebr934650988132801477me_nat: nat > nat > $o ).

thf(func_def_681,type,
    divide6298287555418463151nteger: code_integer > code_integer > code_integer ).

thf(func_def_682,type,
    divide5121882707175180666atural: code_natural > code_natural > code_natural ).

thf(func_def_683,type,
    divide_divide_int: int > int > int ).

thf(func_def_684,type,
    divide_divide_nat: nat > nat > nat ).

thf(func_def_685,type,
    divide_divide_rat: rat > rat > rat ).

thf(func_def_686,type,
    dvd_dvd_Code_integer: code_integer > code_integer > $o ).

thf(func_def_687,type,
    dvd_dvd_int: int > int > $o ).

thf(func_def_688,type,
    dvd_dvd_nat: nat > nat > $o ).

thf(func_def_689,type,
    modulo364778990260209775nteger: code_integer > code_integer > code_integer ).

thf(func_def_690,type,
    modulo8411746178871703098atural: code_natural > code_natural > code_natural ).

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

thf(func_def_692,type,
    modulo_modulo_nat: nat > nat > nat ).

thf(func_def_693,type,
    zero_n356916108424825756nteger: $o > code_integer ).

thf(func_def_694,type,
    zero_n2684676970156552555ol_int: $o > int ).

thf(func_def_695,type,
    zero_n2687167440665602831ol_nat: $o > nat ).

thf(func_def_696,type,
    collect_int: ( int > $o ) > set_int ).

thf(func_def_697,type,
    collect_list_nat: ( list_nat > $o ) > set_list_nat ).

thf(func_def_698,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_699,type,
    collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).

thf(func_def_700,type,
    collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).

thf(func_def_701,type,
    collect_set_nat: ( set_nat > $o ) > set_set_nat ).

thf(func_def_702,type,
    collec5210948495886036740nt_int: ( set_Pr958786334691620121nt_int > $o ) > set_se6260736226359567993nt_int ).

thf(func_def_703,type,
    pow_nat: set_nat > set_set_nat ).

thf(func_def_704,type,
    image_4470545334726330049nteger: ( code_integer > code_integer ) > set_Code_integer > set_Code_integer ).

thf(func_def_705,type,
    image_int_int: ( int > int ) > set_int > set_int ).

thf(func_def_706,type,
    image_int_nat: ( int > nat ) > set_int > set_nat ).

thf(func_def_707,type,
    image_1215581382706833972nteger: ( nat > code_integer ) > set_nat > set_Code_integer ).

thf(func_def_708,type,
    image_nat_int: ( nat > int ) > set_nat > set_int ).

thf(func_def_709,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_710,type,
    image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).

thf(func_def_711,type,
    image_nat_char: ( nat > char ) > set_nat > set_char ).

thf(func_def_712,type,
    image_char_nat: ( char > nat ) > set_char > set_nat ).

thf(func_def_713,type,
    insert_int: int > set_int > set_int ).

thf(func_def_714,type,
    insert_nat: nat > set_nat > set_nat ).

thf(func_def_715,type,
    vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_716,type,
    set_fo1084959871951514735nteger: ( nat > code_integer > code_integer ) > nat > nat > code_integer > code_integer ).

thf(func_def_717,type,
    set_fo9131927060563008058atural: ( nat > code_natural > code_natural ) > nat > nat > code_natural > code_natural ).

thf(func_def_718,type,
    set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).

thf(func_def_719,type,
    set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).

thf(func_def_720,type,
    set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).

thf(func_def_721,type,
    set_or189985376899183464nteger: code_integer > code_integer > set_Code_integer ).

thf(func_def_722,type,
    set_or1266510415728281911st_int: int > int > set_int ).

thf(func_def_723,type,
    set_or1269000886237332187st_nat: nat > nat > set_nat ).

thf(func_def_724,type,
    set_or8404916559141939852nteger: code_integer > code_integer > set_Code_integer ).

thf(func_def_725,type,
    set_or4662586982721622107an_int: int > int > set_int ).

thf(func_def_726,type,
    set_or4665077453230672383an_nat: nat > nat > set_nat ).

thf(func_def_727,type,
    set_ord_atLeast_nat: nat > set_nat ).

thf(func_def_728,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(func_def_729,type,
    set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer ).

thf(func_def_730,type,
    set_or6656581121297822940st_int: int > int > set_int ).

thf(func_def_731,type,
    set_or6659071591806873216st_nat: nat > nat > set_nat ).

thf(func_def_732,type,
    set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer ).

thf(func_def_733,type,
    set_or5832277885323065728an_int: int > int > set_int ).

thf(func_def_734,type,
    set_or5834768355832116004an_nat: nat > nat > set_nat ).

thf(func_def_735,type,
    set_or1210151606488870762an_nat: nat > set_nat ).

thf(func_def_736,type,
    set_ord_lessThan_nat: nat > set_nat ).

thf(func_def_737,type,
    char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).

thf(func_def_738,type,
    size_char: char > nat ).

thf(func_def_739,type,
    char_of_integer: code_integer > char ).

thf(func_def_740,type,
    comm_s629917340098488124ar_nat: char > nat ).

thf(func_def_741,type,
    integer_of_char: char > code_integer ).

thf(func_def_742,type,
    unique3096191561947761185of_nat: nat > char ).

thf(func_def_743,type,
    time_EQ_o: $o > $o > $o ).

thf(func_def_744,type,
    time_T7469515765551943773t_unit: heap_T5738788834812785303t_unit > nat > $o ).

thf(func_def_745,type,
    time_TBOUND_a: heap_Time_Heap_a > nat > $o ).

thf(func_def_746,type,
    time_f8834461667527620124t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > $o ).

thf(func_def_747,type,
    time_fails_a: heap_Time_Heap_a > heap_e7401611519738050253t_unit > $o ).

thf(func_def_748,type,
    time_t3350536682685678164t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).

thf(func_def_749,type,
    time_the_heap_a: heap_Time_Heap_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).

thf(func_def_750,type,
    time_t2745601220510131320t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > product_unit ).

thf(func_def_751,type,
    time_the_res_a: heap_Time_Heap_a > heap_e7401611519738050253t_unit > a ).

thf(func_def_752,type,
    time_time_array_o: heap_T5660665574680485309rray_o > heap_e7401611519738050253t_unit > nat ).

thf(func_def_753,type,
    time_time_array_int: heap_T1346037964561226099ay_int > heap_e7401611519738050253t_unit > nat ).

thf(func_def_754,type,
    time_time_array_nat: heap_T3836121109492952855ay_nat > heap_e7401611519738050253t_unit > nat ).

thf(func_def_755,type,
    time_t4224138285095624986t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > nat ).

thf(func_def_756,type,
    time_time_a: heap_Time_Heap_a > heap_e7401611519738050253t_unit > nat ).

thf(func_def_757,type,
    bi_tot1331153423839324337nteger: ( int > code_integer > $o ) > $o ).

thf(func_def_758,type,
    bi_tot896582865486249351at_int: ( product_prod_nat_nat > int > $o ) > $o ).

thf(func_def_759,type,
    bi_uni8663861020805155098nteger: ( int > code_integer > $o ) > $o ).

thf(func_def_760,type,
    left_t3131394472396969446nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > $o ).

thf(func_def_761,type,
    left_u6795595883297946906nteger: ( int > code_integer > $o ) > $o ).

thf(func_def_762,type,
    right_7281159819619925802nteger: ( int > code_integer > $o ) > $o ).

thf(func_def_763,type,
    right_1157779049177982926at_int: ( product_prod_nat_nat > int > $o ) > $o ).

thf(func_def_764,type,
    transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_765,type,
    type_d8366093980585677751er_int: ( code_integer > int ) > ( int > code_integer ) > set_int > $o ).

thf(func_def_766,type,
    type_d4410041424927559462al_nat: ( code_natural > nat ) > ( nat > code_natural ) > set_nat > $o ).

thf(func_def_767,type,
    type_d8554052265237484179nt_int: ( rat > set_Pr958786334691620121nt_int ) > ( set_Pr958786334691620121nt_int > rat ) > set_se6260736226359567993nt_int > $o ).

thf(func_def_768,type,
    accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).

thf(func_def_769,type,
    accp_nat: ( nat > nat > $o ) > nat > $o ).

thf(func_def_770,type,
    accp_P8126237942716283194atural: ( produc7822875418678951345atural > produc7822875418678951345atural > $o ) > produc7822875418678951345atural > $o ).

thf(func_def_771,type,
    accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_772,type,
    accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_773,type,
    accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).

thf(func_def_774,type,
    pred_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_775,type,
    wf_int: set_Pr958786334691620121nt_int > $o ).

thf(func_def_776,type,
    wf_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_777,type,
    fChoice_int: ( int > $o ) > int ).

thf(func_def_778,type,
    fChoice_nat: ( nat > $o ) > nat ).

thf(func_def_779,type,
    fChoic6978938873391328853at_nat: ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).

thf(func_def_780,type,
    fChoice_set_nat: ( set_nat > $o ) > set_nat ).

thf(func_def_781,type,
    fChoic2749331249758569069nt_int: ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int ).

thf(func_def_782,type,
    member_Code_integer: code_integer > set_Code_integer > $o ).

thf(func_def_783,type,
    member_int: int > set_int > $o ).

thf(func_def_784,type,
    member_list_nat: list_nat > set_list_nat > $o ).

thf(func_def_785,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_786,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_787,type,
    member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).

thf(func_def_788,type,
    member_rat: rat > set_rat > $o ).

thf(func_def_789,type,
    member_set_nat: set_nat > set_set_nat > $o ).

thf(func_def_790,type,
    member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o ).

thf(func_def_792,type,
    h: heap_e7401611519738050253t_unit ).

thf(func_def_793,type,
    m: heap_Time_Heap_a ).

thf(func_def_794,type,
    t: nat ).

thf(func_def_817,type,
    sP0: nat > nat > nat > $o ).

thf(func_def_818,type,
    sP1: nat > nat > nat > $o ).

thf(func_def_819,type,
    sP2: nat > nat > nat > $o ).

thf(func_def_820,type,
    sK3: heap_T5738788834812785303t_unit > nat > ( product_unit > heap_Time_Heap_a ) > product_unit ).

thf(func_def_821,type,
    sK4: heap_T5738788834812785303t_unit > nat > ( product_unit > heap_Time_Heap_a ) > heap_e7401611519738050253t_unit ).

thf(func_def_822,type,
    sK5: nat > nat ).

thf(func_def_823,type,
    sK6: ( nat > $o ) > nat ).

thf(func_def_824,type,
    sK7: nat > ( nat > $o ) > nat ).

thf(func_def_825,type,
    sK8: heap_Time_Heap_a > nat > heap_e7401611519738050253t_unit ).

thf(func_def_826,type,
    sK9: ( nat > $o ) > nat > nat ).

thf(func_def_827,type,
    sK10: ( nat > $o ) > nat > nat ).

thf(func_def_828,type,
    sK11: heap_Time_Heap_a > nat > heap_e7401611519738050253t_unit ).

thf(func_def_829,type,
    sK12: nat > nat ).

thf(func_def_830,type,
    sK13: ( nat > $o ) > nat ).

thf(func_def_831,type,
    sK14: ( nat > $o ) > nat > nat ).

thf(func_def_832,type,
    sK15: ( nat > nat ) > nat ).

thf(func_def_833,type,
    sK16: ( nat > nat ) > nat ).

thf(func_def_834,type,
    sK17: nat > nat ).

thf(func_def_835,type,
    sK18: ( nat > nat > $o ) > nat ).

thf(func_def_836,type,
    sK19: ( nat > nat > $o ) > nat ).

thf(func_def_837,type,
    sK20: ( nat > nat > $o ) > nat ).

thf(func_def_838,type,
    sK21: ( nat > nat > $o ) > nat ).

thf(func_def_839,type,
    sK22: nat > nat ).

thf(func_def_840,type,
    sK23: nat > ( nat > $o ) > nat ).

thf(func_def_841,type,
    sK24: nat > ( nat > $o ) > nat ).

thf(func_def_842,type,
    sK25: ( nat > $o ) > nat > nat > nat ).

thf(func_def_843,type,
    sK26: nat > ( nat > $o ) > nat > nat ).

thf(func_def_844,type,
    sK27: ( product_unit > heap_Time_Heap_a ) > ( product_unit > heap_Time_Heap_a ) > product_unit ).

thf(func_def_846,type,
    ph29: 
      !>[X0: $tType] : X0 ).

thf(func_def_847,type,
    sK30: heap_e7401611519738050253t_unit ).

thf(f14711,plain,
    $false,
    inference(subsumption_resolution,[status(thm)],[f14710,f14141]) ).

thf(f14141,plain,
    ! [X0: nat] :
      ( $true
      = ( ord_less_eq_nat @ zero_zero_nat @ X0 ) ),
    inference(cnf_transformation,[status(thm)],[f6122]) ).

thf(f6122,plain,
    ! [X0: nat] :
      ( $true
      = ( ord_less_eq_nat @ zero_zero_nat @ X0 ) ),
    inference(fool_elimination,[status(thm)],[f6121]) ).

thf(f6121,plain,
    ! [X0: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X0 ),
    inference(rectify,[status(thm)],[f229]) ).

thf(f229,axiom,
    ! [X16: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X16 ),
    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_228_less__eq__nat_Osimps_I1_J) ).

thf(f14710,plain,
    ( $true
   != ( ord_less_eq_nat @ zero_zero_nat @ t ) ),
    inference(forward_demodulation,[status(thm)],[f14709,f14099]) ).

thf(f14099,plain,
    ! [X0: list_char,X1: heap_e7401611519738050253t_unit] :
      ( zero_zero_nat
      = ( time_time_a @ ( heap_Time_raise_a @ X0 ) @ X1 ) ),
    inference(cnf_transformation,[status(thm)],[f13897]) ).

thf(f13897,plain,
    ! [X0: list_char,X1: heap_e7401611519738050253t_unit] :
      ( zero_zero_nat
      = ( time_time_a @ ( heap_Time_raise_a @ X0 ) @ X1 ) ),
    inference(rectify,[status(thm)],[f224]) ).

thf(f224,axiom,
    ! [X47: list_char,X0: heap_e7401611519738050253t_unit] :
      ( zero_zero_nat
      = ( time_time_a @ ( heap_Time_raise_a @ X47 ) @ X0 ) ),
    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_223_time__raise) ).

thf(f14709,plain,
    ( ( ord_less_eq_nat @ ( time_time_a @ ( heap_Time_raise_a @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) @ h ) @ t )
   != $true ),
    inference(forward_demodulation,[status(thm)],[f14708,f14090]) ).

thf(f14090,plain,
    ! [X0: list_char,X1: product_unit > heap_Time_Heap_a] :
      ( ( heap_T757603679106148408unit_a @ ( heap_T2927564422264180874t_unit @ X0 ) @ X1 )
      = ( heap_Time_raise_a @ X0 ) ),
    inference(cnf_transformation,[status(thm)],[f13877]) ).

thf(f13877,plain,
    ! [X0: list_char,X1: product_unit > heap_Time_Heap_a] :
      ( ( heap_T757603679106148408unit_a @ ( heap_T2927564422264180874t_unit @ X0 ) @ X1 )
      = ( heap_Time_raise_a @ X0 ) ),
    inference(rectify,[status(thm)],[f164]) ).

thf(f164,axiom,
    ! [X33: list_char,X1: product_unit > heap_Time_Heap_a] :
      ( ( heap_Time_raise_a @ X33 )
      = ( heap_T757603679106148408unit_a @ ( heap_T2927564422264180874t_unit @ X33 ) @ X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_163_raise__bind) ).

thf(f14708,plain,
    ( $true
   != ( ord_less_eq_nat
      @ ( time_time_a
        @ ( heap_T757603679106148408unit_a @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) )
          @ ^ [Y0: product_unit] : m )
        @ h )
      @ t ) ),
    inference(subsumption_resolution,[status(thm)],[f14292,f14640]) ).

thf(f14640,plain,
    p != $true,
    inference(subsumption_resolution,[status(thm)],[f14639,f14194]) ).

thf(f14194,plain,
    ! [X0: heap_e7401611519738050253t_unit] :
      ( ( ( ord_less_eq_nat @ ( time_time_a @ m @ X0 ) @ t )
        = $true )
      | ( p != $true ) ),
    inference(cnf_transformation,[status(thm)],[f13964]) ).

thf(f13964,plain,
    ! [X0: heap_e7401611519738050253t_unit] :
      ( ( p != $true )
      | ( ( ord_less_eq_nat @ ( time_time_a @ m @ X0 ) @ t )
        = $true ) ),
    inference(ennf_transformation,[status(thm)],[f8210]) ).

thf(f8210,plain,
    ! [X0: heap_e7401611519738050253t_unit] :
      ( ( p = $true )
     => ( ( ord_less_eq_nat @ ( time_time_a @ m @ X0 ) @ t )
        = $true ) ),
    inference(fool_elimination,[status(thm)],[f8209]) ).

thf(f8209,plain,
    ! [X0: heap_e7401611519738050253t_unit] :
      ( p
     => ( ord_less_eq_nat @ ( time_time_a @ m @ X0 ) @ t ) ),
    inference(rectify,[status(thm)],[f1]) ).

thf(f1,axiom,
    ! [X0: heap_e7401611519738050253t_unit] :
      ( p
     => ( ord_less_eq_nat @ ( time_time_a @ m @ X0 ) @ t ) ),
    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_0__092_060open_062_092_060And_062h_O_AP_A_092_060Longrightarrow_062_Atime_Am_Ah_A_092_060le_062_At_092_060close_062) ).

thf(f14639,plain,
    ( ( $true
     != ( ord_less_eq_nat @ ( time_time_a @ m @ h ) @ t ) )
    | ( p != $true ) ),
    inference(beta_eta_normalization,[status(thm)],[f14638]) ).

thf(f14638,plain,
    ( ( p != $true )
    | ( ( ord_less_eq_nat
        @ ( time_time_a
          @ ( ^ [Y0: product_unit] : m
            @ product_Unity )
          @ h )
        @ t )
     != $true ) ),
    inference(forward_demodulation,[status(thm)],[f14637,f14136]) ).

thf(f14136,plain,
    ! [X0: product_unit,X1: product_unit > heap_Time_Heap_a] :
      ( ( heap_T757603679106148408unit_a @ ( heap_T4284346855313245393t_unit @ X0 ) @ X1 )
      = ( X1 @ X0 ) ),
    inference(cnf_transformation,[status(thm)],[f13876]) ).

thf(f13876,plain,
    ! [X0: product_unit,X1: product_unit > heap_Time_Heap_a] :
      ( ( heap_T757603679106148408unit_a @ ( heap_T4284346855313245393t_unit @ X0 ) @ X1 )
      = ( X1 @ X0 ) ),
    inference(rectify,[status(thm)],[f218]) ).

thf(f218,axiom,
    ! [X5: product_unit,X1: product_unit > heap_Time_Heap_a] :
      ( ( heap_T757603679106148408unit_a @ ( heap_T4284346855313245393t_unit @ X5 ) @ X1 )
      = ( X1 @ X5 ) ),
    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_217_ureturn__bind) ).

thf(f14637,plain,
    ( ( p != $true )
    | ( $true
     != ( ord_less_eq_nat
        @ ( time_time_a
          @ ( heap_T757603679106148408unit_a @ ( heap_T4284346855313245393t_unit @ product_Unity )
            @ ^ [Y0: product_unit] : m )
          @ h )
        @ t ) ) ),
    inference(forward_demodulation,[status(thm)],[f14619,f14225]) ).

thf(f14225,plain,
    ! [X2: heap_T5738788834812785303t_unit,X3: product_unit > heap_Time_Heap_a,X1: heap_T5738788834812785303t_unit] :
      ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ $true @ X2 @ X1 ) @ X3 )
      = ( heap_T757603679106148408unit_a @ X2 @ X3 ) ),
    inference(equality_resolution,[status(thm)],[f14152]) ).

thf(f14152,plain,
    ! [X2: heap_T5738788834812785303t_unit,X3: product_unit > heap_Time_Heap_a,X0: $o,X1: heap_T5738788834812785303t_unit] :
      ( ( $true != X0 )
      | ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
        = ( heap_T757603679106148408unit_a @ X2 @ X3 ) ) ),
    inference(cnf_transformation,[status(thm)],[f13905]) ).

thf(f13905,plain,
    ! [X0: $o,X1: heap_T5738788834812785303t_unit,X2: heap_T5738788834812785303t_unit,X3: product_unit > heap_Time_Heap_a] :
      ( ( ( $true != X0 )
        | ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
          = ( heap_T757603679106148408unit_a @ X2 @ X3 ) ) )
      & ( ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
          = ( heap_T757603679106148408unit_a @ X1 @ X3 ) )
        | ( $true = X0 ) ) ),
    inference(ennf_transformation,[status(thm)],[f13874]) ).

thf(f13874,plain,
    ! [X0: $o,X1: heap_T5738788834812785303t_unit,X2: heap_T5738788834812785303t_unit,X3: product_unit > heap_Time_Heap_a] :
      ( ( ( $true = X0 )
       => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
          = ( heap_T757603679106148408unit_a @ X2 @ X3 ) ) )
      & ( ( $true != X0 )
       => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
          = ( heap_T757603679106148408unit_a @ X1 @ X3 ) ) ) ),
    inference(flattening,[status(thm)],[f12872]) ).

thf(f12872,plain,
    ! [X0: $o,X1: heap_T5738788834812785303t_unit,X2: heap_T5738788834812785303t_unit,X3: product_unit > heap_Time_Heap_a] :
      ( ( ( $true = X0 )
       => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
          = ( heap_T757603679106148408unit_a @ X2 @ X3 ) ) )
      & ( ( $true != X0 )
       => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
          = ( heap_T757603679106148408unit_a @ X1 @ X3 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f12871]) ).

thf(f12871,plain,
    ! [X0: $o,X1: heap_T5738788834812785303t_unit,X2: heap_T5738788834812785303t_unit,X3: product_unit > heap_Time_Heap_a] :
      ( ( X0
       => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
          = ( heap_T757603679106148408unit_a @ X2 @ X3 ) ) )
      & ( ~ X0
       => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
          = ( heap_T757603679106148408unit_a @ X1 @ X3 ) ) ) ),
    inference(rectify,[status(thm)],[f21]) ).

thf(f21,axiom,
    ! [X7: $o,X9: heap_T5738788834812785303t_unit,X8: heap_T5738788834812785303t_unit,X1: product_unit > heap_Time_Heap_a] :
      ( ( X7
       => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X7 @ X8 @ X9 ) @ X1 )
          = ( heap_T757603679106148408unit_a @ X8 @ X1 ) ) )
      & ( ~ X7
       => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X7 @ X8 @ X9 ) @ X1 )
          = ( heap_T757603679106148408unit_a @ X9 @ X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_20_distrib__if__bind) ).

thf(f14619,plain,
    ( ( p != $true )
    | ( ( ord_less_eq_nat
        @ ( time_time_a
          @ ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ $true @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) )
            @ ^ [Y0: product_unit] : m )
          @ h )
        @ t )
     != $true ) ),
    inference(beta_eta_normalization,[status(thm)],[f14265]) ).

thf(f14265,plain,
    ! [X0: nat] :
      ( ( ( ord_less_eq_nat
          @ ( time_time_a
            @ ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ $true @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) )
              @ ^ [Y0: product_unit] : m )
            @ h )
          @ t )
       != $true )
      | ( $true
       != ( ^ [Y0: nat] : p
          @ X0 ) ) ),
    inference(superposition,[status(thm)],[f14251,f14081]) ).

thf(f14081,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ( ( X1 @ ( sK10 @ X1 @ X0 ) )
        = $true )
      | ( ( X1 @ X0 )
       != $true ) ),
    inference(cnf_transformation,[status(thm)],[f14018]) ).

thf(f14018,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ( ( ( X1 @ ( sK10 @ X1 @ X0 ) )
          = $true )
        & ( ( ord_less_eq_nat @ ( sK10 @ X1 @ X0 ) @ X0 )
          = $true ) )
      | ( ( ( X1 @ X0 )
         != $true )
        & ! [X3: nat] :
            ( ( ( ord_less_nat @ X3 @ X0 )
             != $true )
            | ( $true
             != ( X1 @ X3 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f14016,f14017]) ).

thf(f14017,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ? [X2: nat] :
          ( ( $true
            = ( X1 @ X2 ) )
          & ( $true
            = ( ord_less_eq_nat @ X2 @ X0 ) ) )
     => ( ( ( X1 @ ( sK10 @ X1 @ X0 ) )
          = $true )
        & ( ( ord_less_eq_nat @ ( sK10 @ X1 @ X0 ) @ X0 )
          = $true ) ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f14016,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ? [X2: nat] :
          ( ( $true
            = ( X1 @ X2 ) )
          & ( $true
            = ( ord_less_eq_nat @ X2 @ X0 ) ) )
      | ( ( ( X1 @ X0 )
         != $true )
        & ! [X3: nat] :
            ( ( ( ord_less_nat @ X3 @ X0 )
             != $true )
            | ( $true
             != ( X1 @ X3 ) ) ) ) ),
    inference(rectify,[status(thm)],[f13909]) ).

thf(f13909,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ? [X3: nat] :
          ( ( $true
            = ( X1 @ X3 ) )
          & ( $true
            = ( ord_less_eq_nat @ X3 @ X0 ) ) )
      | ( ( ( X1 @ X0 )
         != $true )
        & ! [X2: nat] :
            ( ( $true
             != ( ord_less_nat @ X2 @ X0 ) )
            | ( $true
             != ( X1 @ X2 ) ) ) ) ),
    inference(ennf_transformation,[status(thm)],[f13883]) ).

thf(f13883,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ( ! [X2: nat] :
            ( ( $true
              = ( ord_less_nat @ X2 @ X0 ) )
           => ( $true
             != ( X1 @ X2 ) ) )
       => ( ( X1 @ X0 )
          = $true ) )
     => ? [X3: nat] :
          ( ( $true
            = ( X1 @ X3 ) )
          & ( $true
            = ( ord_less_eq_nat @ X3 @ X0 ) ) ) ),
    inference(flattening,[status(thm)],[f10860]) ).

thf(f10860,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ( ! [X2: nat] :
            ( ( $true
              = ( ord_less_nat @ X2 @ X0 ) )
           => ( $true
             != ( X1 @ X2 ) ) )
       => ( ( X1 @ X0 )
          = $true ) )
     => ? [X3: nat] :
          ( ( $true
            = ( X1 @ X3 ) )
          & ( $true
            = ( ord_less_eq_nat @ X3 @ X0 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f10859]) ).

thf(f10859,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ( ! [X2: nat] :
            ( ( ord_less_nat @ X2 @ X0 )
           => ~ ( X1 @ X2 ) )
       => ( X1 @ X0 ) )
     => ? [X3: nat] :
          ( ( ord_less_eq_nat @ X3 @ X0 )
          & ( X1 @ X3 ) ) ),
    inference(rectify,[status(thm)],[f1402]) ).

thf(f1402,axiom,
    ! [X16: nat,X27: nat > $o] :
      ( ( ! [X86: nat] :
            ( ( ord_less_nat @ X86 @ X16 )
           => ~ ( X27 @ X86 ) )
       => ( X27 @ X16 ) )
     => ? [X87: nat] :
          ( ( ord_less_eq_nat @ X87 @ X16 )
          & ( X27 @ X87 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_1401_exists__leI) ).

thf(f14251,plain,
    ( $true
   != ( ord_less_eq_nat
      @ ( time_time_a
        @ ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ p @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) )
          @ ^ [Y0: product_unit] : m )
        @ h )
      @ t ) ),
    inference(beta_eta_normalization,[status(thm)],[f14203]) ).

thf(f14203,plain,
    ( $true
   != ( ord_less_eq_nat
      @ ( time_time_a
        @ ( heap_T757603679106148408unit_a
          @ ( ^ [Y0: $o] : ( if_Hea8138950348631371857t_unit @ Y0 @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) )
            @ p )
          @ ^ [Y0: product_unit] : m )
        @ h )
      @ t ) ),
    inference(definition_unfolding,[status(thm)],[f14051,f14140]) ).

thf(f14140,plain,
    ( refine_Imp_assert
    = ( ^ [Y0: $o] : ( if_Hea8138950348631371857t_unit @ Y0 @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f7010]) ).

thf(f7010,plain,
    ( refine_Imp_assert
    = ( ^ [Y0: $o] : ( if_Hea8138950348631371857t_unit @ Y0 @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[status(thm)],[f7009]) ).

thf(f7009,plain,
    ( refine_Imp_assert
    = ( ^ [X0: $o] : ( if_Hea8138950348631371857t_unit @ X0 @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) ) ) ),
    inference(rectify,[status(thm)],[f5899]) ).

thf(f5899,axiom,
    ( refine_Imp_assert
    = ( ^ [X81: $o] : ( if_Hea8138950348631371857t_unit @ X81 @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_5898_assert_H__def) ).

thf(f14051,plain,
    ( $true
   != ( ord_less_eq_nat
      @ ( time_time_a
        @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ p )
          @ ^ [Y0: product_unit] : m )
        @ h )
      @ t ) ),
    inference(cnf_transformation,[status(thm)],[f13873]) ).

thf(f13873,plain,
    ( $true
   != ( ord_less_eq_nat
      @ ( time_time_a
        @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ p )
          @ ^ [Y0: product_unit] : m )
        @ h )
      @ t ) ),
    inference(flattening,[status(thm)],[f11690]) ).

thf(f11690,plain,
    ( $true
   != ( ord_less_eq_nat
      @ ( time_time_a
        @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ p )
          @ ^ [Y0: product_unit] : m )
        @ h )
      @ t ) ),
    inference(fool_elimination,[status(thm)],[f11689]) ).

thf(f11689,plain,
    ~ ( ord_less_eq_nat
      @ ( time_time_a
        @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ p )
          @ ^ [X0: product_unit] : m )
        @ h )
      @ t ),
    inference(rectify,[status(thm)],[f6109]) ).

thf(f6109,negated_conjecture,
    ~ ( ord_less_eq_nat
      @ ( time_time_a
        @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ p )
          @ ^ [X37: product_unit] : m )
        @ h )
      @ t ),
    inference(negated_conjecture,[status(cth)],[f6108]) ).

thf(f6108,conjecture,
    ( ord_less_eq_nat
    @ ( time_time_a
      @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ p )
        @ ^ [X37: product_unit] : m )
      @ h )
    @ t ),
    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',conj_0) ).

thf(f14292,plain,
    ( ( $true
     != ( ord_less_eq_nat
        @ ( time_time_a
          @ ( heap_T757603679106148408unit_a @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) )
            @ ^ [Y0: product_unit] : m )
          @ h )
        @ t ) )
    | ( p = $true ) ),
    inference(superposition,[status(thm)],[f14251,f14151]) ).

thf(f14151,plain,
    ! [X2: heap_T5738788834812785303t_unit,X3: product_unit > heap_Time_Heap_a,X0: $o,X1: heap_T5738788834812785303t_unit] :
      ( ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1 ) @ X3 )
        = ( heap_T757603679106148408unit_a @ X1 @ X3 ) )
      | ( $true = X0 ) ),
    inference(cnf_transformation,[status(thm)],[f13905]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP217^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.12/0.13  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34  % Computer : n013.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit : 300
% 0.17/0.34  % WCLimit  : 300
% 0.17/0.34  % DateTime : Thu Feb 26 05:29:38 EST 2026
% 0.17/0.34  % CPUTime  : 
% 0.17/0.34  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.49  ---- Original DTF file ---
% 0.32/0.49  thf(spec,logic,$$dhol).
% 0.32/0.49  %------------------------------------------------------------------------------
% 0.32/0.49  % File     : ITP217^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.32/0.49  % Domain   : Interactive Theorem Proving
% 0.32/0.49  % Problem  : Sledgehammer problem Time_Reasoning 00330_012302
% 0.32/0.49  % Version  : [Des22] axioms.
% 0.32/0.49  % English  :
% 0.32/0.49  
% 0.32/0.49  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.32/0.49  %          : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.32/0.49  % Source   : [Des22]
% 0.32/0.49  % Names    : 0029_Time_Reasoning_00330_012302 [Des22]
% 0.32/0.49  
% 0.32/0.49  % Status   : Theorem
% 0.32/0.49  % Rating   : ? v9.2.1
% 0.32/0.49  % Syntax   : Number of formulae    : 6903 (3552 unt; 795 typ;   0 def)
% 0.32/0.49  %            Number of atoms       : 15461 (6666 equ;   0 cnn)
% 0.32/0.49  %            Maximal formula atoms :   48 (   2 avg)
% 0.32/0.49  %            Number of connectives : 53271 (1326   ~; 301   |; 740   &;45698   @)
% 0.32/0.49  %                                         (   0 <=>;5206  =>;   0  <=;   0 <~>)
% 0.32/0.49  %            Maximal formula depth :   29 (   5 avg)
% 0.32/0.49  %            Number of types       :   55 (  54 usr)
% 0.32/0.49  %            Number of type conns  : 2845 (2845   >;   0   *;   0   +;   0  <<)
% 0.32/0.49  %            Number of symbols     :  744 ( 741 usr;  42 con; 0-8 aty)
% 0.32/0.49  %            Number of variables   : 14310 (1438   ^;12595   !; 277   ?;14310   :)
% 0.32/0.49  % SPC      : TH0_THM_EQU_NAR
% 0.32/0.49  
% 0.32/0.49  % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.32/0.49  %            from the van Emde Boas Trees session in the Archive of Formal
% 0.32/0.49  %            proofs - 
% 0.32/0.49  %            www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.32/0.49  %            2022-02-17 16:31:50.969
% 0.32/0.49  % Bugfixes : Added ()s around negated sides of equations.
% 0.32/0.49  %------------------------------------------------------------------------------
% 0.32/0.49  % Could-be-implicit typings (54)
% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 0.32/0.49      produc6756470014200349799atural: $tType ).
% 0.32/0.49  
% 0.32/0.49  thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 0.32/0.49      option8956607266484857688it_nat: $tType ).
% 0.32/0.49  
% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.32/0.49      produc8923325533196201883nteger: $tType ).
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% 0.32/0.49  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Heap____Time____Monad__OHeap_It__Heap__Oarray_It__Nat__Onat_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Heap____Time____Monad__OHeap_It__Heap__Oarray_It__Int__Oint_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
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% 0.32/0.49  thf(ty_n_t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J,type,
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% 0.32/0.49  thf(ty_n_t__Heap____Time____Monad__OHeap_It__Heap__Oarray_I_Eo_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.32/0.49  thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 0.32/0.49  thf(ty_n_t__Filter__Ofilter_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.32/0.49      set_list_nat: $tType ).
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% 0.32/0.49  thf(ty_n_t__List__Olist_It__Code____Numeral__Ointeger_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 0.32/0.49  
% 0.32/0.49  thf(ty_n_t__Heap__Oarray_It__Product____Type__Ounit_J,type,
% 0.32/0.49      array_Product_unit: $tType ).
% 0.32/0.49  
% 0.32/0.49  thf(ty_n_t__Heap__Oref_It__Product____Type__Ounit_J,type,
% 0.32/0.49      ref_Product_unit: $tType ).
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.32/0.49      set_Product_unit: $tType ).
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% 0.32/0.49  thf(ty_n_t__Heap____Time____Monad__OHeap_Itf__a_J,type,
% 0.32/0.49      heap_Time_Heap_a: $tType ).
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% 0.32/0.49  thf(ty_n_t__Multiset__Omultiset_It__Nat__Onat_J,type,
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% 0.32/0.49  thf(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
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% 0.32/0.49  thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
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% 0.32/0.49  thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 0.32/0.49      set_char: $tType ).
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% 0.32/0.49  thf(ty_n_t__List__Olist_It__Rat__Orat_J,type,
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% 0.32/0.49  thf(ty_n_t__List__Olist_It__Num__Onum_J,type,
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% 0.32/0.49  thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
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% 0.32/0.49  thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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% 0.32/0.49  thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
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% 0.32/0.49  thf(ty_n_t__Code____Numeral__Onatural,type,
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% 0.32/0.49  
% 0.32/0.49  thf(ty_n_t__Code____Numeral__Ointeger,type,
% 0.32/0.49      code_integer: $tType ).
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% 0.32/0.49  thf(ty_n_t__Product____Type__Ounit,type,
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% 0.32/0.49  thf(ty_n_t__List__Olist_I_Eo_J,type,
% 0.32/0.49      list_o: $tType ).
% 0.32/0.49  
% 0.32/0.49  thf(ty_n_t__String__Ochar,type,
% 0.32/0.49      char: $tType ).
% 0.32/0.49  
% 0.32/0.49  thf(ty_n_t__Rat__Orat,type,
% 0.32/0.49      rat: $tType ).
% 0.32/0.49  
% 0.32/0.49  thf(ty_n_t__Num__Onum,type,
% 0.32/0.49      num: $tType ).
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% 0.32/0.49  thf(ty_n_t__Nat__Onat,type,
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% 0.32/0.49  thf(ty_n_t__Int__Oint,type,
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% 0.32/0.49  
% 0.32/0.49  thf(ty_n_tf__a,type,
% 0.32/0.49      a: $tType ).
% 0.32/0.49  
% 0.32/0.49  % Explicit typings (741)
% 0.32/0.49  thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 0.32/0.49      archim2889992004027027881ng_rat: rat > int ).
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% 0.32/0.49  thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 0.32/0.49      archim3151403230148437115or_rat: rat > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
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% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Array__Time_Omake_001_Eo,type,
% 0.32/0.49      array_make_o: nat > ( nat > $o ) > heap_T5660665574680485309rray_o ).
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% 0.32/0.49  thf(sy_c_Array__Time_Omake_001t__Int__Oint,type,
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% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Array__Time_Omake_001t__Nat__Onat,type,
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% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Array__Time_Onth_001t__Product____Type__Ounit,type,
% 0.32/0.49      array_7872002506669749220t_unit: array_Product_unit > nat > heap_T5738788834812785303t_unit ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Array__Time_Oof__list_001_Eo,type,
% 0.32/0.49      array_of_list_o: list_o > heap_T5660665574680485309rray_o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Array__Time_Oof__list_001t__Int__Oint,type,
% 0.32/0.49      array_of_list_int: list_int > heap_T1346037964561226099ay_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Array__Time_Oof__list_001t__Nat__Onat,type,
% 0.32/0.49      array_of_list_nat: list_nat > heap_T3836121109492952855ay_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 0.32/0.49      bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 0.32/0.49      bNF_re6321650412969554871eger_o: ( int > code_integer > $o ) > ( ( int > $o ) > ( code_integer > $o ) > $o ) > ( int > int > $o ) > ( code_integer > code_integer > $o ) > $o ).
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% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.32/0.49      bNF_re398004352372739002nteger: ( int > code_integer > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( int > int > int ) > ( code_integer > code_integer > code_integer ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.32/0.49      bNF_re4711666741709854504_nat_o: ( int > code_integer > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( code_integer > nat > $o ) > $o ).
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% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 0.32/0.49      bNF_re6574881592172037608er_o_o: ( int > code_integer > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( code_integer > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
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% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
% 0.32/0.49      bNF_re3804157879324367682nt_int: ( int > code_integer > $o ) > ( int > int > $o ) > ( int > int ) > ( code_integer > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
% 0.32/0.49      bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.32/0.49      bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.32/0.49      bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.32/0.49      bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 0.32/0.49      bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.32/0.49      bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 0.32/0.49      bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.32/0.49      bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.32/0.49      bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 0.32/0.49      bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.32/0.49      bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 0.32/0.49      bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.32/0.49      bNF_re4935368626670024657nteger: ( nat > nat > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( nat > int > int ) > ( nat > code_integer > code_integer ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.32/0.49      bNF_re4785983289428654063nt_int: ( nat > nat > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( nat > int > int ) > ( nat > int > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.32/0.49      bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.49      bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 0.32/0.49      bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.32/0.49      bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 0.32/0.49      bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.32/0.49      bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 0.32/0.49      bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 0.32/0.49      bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.32/0.49      bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 0.32/0.49      bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.32/0.49      bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 0.32/0.49      bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.32/0.49      bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 0.32/0.49      bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
% 0.32/0.49      bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 0.32/0.49      bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.32/0.49      bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.32/0.49      bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 0.32/0.49      bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.32/0.49      bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.32/0.49      bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.32/0.49      bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 0.32/0.49      bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.32/0.49      bNF_re7934895593101944656at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.49      bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Basic__BNFs_Opred__prod_001t__Int__Oint_001t__Int__Oint,type,
% 0.32/0.49      basic_1567116559311922317nt_int: ( int > $o ) > ( int > $o ) > product_prod_int_int > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Basic__BNFs_Opred__prod_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      basic_570253317919918037at_nat: ( nat > $o ) > ( nat > $o ) > product_prod_nat_nat > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Basic__BNFs_Orel__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.32/0.49      basic_4387203522000727145nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Basic__BNFs_Orel__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      basic_5328504652464829177at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Binomial_Obinomial,type,
% 0.32/0.49      binomial: nat > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Binomial_Ogbinomial_001t__Code____Numeral__Ointeger,type,
% 0.32/0.49      gbinom8545251970709558553nteger: code_integer > nat > code_integer ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Binomial_Ogbinomial_001t__Code____Numeral__Onatural,type,
% 0.32/0.49      gbinom7368847122466276068atural: code_natural > nat > code_natural ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 0.32/0.49      gbinomial_int: int > nat > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 0.32/0.49      gbinomial_nat: nat > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
% 0.32/0.49      gbinomial_rat: rat > nat > rat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 0.32/0.49      bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Oand__not__num,type,
% 0.32/0.49      bit_and_not_num: num > num > option_num ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
% 0.32/0.49      bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 0.32/0.49      bit_concat_bit: nat > int > int > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 0.32/0.49      bit_or_not_num_neg: num > num > num ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Code____Numeral__Ointeger,type,
% 0.32/0.49      bit_ri7632146776885996613nteger: code_integer > code_integer ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 0.32/0.49      bit_ri7919022796975470100ot_int: int > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
% 0.32/0.49      bit_ri631733984087533419it_int: nat > int > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
% 0.32/0.49      bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Onatural,type,
% 0.32/0.49      bit_se2773287842338716102atural: code_natural > code_natural > code_natural ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 0.32/0.49      bit_se725231765392027082nd_int: int > int > int ).
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% 0.32/0.49      if_rat: $o > rat > rat > rat ).
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% 0.32/0.49  thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 0.32/0.49      if_set_int: $o > set_int > set_int > set_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Infinite__Set_Owellorder__class_Oenumerate_001t__Nat__Onat,type,
% 0.32/0.49      infini8530281810654367211te_nat: set_nat > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_OAbs__Integ,type,
% 0.32/0.49      abs_Integ: product_prod_nat_nat > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_ORep__Integ,type,
% 0.32/0.49      rep_Integ: int > product_prod_nat_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Ocr__int,type,
% 0.32/0.49      cr_int: product_prod_nat_nat > int > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Oint__ge__less__than,type,
% 0.32/0.49      int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Oint__ge__less__than2,type,
% 0.32/0.49      int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Ointrel,type,
% 0.32/0.49      intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Onat,type,
% 0.32/0.49      nat2: int > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Opcr__int,type,
% 0.32/0.49      pcr_int: product_prod_nat_nat > int > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Opower__int_001t__Rat__Orat,type,
% 0.32/0.49      power_int_rat: rat > int > rat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Oring__1__class_OInts_001t__Code____Numeral__Ointeger,type,
% 0.32/0.49      ring_11222124179247155820nteger: set_Code_integer ).
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% 0.32/0.49  thf(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint,type,
% 0.32/0.49      ring_1_Ints_int: set_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
% 0.32/0.49      ring_1_Ints_rat: set_rat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
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% 0.32/0.49  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 0.32/0.49      ring_1_of_int_int: int > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 0.32/0.49      ring_1_of_int_rat: int > rat ).
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% 0.32/0.49  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 0.32/0.49      inf_in3604695632404883862_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 0.32/0.49      inf_inf_int: int > int > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 0.32/0.49      inf_inf_nat: nat > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 0.32/0.49      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 0.32/0.49      sup_sup_int: int > int > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 0.32/0.49      sup_sup_nat: nat > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.32/0.49      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 0.32/0.49      lattic8263393255366662781ax_int: set_int > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 0.32/0.49      lattic8265883725875713057ax_nat: set_nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Lifting_OQuotient_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.32/0.49      quotie1194848508323700631at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int > $o ) > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 0.32/0.49      append_int: list_int > list_int > list_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.32/0.49      append_nat: list_nat > list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 0.32/0.49      butlast_nat: list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 0.32/0.49      drop_nat: nat > list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
% 0.32/0.49      filter_nat2: ( nat > $o ) > list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Ofold_001t__Int__Oint_001t__Int__Oint,type,
% 0.32/0.49      fold_int_int: ( int > int > int ) > list_int > int > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Ofoldr_001_Eo_001t__Nat__Onat,type,
% 0.32/0.49      foldr_o_nat: ( $o > nat > nat ) > list_o > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Ofoldr_001t__Int__Oint_001t__Nat__Onat,type,
% 0.32/0.49      foldr_int_nat: ( int > nat > nat ) > list_int > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Ofoldr_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Ogen__length_001_Eo,type,
% 0.32/0.49      gen_length_o: nat > list_o > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Ogen__length_001t__Int__Oint,type,
% 0.32/0.49      gen_length_int: nat > list_int > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Ogen__length_001t__Nat__Onat,type,
% 0.32/0.49      gen_length_nat: nat > list_nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 0.32/0.49      last_nat: list_nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 0.32/0.49      linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 0.32/0.49      linord2614967742042102400et_nat: set_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_OCons_001_Eo,type,
% 0.32/0.49      cons_o: $o > list_o > list_o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 0.32/0.49      cons_int: int > list_int > list_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.32/0.49      cons_nat: nat > list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_OCons_001t__Num__Onum,type,
% 0.32/0.49      cons_num: num > list_num > list_num ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_OCons_001t__Rat__Orat,type,
% 0.32/0.49      cons_rat: rat > list_rat > list_rat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_OCons_001t__String__Ochar,type,
% 0.32/0.49      cons_char: char > list_char > list_char ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_ONil_001_Eo,type,
% 0.32/0.49      nil_o: list_o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 0.32/0.49      nil_int: list_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.32/0.49      nil_nat: list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_ONil_001t__Num__Onum,type,
% 0.32/0.49      nil_num: list_num ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_ONil_001t__Rat__Orat,type,
% 0.32/0.49      nil_rat: list_rat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_ONil_001t__String__Ochar,type,
% 0.32/0.49      nil_char: list_char ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.49      map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 0.32/0.49      set_int2: list_int > set_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 0.32/0.49      set_nat2: list_nat > set_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Onth_001_Eo,type,
% 0.32/0.49      nth_o: list_o > nat > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 0.32/0.49      nth_Code_integer: list_Code_integer > nat > code_integer ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Onth_001t__Int__Oint,type,
% 0.32/0.49      nth_int: list_int > nat > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 0.32/0.49      nth_nat: list_nat > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Onth_001t__Num__Onum,type,
% 0.32/0.49      nth_num: list_num > nat > num ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Onth_001t__Rat__Orat,type,
% 0.32/0.49      nth_rat: list_rat > nat > rat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Onth_001t__String__Ochar,type,
% 0.32/0.49      nth_char: list_char > nat > char ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Orotate1_001_Eo,type,
% 0.32/0.49      rotate1_o: list_o > list_o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 0.32/0.49      rotate1_int: list_int > list_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 0.32/0.49      rotate1_nat: list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Orotate_001_Eo,type,
% 0.32/0.49      rotate_o: nat > list_o > list_o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Orotate_001t__Int__Oint,type,
% 0.32/0.49      rotate_int: nat > list_int > list_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Orotate_001t__Nat__Onat,type,
% 0.32/0.49      rotate_nat: nat > list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Osorted__wrt_001_Eo,type,
% 0.32/0.49      sorted_wrt_o: ( $o > $o > $o ) > list_o > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Osorted__wrt_001t__Code____Numeral__Ointeger,type,
% 0.32/0.49      sorted710888440204495920nteger: ( code_integer > code_integer > $o ) > list_Code_integer > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 0.32/0.49      sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 0.32/0.49      sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Osorted__wrt_001t__Num__Onum,type,
% 0.32/0.49      sorted_wrt_num: ( num > num > $o ) > list_num > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Osorted__wrt_001t__Rat__Orat,type,
% 0.32/0.49      sorted_wrt_rat: ( rat > rat > $o ) > list_rat > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 0.32/0.49      take_nat: nat > list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Oupt,type,
% 0.32/0.49      upt: nat > nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Oupto,type,
% 0.32/0.49      upto: int > int > list_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Oupto__aux,type,
% 0.32/0.49      upto_aux: int > int > list_int > list_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_List_Oupto__rel,type,
% 0.32/0.49      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Misc_Oslice_001_Eo,type,
% 0.32/0.49      slice_o: nat > nat > list_o > list_o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Misc_Oslice_001t__Int__Oint,type,
% 0.32/0.49      slice_int: nat > nat > list_int > list_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Misc_Oslice_001t__Nat__Onat,type,
% 0.32/0.49      slice_nat: nat > nat > list_nat > list_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Misc_Oslice_001t__String__Ochar,type,
% 0.32/0.49      slice_char: nat > nat > list_char > list_char ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Multiset_Omset_001t__Nat__Onat,type,
% 0.32/0.49      mset_nat: list_nat > multiset_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Multiset_Omset__set_001t__Nat__Onat,type,
% 0.32/0.49      mset_set_nat: set_nat > multiset_nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_OSuc,type,
% 0.32/0.49      suc: nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.49      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 0.32/0.49      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 0.32/0.49      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.32/0.49      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Onat_Opred,type,
% 0.32/0.49      pred: nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 0.32/0.49      semiring_1_Nats_int: set_int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
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% 0.32/0.49      semiri3763490453095760265atural: nat > code_natural ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.32/0.49      semiri1314217659103216013at_int: nat > int ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.32/0.49      semiri1316708129612266289at_nat: nat > nat ).
% 0.32/0.49  
% 0.32/0.49  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 0.32/0.49      semiri681578069525770553at_rat: nat > rat ).
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% 0.32/0.49      nat_prod_decode: nat > product_prod_nat_nat ).
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% 0.32/0.49      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
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% 0.32/0.49      nat_prod_encode: product_prod_nat_nat > nat ).
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% 0.32/0.49      nat_set_encode: set_nat > nat ).
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% 0.32/0.49  thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.32/0.49      nat_triangle: nat > nat ).
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% 0.32/0.49      bitM: num > num ).
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% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 0.32/0.50      transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 0.32/0.50      type_d8366093980585677751er_int: ( code_integer > int ) > ( int > code_integer ) > set_int > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Onatural_001t__Nat__Onat,type,
% 0.32/0.50      type_d4410041424927559462al_nat: ( code_natural > nat ) > ( nat > code_natural ) > set_nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Typedef_Otype__definition_001t__Rat__Orat_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.32/0.50      type_d8554052265237484179nt_int: ( rat > set_Pr958786334691620121nt_int ) > ( set_Pr958786334691620121nt_int > rat ) > set_se6260736226359567993nt_int > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 0.32/0.50      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 0.32/0.50      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 0.32/0.50      accp_P8126237942716283194atural: ( produc7822875418678951345atural > produc7822875418678951345atural > $o ) > produc7822875418678951345atural > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.32/0.50      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.50      accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 0.32/0.50      accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Wellfounded_Opred__nat,type,
% 0.32/0.50      pred_nat: set_Pr1261947904930325089at_nat ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Wellfounded_Owf_001t__Int__Oint,type,
% 0.32/0.50      wf_int: set_Pr958786334691620121nt_int > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 0.32/0.50      wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_fChoice_001t__Int__Oint,type,
% 0.32/0.50      fChoice_int: ( int > $o ) > int ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_fChoice_001t__Nat__Onat,type,
% 0.32/0.50      fChoice_nat: ( nat > $o ) > nat ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_fChoice_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.50      fChoic6978938873391328853at_nat: ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_fChoice_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.32/0.50      fChoice_set_nat: ( set_nat > $o ) > set_nat ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_fChoice_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.32/0.50      fChoic2749331249758569069nt_int: ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 0.32/0.50      member_Code_integer: code_integer > set_Code_integer > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_member_001t__Int__Oint,type,
% 0.32/0.50      member_int: int > set_int > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.32/0.50      member_list_nat: list_nat > set_list_nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_member_001t__Nat__Onat,type,
% 0.32/0.50      member_nat: nat > set_nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.50      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.32/0.50      member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_member_001t__Rat__Orat,type,
% 0.32/0.50      member_rat: rat > set_rat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.32/0.50      member_set_nat: set_nat > set_set_nat > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.32/0.50      member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_v_P,type,
% 0.32/0.50      p: $o ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_v_h,type,
% 0.32/0.50      h: heap_e7401611519738050253t_unit ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_v_m,type,
% 0.32/0.50      m: heap_Time_Heap_a ).
% 0.32/0.50  
% 0.32/0.50  thf(sy_v_t,type,
% 0.32/0.50      t: nat ).
% 0.32/0.50  
% 0.32/0.50  % Relevant facts (6071)
% 0.32/0.50  thf(fact_0__092_060open_062_092_060And_062h_O_AP_A_092_060Longrightarrow_062_Atime_Am_Ah_A_092_060le_062_At_092_060close_062,axiom,
% 0.32/0.50      ! [H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( p
% 0.32/0.50       => ( ord_less_eq_nat @ ( time_time_a @ m @ H ) @ t ) ) ).
% 0.32/0.50  
% 0.32/0.50  % \<open>\<And>h. P \<Longrightarrow> time m h \<le> t\<close>
% 0.32/0.50  thf(fact_1_assms,axiom,
% 0.32/0.50      ( p
% 0.32/0.50     => ( time_TBOUND_a @ m @ t ) ) ).
% 0.32/0.50  
% 0.32/0.50  % assms
% 0.32/0.50  thf(fact_2_Heap__Time__Monad_Obind__bind,axiom,
% 0.32/0.50      ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_Time_Heap_a,K: a > heap_T5738788834812785303t_unit] :
% 0.32/0.50        ( ( heap_T8685611227969916822t_unit @ ( heap_T757603679106148408unit_a @ F @ G ) @ K )
% 0.32/0.50        = ( heap_T2633723481742716231t_unit @ F
% 0.32/0.50          @ ^ [X: product_unit] : ( heap_T8685611227969916822t_unit @ ( G @ X ) @ K ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Heap_Time_Monad.bind_bind
% 0.32/0.50  thf(fact_3_Heap__Time__Monad_Obind__bind,axiom,
% 0.32/0.50      ! [F: heap_Time_Heap_a,G: a > heap_T5738788834812785303t_unit,K: product_unit > heap_Time_Heap_a] :
% 0.32/0.50        ( ( heap_T757603679106148408unit_a @ ( heap_T8685611227969916822t_unit @ F @ G ) @ K )
% 0.32/0.50        = ( heap_Time_bind_a_a @ F
% 0.32/0.50          @ ^ [X: a] : ( heap_T757603679106148408unit_a @ ( G @ X ) @ K ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Heap_Time_Monad.bind_bind
% 0.32/0.50  thf(fact_4_Heap__Time__Monad_Obind__bind,axiom,
% 0.32/0.50      ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_T5738788834812785303t_unit,K: product_unit > heap_T5738788834812785303t_unit] :
% 0.32/0.50        ( ( heap_T2633723481742716231t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ K )
% 0.32/0.50        = ( heap_T2633723481742716231t_unit @ F
% 0.32/0.50          @ ^ [X: product_unit] : ( heap_T2633723481742716231t_unit @ ( G @ X ) @ K ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Heap_Time_Monad.bind_bind
% 0.32/0.50  thf(fact_5_Heap__Time__Monad_Obind__bind,axiom,
% 0.32/0.50      ! [F: heap_Time_Heap_a,G: a > heap_Time_Heap_a,K: a > heap_Time_Heap_a] :
% 0.32/0.50        ( ( heap_Time_bind_a_a @ ( heap_Time_bind_a_a @ F @ G ) @ K )
% 0.32/0.50        = ( heap_Time_bind_a_a @ F
% 0.32/0.50          @ ^ [X: a] : ( heap_Time_bind_a_a @ ( G @ X ) @ K ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Heap_Time_Monad.bind_bind
% 0.32/0.50  thf(fact_6_Heap__Time__Monad_Obind__bind,axiom,
% 0.32/0.50      ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_Time_Heap_a,K: a > heap_Time_Heap_a] :
% 0.32/0.50        ( ( heap_Time_bind_a_a @ ( heap_T757603679106148408unit_a @ F @ G ) @ K )
% 0.32/0.50        = ( heap_T757603679106148408unit_a @ F
% 0.32/0.50          @ ^ [X: product_unit] : ( heap_Time_bind_a_a @ ( G @ X ) @ K ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Heap_Time_Monad.bind_bind
% 0.32/0.50  thf(fact_7_Heap__Time__Monad_Obind__bind,axiom,
% 0.32/0.50      ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_T5738788834812785303t_unit,K: product_unit > heap_Time_Heap_a] :
% 0.32/0.50        ( ( heap_T757603679106148408unit_a @ ( heap_T2633723481742716231t_unit @ F @ G ) @ K )
% 0.32/0.50        = ( heap_T757603679106148408unit_a @ F
% 0.32/0.50          @ ^ [X: product_unit] : ( heap_T757603679106148408unit_a @ ( G @ X ) @ K ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Heap_Time_Monad.bind_bind
% 0.32/0.50  thf(fact_8_order__refl,axiom,
% 0.32/0.50      ! [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ X2 ) ).
% 0.32/0.50  
% 0.32/0.50  % order_refl
% 0.32/0.50  thf(fact_9_order__refl,axiom,
% 0.32/0.50      ! [X2: rat] : ( ord_less_eq_rat @ X2 @ X2 ) ).
% 0.32/0.50  
% 0.32/0.50  % order_refl
% 0.32/0.50  thf(fact_10_order__refl,axiom,
% 0.32/0.50      ! [X2: num] : ( ord_less_eq_num @ X2 @ X2 ) ).
% 0.32/0.50  
% 0.32/0.50  % order_refl
% 0.32/0.50  thf(fact_11_order__refl,axiom,
% 0.32/0.50      ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.32/0.50  
% 0.32/0.50  % order_refl
% 0.32/0.50  thf(fact_12_order__refl,axiom,
% 0.32/0.50      ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 0.32/0.50  
% 0.32/0.50  % order_refl
% 0.32/0.50  thf(fact_13_dual__order_Orefl,axiom,
% 0.32/0.50      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.refl
% 0.32/0.50  thf(fact_14_dual__order_Orefl,axiom,
% 0.32/0.50      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.refl
% 0.32/0.50  thf(fact_15_dual__order_Orefl,axiom,
% 0.32/0.50      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.refl
% 0.32/0.50  thf(fact_16_dual__order_Orefl,axiom,
% 0.32/0.50      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.refl
% 0.32/0.50  thf(fact_17_dual__order_Orefl,axiom,
% 0.32/0.50      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.refl
% 0.32/0.50  thf(fact_18_distrib__if__bind,axiom,
% 0.32/0.50      ! [B: $o,C: heap_T5738788834812785303t_unit,D: heap_T5738788834812785303t_unit,F: product_unit > heap_T5738788834812785303t_unit] :
% 0.32/0.50        ( ( B
% 0.32/0.50         => ( ( heap_T2633723481742716231t_unit @ ( if_Hea8138950348631371857t_unit @ B @ C @ D ) @ F )
% 0.32/0.50            = ( heap_T2633723481742716231t_unit @ C @ F ) ) )
% 0.32/0.50        & ( ~ B
% 0.32/0.50         => ( ( heap_T2633723481742716231t_unit @ ( if_Hea8138950348631371857t_unit @ B @ C @ D ) @ F )
% 0.32/0.50            = ( heap_T2633723481742716231t_unit @ D @ F ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % distrib_if_bind
% 0.32/0.50  thf(fact_19_distrib__if__bind,axiom,
% 0.32/0.50      ! [B: $o,C: heap_Time_Heap_a,D: heap_Time_Heap_a,F: a > heap_Time_Heap_a] :
% 0.32/0.50        ( ( B
% 0.32/0.50         => ( ( heap_Time_bind_a_a @ ( if_Heap_Time_Heap_a @ B @ C @ D ) @ F )
% 0.32/0.50            = ( heap_Time_bind_a_a @ C @ F ) ) )
% 0.32/0.50        & ( ~ B
% 0.32/0.50         => ( ( heap_Time_bind_a_a @ ( if_Heap_Time_Heap_a @ B @ C @ D ) @ F )
% 0.32/0.50            = ( heap_Time_bind_a_a @ D @ F ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % distrib_if_bind
% 0.32/0.50  thf(fact_20_distrib__if__bind,axiom,
% 0.32/0.50      ! [B: $o,C: heap_T5738788834812785303t_unit,D: heap_T5738788834812785303t_unit,F: product_unit > heap_Time_Heap_a] :
% 0.32/0.50        ( ( B
% 0.32/0.50         => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ B @ C @ D ) @ F )
% 0.32/0.50            = ( heap_T757603679106148408unit_a @ C @ F ) ) )
% 0.32/0.50        & ( ~ B
% 0.32/0.50         => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ B @ C @ D ) @ F )
% 0.32/0.50            = ( heap_T757603679106148408unit_a @ D @ F ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % distrib_if_bind
% 0.32/0.50  thf(fact_21_TBOUNDD,axiom,
% 0.32/0.50      ! [M: heap_T5738788834812785303t_unit,T: nat,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_T7469515765551943773t_unit @ M @ T )
% 0.32/0.50       => ( ord_less_eq_nat @ ( time_t4224138285095624986t_unit @ M @ H ) @ T ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUNDD
% 0.32/0.50  thf(fact_22_TBOUNDD,axiom,
% 0.32/0.50      ! [M: heap_Time_Heap_a,T: nat,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_TBOUND_a @ M @ T )
% 0.32/0.50       => ( ord_less_eq_nat @ ( time_time_a @ M @ H ) @ T ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUNDD
% 0.32/0.50  thf(fact_23_TBOUNDI,axiom,
% 0.32/0.50      ! [M: heap_T5738788834812785303t_unit,T: nat] :
% 0.32/0.50        ( ! [H2: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_t4224138285095624986t_unit @ M @ H2 ) @ T )
% 0.32/0.50       => ( time_T7469515765551943773t_unit @ M @ T ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUNDI
% 0.32/0.50  thf(fact_24_TBOUNDI,axiom,
% 0.32/0.50      ! [M: heap_Time_Heap_a,T: nat] :
% 0.32/0.50        ( ! [H2: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_a @ M @ H2 ) @ T )
% 0.32/0.50       => ( time_TBOUND_a @ M @ T ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUNDI
% 0.32/0.50  thf(fact_25_TBOUND__def,axiom,
% 0.32/0.50      ( time_T7469515765551943773t_unit
% 0.32/0.50      = ( ^ [M2: heap_T5738788834812785303t_unit,T2: nat] :
% 0.32/0.50          ! [H3: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_t4224138285095624986t_unit @ M2 @ H3 ) @ T2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_def
% 0.32/0.50  thf(fact_26_TBOUND__def,axiom,
% 0.32/0.50      ( time_TBOUND_a
% 0.32/0.50      = ( ^ [M2: heap_Time_Heap_a,T2: nat] :
% 0.32/0.50          ! [H3: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_a @ M2 @ H3 ) @ T2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_def
% 0.32/0.50  thf(fact_27_le__refl,axiom,
% 0.32/0.50      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.32/0.50  
% 0.32/0.50  % le_refl
% 0.32/0.50  thf(fact_28_le__trans,axiom,
% 0.32/0.50      ! [I: nat,J: nat,K: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.50       => ( ( ord_less_eq_nat @ J @ K )
% 0.32/0.50         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_trans
% 0.32/0.50  thf(fact_29_eq__imp__le,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( M = N )
% 0.32/0.50       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % eq_imp_le
% 0.32/0.50  thf(fact_30_le__antisym,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.50       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.50         => ( M = N ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_antisym
% 0.32/0.50  thf(fact_31_nat__le__linear,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.50        | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nat_le_linear
% 0.32/0.50  thf(fact_32_TBOUND__mono,axiom,
% 0.32/0.50      ! [C: heap_Time_Heap_a,T: nat,T3: nat] :
% 0.32/0.50        ( ( time_TBOUND_a @ C @ T )
% 0.32/0.50       => ( ( ord_less_eq_nat @ T @ T3 )
% 0.32/0.50         => ( time_TBOUND_a @ C @ T3 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_mono
% 0.32/0.50  thf(fact_33_TBOUND__mono,axiom,
% 0.32/0.50      ! [C: heap_T5738788834812785303t_unit,T: nat,T3: nat] :
% 0.32/0.50        ( ( time_T7469515765551943773t_unit @ C @ T )
% 0.32/0.50       => ( ( ord_less_eq_nat @ T @ T3 )
% 0.32/0.50         => ( time_T7469515765551943773t_unit @ C @ T3 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_mono
% 0.32/0.50  thf(fact_34_TBOUND__eqI,axiom,
% 0.32/0.50      ! [M: heap_Time_Heap_a,T: nat] :
% 0.32/0.50        ( ! [H2: heap_e7401611519738050253t_unit] :
% 0.32/0.50            ( ( time_time_a @ M @ H2 )
% 0.32/0.50            = T )
% 0.32/0.50       => ( time_TBOUND_a @ M @ T ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_eqI
% 0.32/0.50  thf(fact_35_TBOUND__eqI,axiom,
% 0.32/0.50      ! [M: heap_T5738788834812785303t_unit,T: nat] :
% 0.32/0.50        ( ! [H2: heap_e7401611519738050253t_unit] :
% 0.32/0.50            ( ( time_t4224138285095624986t_unit @ M @ H2 )
% 0.32/0.50            = T )
% 0.32/0.50       => ( time_T7469515765551943773t_unit @ M @ T ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_eqI
% 0.32/0.50  thf(fact_36_order__antisym__conv,axiom,
% 0.32/0.50      ! [Y: set_nat,X2: set_nat] :
% 0.32/0.50        ( ( ord_less_eq_set_nat @ Y @ X2 )
% 0.32/0.50       => ( ( ord_less_eq_set_nat @ X2 @ Y )
% 0.32/0.50          = ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym_conv
% 0.32/0.50  thf(fact_37_order__antisym__conv,axiom,
% 0.32/0.50      ! [Y: rat,X2: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ Y @ X2 )
% 0.32/0.50       => ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.50          = ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym_conv
% 0.32/0.50  thf(fact_38_order__antisym__conv,axiom,
% 0.32/0.50      ! [Y: num,X2: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ Y @ X2 )
% 0.32/0.50       => ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.50          = ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym_conv
% 0.32/0.50  thf(fact_39_order__antisym__conv,axiom,
% 0.32/0.50      ! [Y: nat,X2: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ Y @ X2 )
% 0.32/0.50       => ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.50          = ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym_conv
% 0.32/0.50  thf(fact_40_order__antisym__conv,axiom,
% 0.32/0.50      ! [Y: int,X2: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ Y @ X2 )
% 0.32/0.50       => ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.50          = ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym_conv
% 0.32/0.50  thf(fact_41_linorder__le__cases,axiom,
% 0.32/0.50      ! [X2: rat,Y: rat] :
% 0.32/0.50        ( ~ ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.50       => ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_le_cases
% 0.32/0.50  thf(fact_42_linorder__le__cases,axiom,
% 0.32/0.50      ! [X2: num,Y: num] :
% 0.32/0.50        ( ~ ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.50       => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_le_cases
% 0.32/0.50  thf(fact_43_linorder__le__cases,axiom,
% 0.32/0.50      ! [X2: nat,Y: nat] :
% 0.32/0.50        ( ~ ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.50       => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_le_cases
% 0.32/0.50  thf(fact_44_linorder__le__cases,axiom,
% 0.32/0.50      ! [X2: int,Y: int] :
% 0.32/0.50        ( ~ ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.50       => ( ord_less_eq_int @ Y @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_le_cases
% 0.32/0.50  thf(fact_45_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_46_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_47_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_48_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_49_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_50_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: num,B: num,F: num > num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_51_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_52_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: num,B: num,F: num > int,C: int] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_53_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.50                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_54_ord__le__eq__subst,axiom,
% 0.32/0.50      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.50       => ( ( ( F @ B )
% 0.32/0.50            = C )
% 0.32/0.50         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.50                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_subst
% 0.32/0.50  thf(fact_55_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_56_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_57_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_58_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_59_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_60_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: num,F: num > num,B: num,C: num] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_61_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_62_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: int,F: num > int,B: num,C: num] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_63_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.50         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.50                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_64_ord__eq__le__subst,axiom,
% 0.32/0.50      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.50         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.50                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_subst
% 0.32/0.50  thf(fact_65_linorder__linear,axiom,
% 0.32/0.50      ! [X2: rat,Y: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.50        | ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_linear
% 0.32/0.50  thf(fact_66_linorder__linear,axiom,
% 0.32/0.50      ! [X2: num,Y: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.50        | ( ord_less_eq_num @ Y @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_linear
% 0.32/0.50  thf(fact_67_linorder__linear,axiom,
% 0.32/0.50      ! [X2: nat,Y: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.50        | ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_linear
% 0.32/0.50  thf(fact_68_linorder__linear,axiom,
% 0.32/0.50      ! [X2: int,Y: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.50        | ( ord_less_eq_int @ Y @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_linear
% 0.32/0.50  thf(fact_69_order__eq__refl,axiom,
% 0.32/0.50      ! [X2: set_nat,Y: set_nat] :
% 0.32/0.50        ( ( X2 = Y )
% 0.32/0.50       => ( ord_less_eq_set_nat @ X2 @ Y ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_eq_refl
% 0.32/0.50  thf(fact_70_order__eq__refl,axiom,
% 0.32/0.50      ! [X2: rat,Y: rat] :
% 0.32/0.50        ( ( X2 = Y )
% 0.32/0.50       => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_eq_refl
% 0.32/0.50  thf(fact_71_order__eq__refl,axiom,
% 0.32/0.50      ! [X2: num,Y: num] :
% 0.32/0.50        ( ( X2 = Y )
% 0.32/0.50       => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_eq_refl
% 0.32/0.50  thf(fact_72_order__eq__refl,axiom,
% 0.32/0.50      ! [X2: nat,Y: nat] :
% 0.32/0.50        ( ( X2 = Y )
% 0.32/0.50       => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_eq_refl
% 0.32/0.50  thf(fact_73_order__eq__refl,axiom,
% 0.32/0.50      ! [X2: int,Y: int] :
% 0.32/0.50        ( ( X2 = Y )
% 0.32/0.50       => ( ord_less_eq_int @ X2 @ Y ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_eq_refl
% 0.32/0.50  thf(fact_74_order__subst2,axiom,
% 0.32/0.50      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_75_order__subst2,axiom,
% 0.32/0.50      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_76_order__subst2,axiom,
% 0.32/0.50      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_77_order__subst2,axiom,
% 0.32/0.50      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_78_order__subst2,axiom,
% 0.32/0.50      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_79_order__subst2,axiom,
% 0.32/0.50      ! [A: num,B: num,F: num > num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_80_order__subst2,axiom,
% 0.32/0.50      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_81_order__subst2,axiom,
% 0.32/0.50      ! [A: num,B: num,F: num > int,C: int] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_82_order__subst2,axiom,
% 0.32/0.50      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.50                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_83_order__subst2,axiom,
% 0.32/0.50      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.32/0.50         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.50                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst2
% 0.32/0.50  thf(fact_84_order__subst1,axiom,
% 0.32/0.50      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_85_order__subst1,axiom,
% 0.32/0.50      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_86_order__subst1,axiom,
% 0.32/0.50      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.50         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.50                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_87_order__subst1,axiom,
% 0.32/0.50      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.50         => ( ! [X3: int,Y2: int] :
% 0.32/0.50                ( ( ord_less_eq_int @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_88_order__subst1,axiom,
% 0.32/0.50      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_89_order__subst1,axiom,
% 0.32/0.50      ! [A: num,F: num > num,B: num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_90_order__subst1,axiom,
% 0.32/0.50      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.50         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.50                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_91_order__subst1,axiom,
% 0.32/0.50      ! [A: num,F: int > num,B: int,C: int] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.50         => ( ! [X3: int,Y2: int] :
% 0.32/0.50                ( ( ord_less_eq_int @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_92_order__subst1,axiom,
% 0.32/0.50      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.50                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_93_order__subst1,axiom,
% 0.32/0.50      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ! [X3: num,Y2: num] :
% 0.32/0.50                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.50               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.50           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_subst1
% 0.32/0.50  thf(fact_94_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: set_nat,Z: set_nat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: set_nat,B2: set_nat] :
% 0.32/0.50            ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.50            & ( ord_less_eq_set_nat @ B2 @ A2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Orderings.order_eq_iff
% 0.32/0.50  thf(fact_95_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: rat,Z: rat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: rat,B2: rat] :
% 0.32/0.50            ( ( ord_less_eq_rat @ A2 @ B2 )
% 0.32/0.50            & ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Orderings.order_eq_iff
% 0.32/0.50  thf(fact_96_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: num,Z: num] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: num,B2: num] :
% 0.32/0.50            ( ( ord_less_eq_num @ A2 @ B2 )
% 0.32/0.50            & ( ord_less_eq_num @ B2 @ A2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Orderings.order_eq_iff
% 0.32/0.50  thf(fact_97_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: nat,B2: nat] :
% 0.32/0.50            ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.50            & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Orderings.order_eq_iff
% 0.32/0.50  thf(fact_98_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: int,B2: int] :
% 0.32/0.50            ( ( ord_less_eq_int @ A2 @ B2 )
% 0.32/0.50            & ( ord_less_eq_int @ B2 @ A2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Orderings.order_eq_iff
% 0.32/0.50  thf(fact_99_antisym,axiom,
% 0.32/0.50      ! [A: set_nat,B: set_nat] :
% 0.32/0.50        ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_set_nat @ B @ A )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % antisym
% 0.32/0.50  thf(fact_100_antisym,axiom,
% 0.32/0.50      ! [A: rat,B: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % antisym
% 0.32/0.50  thf(fact_101_antisym,axiom,
% 0.32/0.50      ! [A: num,B: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ A )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % antisym
% 0.32/0.50  thf(fact_102_antisym,axiom,
% 0.32/0.50      ! [A: nat,B: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % antisym
% 0.32/0.50  thf(fact_103_antisym,axiom,
% 0.32/0.50      ! [A: int,B: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_int @ B @ A )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % antisym
% 0.32/0.50  thf(fact_104_dual__order_Otrans,axiom,
% 0.32/0.50      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.32/0.50        ( ( ord_less_eq_set_nat @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_set_nat @ C @ B )
% 0.32/0.50         => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.trans
% 0.32/0.50  thf(fact_105_dual__order_Otrans,axiom,
% 0.32/0.50      ! [B: rat,A: rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_rat @ C @ B )
% 0.32/0.50         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.trans
% 0.32/0.50  thf(fact_106_dual__order_Otrans,axiom,
% 0.32/0.50      ! [B: num,A: num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_num @ C @ B )
% 0.32/0.50         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.trans
% 0.32/0.50  thf(fact_107_dual__order_Otrans,axiom,
% 0.32/0.50      ! [B: nat,A: nat,C: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_nat @ C @ B )
% 0.32/0.50         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.trans
% 0.32/0.50  thf(fact_108_dual__order_Otrans,axiom,
% 0.32/0.50      ! [B: int,A: int,C: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_int @ C @ B )
% 0.32/0.50         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.trans
% 0.32/0.50  thf(fact_109_dual__order_Oantisym,axiom,
% 0.32/0.50      ! [B: set_nat,A: set_nat] :
% 0.32/0.50        ( ( ord_less_eq_set_nat @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.antisym
% 0.32/0.50  thf(fact_110_dual__order_Oantisym,axiom,
% 0.32/0.50      ! [B: rat,A: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.antisym
% 0.32/0.50  thf(fact_111_dual__order_Oantisym,axiom,
% 0.32/0.50      ! [B: num,A: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.antisym
% 0.32/0.50  thf(fact_112_dual__order_Oantisym,axiom,
% 0.32/0.50      ! [B: nat,A: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.antisym
% 0.32/0.50  thf(fact_113_dual__order_Oantisym,axiom,
% 0.32/0.50      ! [B: int,A: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.50       => ( ( ord_less_eq_int @ A @ B )
% 0.32/0.50         => ( A = B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.antisym
% 0.32/0.50  thf(fact_114_dual__order_Oeq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: set_nat,Z: set_nat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: set_nat,B2: set_nat] :
% 0.32/0.50            ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.32/0.50            & ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.eq_iff
% 0.32/0.50  thf(fact_115_dual__order_Oeq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: rat,Z: rat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: rat,B2: rat] :
% 0.32/0.50            ( ( ord_less_eq_rat @ B2 @ A2 )
% 0.32/0.50            & ( ord_less_eq_rat @ A2 @ B2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.eq_iff
% 0.32/0.50  thf(fact_116_dual__order_Oeq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: num,Z: num] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: num,B2: num] :
% 0.32/0.50            ( ( ord_less_eq_num @ B2 @ A2 )
% 0.32/0.50            & ( ord_less_eq_num @ A2 @ B2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.eq_iff
% 0.32/0.50  thf(fact_117_dual__order_Oeq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: nat,B2: nat] :
% 0.32/0.50            ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.32/0.50            & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.eq_iff
% 0.32/0.50  thf(fact_118_dual__order_Oeq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: int,B2: int] :
% 0.32/0.50            ( ( ord_less_eq_int @ B2 @ A2 )
% 0.32/0.50            & ( ord_less_eq_int @ A2 @ B2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dual_order.eq_iff
% 0.32/0.50  thf(fact_119_linorder__wlog,axiom,
% 0.32/0.50      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.32/0.50        ( ! [A3: rat,B3: rat] :
% 0.32/0.50            ( ( ord_less_eq_rat @ A3 @ B3 )
% 0.32/0.50           => ( P @ A3 @ B3 ) )
% 0.32/0.50       => ( ! [A3: rat,B3: rat] :
% 0.32/0.50              ( ( P @ B3 @ A3 )
% 0.32/0.50             => ( P @ A3 @ B3 ) )
% 0.32/0.50         => ( P @ A @ B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_wlog
% 0.32/0.50  thf(fact_120_linorder__wlog,axiom,
% 0.32/0.50      ! [P: num > num > $o,A: num,B: num] :
% 0.32/0.50        ( ! [A3: num,B3: num] :
% 0.32/0.50            ( ( ord_less_eq_num @ A3 @ B3 )
% 0.32/0.50           => ( P @ A3 @ B3 ) )
% 0.32/0.50       => ( ! [A3: num,B3: num] :
% 0.32/0.50              ( ( P @ B3 @ A3 )
% 0.32/0.50             => ( P @ A3 @ B3 ) )
% 0.32/0.50         => ( P @ A @ B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_wlog
% 0.32/0.50  thf(fact_121_linorder__wlog,axiom,
% 0.32/0.50      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.32/0.50        ( ! [A3: nat,B3: nat] :
% 0.32/0.50            ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.32/0.50           => ( P @ A3 @ B3 ) )
% 0.32/0.50       => ( ! [A3: nat,B3: nat] :
% 0.32/0.50              ( ( P @ B3 @ A3 )
% 0.32/0.50             => ( P @ A3 @ B3 ) )
% 0.32/0.50         => ( P @ A @ B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_wlog
% 0.32/0.50  thf(fact_122_linorder__wlog,axiom,
% 0.32/0.50      ! [P: int > int > $o,A: int,B: int] :
% 0.32/0.50        ( ! [A3: int,B3: int] :
% 0.32/0.50            ( ( ord_less_eq_int @ A3 @ B3 )
% 0.32/0.50           => ( P @ A3 @ B3 ) )
% 0.32/0.50       => ( ! [A3: int,B3: int] :
% 0.32/0.50              ( ( P @ B3 @ A3 )
% 0.32/0.50             => ( P @ A3 @ B3 ) )
% 0.32/0.50         => ( P @ A @ B ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % linorder_wlog
% 0.32/0.50  thf(fact_123_order__trans,axiom,
% 0.32/0.50      ! [X2: set_nat,Y: set_nat,Z2: set_nat] :
% 0.32/0.50        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_set_nat @ Y @ Z2 )
% 0.32/0.50         => ( ord_less_eq_set_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_trans
% 0.32/0.50  thf(fact_124_order__trans,axiom,
% 0.32/0.50      ! [X2: rat,Y: rat,Z2: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_rat @ Y @ Z2 )
% 0.32/0.50         => ( ord_less_eq_rat @ X2 @ Z2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_trans
% 0.32/0.50  thf(fact_125_order__trans,axiom,
% 0.32/0.50      ! [X2: num,Y: num,Z2: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_num @ Y @ Z2 )
% 0.32/0.50         => ( ord_less_eq_num @ X2 @ Z2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_trans
% 0.32/0.50  thf(fact_126_order__trans,axiom,
% 0.32/0.50      ! [X2: nat,Y: nat,Z2: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_nat @ Y @ Z2 )
% 0.32/0.50         => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_trans
% 0.32/0.50  thf(fact_127_order__trans,axiom,
% 0.32/0.50      ! [X2: int,Y: int,Z2: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_int @ Y @ Z2 )
% 0.32/0.50         => ( ord_less_eq_int @ X2 @ Z2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_trans
% 0.32/0.50  thf(fact_128_order_Otrans,axiom,
% 0.32/0.50      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.32/0.50        ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.32/0.50         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order.trans
% 0.32/0.50  thf(fact_129_order_Otrans,axiom,
% 0.32/0.50      ! [A: rat,B: rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order.trans
% 0.32/0.50  thf(fact_130_order_Otrans,axiom,
% 0.32/0.50      ! [A: num,B: num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order.trans
% 0.32/0.50  thf(fact_131_order_Otrans,axiom,
% 0.32/0.50      ! [A: nat,B: nat,C: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.50         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order.trans
% 0.32/0.50  thf(fact_132_order_Otrans,axiom,
% 0.32/0.50      ! [A: int,B: int,C: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.50         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order.trans
% 0.32/0.50  thf(fact_133_order__antisym,axiom,
% 0.32/0.50      ! [X2: set_nat,Y: set_nat] :
% 0.32/0.50        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_set_nat @ Y @ X2 )
% 0.32/0.50         => ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym
% 0.32/0.50  thf(fact_134_order__antisym,axiom,
% 0.32/0.50      ! [X2: rat,Y: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_rat @ Y @ X2 )
% 0.32/0.50         => ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym
% 0.32/0.50  thf(fact_135_order__antisym,axiom,
% 0.32/0.50      ! [X2: num,Y: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_num @ Y @ X2 )
% 0.32/0.50         => ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym
% 0.32/0.50  thf(fact_136_order__antisym,axiom,
% 0.32/0.50      ! [X2: nat,Y: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_nat @ Y @ X2 )
% 0.32/0.50         => ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym
% 0.32/0.50  thf(fact_137_order__antisym,axiom,
% 0.32/0.50      ! [X2: int,Y: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.50       => ( ( ord_less_eq_int @ Y @ X2 )
% 0.32/0.50         => ( X2 = Y ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_antisym
% 0.32/0.50  thf(fact_138_ord__le__eq__trans,axiom,
% 0.32/0.50      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.32/0.50        ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.50       => ( ( B = C )
% 0.32/0.50         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_trans
% 0.32/0.50  thf(fact_139_ord__le__eq__trans,axiom,
% 0.32/0.50      ! [A: rat,B: rat,C: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.50       => ( ( B = C )
% 0.32/0.50         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_trans
% 0.32/0.50  thf(fact_140_ord__le__eq__trans,axiom,
% 0.32/0.50      ! [A: num,B: num,C: num] :
% 0.32/0.50        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.50       => ( ( B = C )
% 0.32/0.50         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_trans
% 0.32/0.50  thf(fact_141_ord__le__eq__trans,axiom,
% 0.32/0.50      ! [A: nat,B: nat,C: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.50       => ( ( B = C )
% 0.32/0.50         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_trans
% 0.32/0.50  thf(fact_142_ord__le__eq__trans,axiom,
% 0.32/0.50      ! [A: int,B: int,C: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.50       => ( ( B = C )
% 0.32/0.50         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_le_eq_trans
% 0.32/0.50  thf(fact_143_ord__eq__le__trans,axiom,
% 0.32/0.50      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.32/0.50         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_trans
% 0.32/0.50  thf(fact_144_ord__eq__le__trans,axiom,
% 0.32/0.50      ! [A: rat,B: rat,C: rat] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_trans
% 0.32/0.50  thf(fact_145_ord__eq__le__trans,axiom,
% 0.32/0.50      ! [A: num,B: num,C: num] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_trans
% 0.32/0.50  thf(fact_146_ord__eq__le__trans,axiom,
% 0.32/0.50      ! [A: nat,B: nat,C: nat] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.50         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_trans
% 0.32/0.50  thf(fact_147_ord__eq__le__trans,axiom,
% 0.32/0.50      ! [A: int,B: int,C: int] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.50         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_trans
% 0.32/0.50  thf(fact_148_order__class_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: set_nat,Z: set_nat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [X: set_nat,Y4: set_nat] :
% 0.32/0.50            ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.50            & ( ord_less_eq_set_nat @ Y4 @ X ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_class.order_eq_iff
% 0.32/0.50  thf(fact_149_order__class_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: rat,Z: rat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [X: rat,Y4: rat] :
% 0.32/0.50            ( ( ord_less_eq_rat @ X @ Y4 )
% 0.32/0.50            & ( ord_less_eq_rat @ Y4 @ X ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_class.order_eq_iff
% 0.32/0.50  thf(fact_150_order__class_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: num,Z: num] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [X: num,Y4: num] :
% 0.32/0.50            ( ( ord_less_eq_num @ X @ Y4 )
% 0.32/0.50            & ( ord_less_eq_num @ Y4 @ X ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_class.order_eq_iff
% 0.32/0.50  thf(fact_151_order__class_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [X: nat,Y4: nat] :
% 0.32/0.50            ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.50            & ( ord_less_eq_nat @ Y4 @ X ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_class.order_eq_iff
% 0.32/0.50  thf(fact_152_order__class_Oorder__eq__iff,axiom,
% 0.32/0.50      ( ( ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [X: int,Y4: int] :
% 0.32/0.50            ( ( ord_less_eq_int @ X @ Y4 )
% 0.32/0.50            & ( ord_less_eq_int @ Y4 @ X ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % order_class.order_eq_iff
% 0.32/0.50  thf(fact_153_le__cases3,axiom,
% 0.32/0.50      ! [X2: rat,Y: rat,Z2: rat] :
% 0.32/0.50        ( ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.50         => ~ ( ord_less_eq_rat @ Y @ Z2 ) )
% 0.32/0.50       => ( ( ( ord_less_eq_rat @ Y @ X2 )
% 0.32/0.50           => ~ ( ord_less_eq_rat @ X2 @ Z2 ) )
% 0.32/0.50         => ( ( ( ord_less_eq_rat @ X2 @ Z2 )
% 0.32/0.50             => ~ ( ord_less_eq_rat @ Z2 @ Y ) )
% 0.32/0.50           => ( ( ( ord_less_eq_rat @ Z2 @ Y )
% 0.32/0.50               => ~ ( ord_less_eq_rat @ Y @ X2 ) )
% 0.32/0.50             => ( ( ( ord_less_eq_rat @ Y @ Z2 )
% 0.32/0.50                 => ~ ( ord_less_eq_rat @ Z2 @ X2 ) )
% 0.32/0.50               => ~ ( ( ord_less_eq_rat @ Z2 @ X2 )
% 0.32/0.50                   => ~ ( ord_less_eq_rat @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_cases3
% 0.32/0.50  thf(fact_154_le__cases3,axiom,
% 0.32/0.50      ! [X2: num,Y: num,Z2: num] :
% 0.32/0.50        ( ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.50         => ~ ( ord_less_eq_num @ Y @ Z2 ) )
% 0.32/0.50       => ( ( ( ord_less_eq_num @ Y @ X2 )
% 0.32/0.50           => ~ ( ord_less_eq_num @ X2 @ Z2 ) )
% 0.32/0.50         => ( ( ( ord_less_eq_num @ X2 @ Z2 )
% 0.32/0.50             => ~ ( ord_less_eq_num @ Z2 @ Y ) )
% 0.32/0.50           => ( ( ( ord_less_eq_num @ Z2 @ Y )
% 0.32/0.50               => ~ ( ord_less_eq_num @ Y @ X2 ) )
% 0.32/0.50             => ( ( ( ord_less_eq_num @ Y @ Z2 )
% 0.32/0.50                 => ~ ( ord_less_eq_num @ Z2 @ X2 ) )
% 0.32/0.50               => ~ ( ( ord_less_eq_num @ Z2 @ X2 )
% 0.32/0.50                   => ~ ( ord_less_eq_num @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_cases3
% 0.32/0.50  thf(fact_155_le__cases3,axiom,
% 0.32/0.50      ! [X2: nat,Y: nat,Z2: nat] :
% 0.32/0.50        ( ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.50         => ~ ( ord_less_eq_nat @ Y @ Z2 ) )
% 0.32/0.50       => ( ( ( ord_less_eq_nat @ Y @ X2 )
% 0.32/0.50           => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 0.32/0.50         => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.32/0.50             => ~ ( ord_less_eq_nat @ Z2 @ Y ) )
% 0.32/0.50           => ( ( ( ord_less_eq_nat @ Z2 @ Y )
% 0.32/0.50               => ~ ( ord_less_eq_nat @ Y @ X2 ) )
% 0.32/0.50             => ( ( ( ord_less_eq_nat @ Y @ Z2 )
% 0.32/0.50                 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 0.32/0.50               => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 0.32/0.50                   => ~ ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_cases3
% 0.32/0.50  thf(fact_156_le__cases3,axiom,
% 0.32/0.50      ! [X2: int,Y: int,Z2: int] :
% 0.32/0.50        ( ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.50         => ~ ( ord_less_eq_int @ Y @ Z2 ) )
% 0.32/0.50       => ( ( ( ord_less_eq_int @ Y @ X2 )
% 0.32/0.50           => ~ ( ord_less_eq_int @ X2 @ Z2 ) )
% 0.32/0.50         => ( ( ( ord_less_eq_int @ X2 @ Z2 )
% 0.32/0.50             => ~ ( ord_less_eq_int @ Z2 @ Y ) )
% 0.32/0.50           => ( ( ( ord_less_eq_int @ Z2 @ Y )
% 0.32/0.50               => ~ ( ord_less_eq_int @ Y @ X2 ) )
% 0.32/0.50             => ( ( ( ord_less_eq_int @ Y @ Z2 )
% 0.32/0.50                 => ~ ( ord_less_eq_int @ Z2 @ X2 ) )
% 0.32/0.50               => ~ ( ( ord_less_eq_int @ Z2 @ X2 )
% 0.32/0.50                   => ~ ( ord_less_eq_int @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_cases3
% 0.32/0.50  thf(fact_157_nle__le,axiom,
% 0.32/0.50      ! [A: rat,B: rat] :
% 0.32/0.50        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 0.32/0.50        = ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.50          & ( B != A ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nle_le
% 0.32/0.50  thf(fact_158_nle__le,axiom,
% 0.32/0.50      ! [A: num,B: num] :
% 0.32/0.50        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 0.32/0.50        = ( ( ord_less_eq_num @ B @ A )
% 0.32/0.50          & ( B != A ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nle_le
% 0.32/0.50  thf(fact_159_nle__le,axiom,
% 0.32/0.50      ! [A: nat,B: nat] :
% 0.32/0.50        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 0.32/0.50        = ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.50          & ( B != A ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nle_le
% 0.32/0.50  thf(fact_160_nle__le,axiom,
% 0.32/0.50      ! [A: int,B: int] :
% 0.32/0.50        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 0.32/0.50        = ( ( ord_less_eq_int @ B @ A )
% 0.32/0.50          & ( B != A ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nle_le
% 0.32/0.50  thf(fact_161_Nat_Oex__has__greatest__nat,axiom,
% 0.32/0.50      ! [P: nat > $o,K: nat,B: nat] :
% 0.32/0.50        ( ( P @ K )
% 0.32/0.50       => ( ! [Y2: nat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.32/0.50         => ? [X3: nat] :
% 0.32/0.50              ( ( P @ X3 )
% 0.32/0.50              & ! [Y5: nat] :
% 0.32/0.50                  ( ( P @ Y5 )
% 0.32/0.50                 => ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Nat.ex_has_greatest_nat
% 0.32/0.50  thf(fact_162_raise__bind,axiom,
% 0.32/0.50      ! [E: list_char,F: a > heap_Time_Heap_a] :
% 0.32/0.50        ( ( heap_Time_bind_a_a @ ( heap_Time_raise_a @ E ) @ F )
% 0.32/0.50        = ( heap_Time_raise_a @ E ) ) ).
% 0.32/0.50  
% 0.32/0.50  % raise_bind
% 0.32/0.50  thf(fact_163_raise__bind,axiom,
% 0.32/0.50      ! [E: list_char,F: product_unit > heap_Time_Heap_a] :
% 0.32/0.50        ( ( heap_T757603679106148408unit_a @ ( heap_T2927564422264180874t_unit @ E ) @ F )
% 0.32/0.50        = ( heap_Time_raise_a @ E ) ) ).
% 0.32/0.50  
% 0.32/0.50  % raise_bind
% 0.32/0.50  thf(fact_164_raise__bind,axiom,
% 0.32/0.50      ! [E: list_char,F: product_unit > heap_T5738788834812785303t_unit] :
% 0.32/0.50        ( ( heap_T2633723481742716231t_unit @ ( heap_T2927564422264180874t_unit @ E ) @ F )
% 0.32/0.50        = ( heap_T2927564422264180874t_unit @ E ) ) ).
% 0.32/0.50  
% 0.32/0.50  % raise_bind
% 0.32/0.50  thf(fact_165_Greatest__equality,axiom,
% 0.32/0.50      ! [P: set_nat > $o,X2: set_nat] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: set_nat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_set_nat @ Y2 @ X2 ) )
% 0.32/0.50         => ( ( order_5724808138429204845et_nat @ P )
% 0.32/0.50            = X2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Greatest_equality
% 0.32/0.50  thf(fact_166_Greatest__equality,axiom,
% 0.32/0.50      ! [P: rat > $o,X2: rat] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: rat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_rat @ Y2 @ X2 ) )
% 0.32/0.50         => ( ( order_Greatest_rat @ P )
% 0.32/0.50            = X2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Greatest_equality
% 0.32/0.50  thf(fact_167_Greatest__equality,axiom,
% 0.32/0.50      ! [P: num > $o,X2: num] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: num] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_num @ Y2 @ X2 ) )
% 0.32/0.50         => ( ( order_Greatest_num @ P )
% 0.32/0.50            = X2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Greatest_equality
% 0.32/0.50  thf(fact_168_Greatest__equality,axiom,
% 0.32/0.50      ! [P: int > $o,X2: int] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: int] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_int @ Y2 @ X2 ) )
% 0.32/0.50         => ( ( order_Greatest_int @ P )
% 0.32/0.50            = X2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Greatest_equality
% 0.32/0.50  thf(fact_169_Greatest__equality,axiom,
% 0.32/0.50      ! [P: nat > $o,X2: nat] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: nat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_nat @ Y2 @ X2 ) )
% 0.32/0.50         => ( ( order_Greatest_nat @ P )
% 0.32/0.50            = X2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Greatest_equality
% 0.32/0.50  thf(fact_170_mem__Collect__eq,axiom,
% 0.32/0.50      ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.32/0.50        ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 0.32/0.50        = ( P @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % mem_Collect_eq
% 0.32/0.50  thf(fact_171_mem__Collect__eq,axiom,
% 0.32/0.50      ! [A: list_nat,P: list_nat > $o] :
% 0.32/0.50        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 0.32/0.50        = ( P @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % mem_Collect_eq
% 0.32/0.50  thf(fact_172_mem__Collect__eq,axiom,
% 0.32/0.50      ! [A: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.32/0.50        ( ( member2340774599025711042nt_int @ A @ ( collec5210948495886036740nt_int @ P ) )
% 0.32/0.50        = ( P @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % mem_Collect_eq
% 0.32/0.50  thf(fact_173_mem__Collect__eq,axiom,
% 0.32/0.50      ! [A: set_nat,P: set_nat > $o] :
% 0.32/0.50        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 0.32/0.50        = ( P @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % mem_Collect_eq
% 0.32/0.50  thf(fact_174_mem__Collect__eq,axiom,
% 0.32/0.50      ! [A: nat,P: nat > $o] :
% 0.32/0.50        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.32/0.50        = ( P @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % mem_Collect_eq
% 0.32/0.50  thf(fact_175_mem__Collect__eq,axiom,
% 0.32/0.50      ! [A: int,P: int > $o] :
% 0.32/0.50        ( ( member_int @ A @ ( collect_int @ P ) )
% 0.32/0.50        = ( P @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % mem_Collect_eq
% 0.32/0.50  thf(fact_176_Collect__mem__eq,axiom,
% 0.32/0.50      ! [A4: set_Pr1261947904930325089at_nat] :
% 0.32/0.50        ( ( collec3392354462482085612at_nat
% 0.32/0.50          @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A4 ) )
% 0.32/0.50        = A4 ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_mem_eq
% 0.32/0.50  thf(fact_177_Collect__mem__eq,axiom,
% 0.32/0.50      ! [A4: set_list_nat] :
% 0.32/0.50        ( ( collect_list_nat
% 0.32/0.50          @ ^ [X: list_nat] : ( member_list_nat @ X @ A4 ) )
% 0.32/0.50        = A4 ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_mem_eq
% 0.32/0.50  thf(fact_178_Collect__mem__eq,axiom,
% 0.32/0.50      ! [A4: set_se6260736226359567993nt_int] :
% 0.32/0.50        ( ( collec5210948495886036740nt_int
% 0.32/0.50          @ ^ [X: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X @ A4 ) )
% 0.32/0.50        = A4 ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_mem_eq
% 0.32/0.50  thf(fact_179_Collect__mem__eq,axiom,
% 0.32/0.50      ! [A4: set_set_nat] :
% 0.32/0.50        ( ( collect_set_nat
% 0.32/0.50          @ ^ [X: set_nat] : ( member_set_nat @ X @ A4 ) )
% 0.32/0.50        = A4 ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_mem_eq
% 0.32/0.50  thf(fact_180_Collect__mem__eq,axiom,
% 0.32/0.50      ! [A4: set_nat] :
% 0.32/0.50        ( ( collect_nat
% 0.32/0.50          @ ^ [X: nat] : ( member_nat @ X @ A4 ) )
% 0.32/0.50        = A4 ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_mem_eq
% 0.32/0.50  thf(fact_181_Collect__mem__eq,axiom,
% 0.32/0.50      ! [A4: set_int] :
% 0.32/0.50        ( ( collect_int
% 0.32/0.50          @ ^ [X: int] : ( member_int @ X @ A4 ) )
% 0.32/0.50        = A4 ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_mem_eq
% 0.32/0.50  thf(fact_182_Collect__cong,axiom,
% 0.32/0.50      ! [P: list_nat > $o,Q: list_nat > $o] :
% 0.32/0.50        ( ! [X3: list_nat] :
% 0.32/0.50            ( ( P @ X3 )
% 0.32/0.50            = ( Q @ X3 ) )
% 0.32/0.50       => ( ( collect_list_nat @ P )
% 0.32/0.50          = ( collect_list_nat @ Q ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_cong
% 0.32/0.50  thf(fact_183_Collect__cong,axiom,
% 0.32/0.50      ! [P: set_Pr958786334691620121nt_int > $o,Q: set_Pr958786334691620121nt_int > $o] :
% 0.32/0.50        ( ! [X3: set_Pr958786334691620121nt_int] :
% 0.32/0.50            ( ( P @ X3 )
% 0.32/0.50            = ( Q @ X3 ) )
% 0.32/0.50       => ( ( collec5210948495886036740nt_int @ P )
% 0.32/0.50          = ( collec5210948495886036740nt_int @ Q ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_cong
% 0.32/0.50  thf(fact_184_Collect__cong,axiom,
% 0.32/0.50      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.32/0.50        ( ! [X3: set_nat] :
% 0.32/0.50            ( ( P @ X3 )
% 0.32/0.50            = ( Q @ X3 ) )
% 0.32/0.50       => ( ( collect_set_nat @ P )
% 0.32/0.50          = ( collect_set_nat @ Q ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_cong
% 0.32/0.50  thf(fact_185_Collect__cong,axiom,
% 0.32/0.50      ! [P: nat > $o,Q: nat > $o] :
% 0.32/0.50        ( ! [X3: nat] :
% 0.32/0.50            ( ( P @ X3 )
% 0.32/0.50            = ( Q @ X3 ) )
% 0.32/0.50       => ( ( collect_nat @ P )
% 0.32/0.50          = ( collect_nat @ Q ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_cong
% 0.32/0.50  thf(fact_186_Collect__cong,axiom,
% 0.32/0.50      ! [P: int > $o,Q: int > $o] :
% 0.32/0.50        ( ! [X3: int] :
% 0.32/0.50            ( ( P @ X3 )
% 0.32/0.50            = ( Q @ X3 ) )
% 0.32/0.50       => ( ( collect_int @ P )
% 0.32/0.50          = ( collect_int @ Q ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Collect_cong
% 0.32/0.50  thf(fact_187_GreatestI2__order,axiom,
% 0.32/0.50      ! [P: set_nat > $o,X2: set_nat,Q: set_nat > $o] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: set_nat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_set_nat @ Y2 @ X2 ) )
% 0.32/0.50         => ( ! [X3: set_nat] :
% 0.32/0.50                ( ( P @ X3 )
% 0.32/0.50               => ( ! [Y5: set_nat] :
% 0.32/0.50                      ( ( P @ Y5 )
% 0.32/0.50                     => ( ord_less_eq_set_nat @ Y5 @ X3 ) )
% 0.32/0.50                 => ( Q @ X3 ) ) )
% 0.32/0.50           => ( Q @ ( order_5724808138429204845et_nat @ P ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % GreatestI2_order
% 0.32/0.50  thf(fact_188_GreatestI2__order,axiom,
% 0.32/0.50      ! [P: rat > $o,X2: rat,Q: rat > $o] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: rat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_rat @ Y2 @ X2 ) )
% 0.32/0.50         => ( ! [X3: rat] :
% 0.32/0.50                ( ( P @ X3 )
% 0.32/0.50               => ( ! [Y5: rat] :
% 0.32/0.50                      ( ( P @ Y5 )
% 0.32/0.50                     => ( ord_less_eq_rat @ Y5 @ X3 ) )
% 0.32/0.50                 => ( Q @ X3 ) ) )
% 0.32/0.50           => ( Q @ ( order_Greatest_rat @ P ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % GreatestI2_order
% 0.32/0.50  thf(fact_189_GreatestI2__order,axiom,
% 0.32/0.50      ! [P: num > $o,X2: num,Q: num > $o] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: num] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_num @ Y2 @ X2 ) )
% 0.32/0.50         => ( ! [X3: num] :
% 0.32/0.50                ( ( P @ X3 )
% 0.32/0.50               => ( ! [Y5: num] :
% 0.32/0.50                      ( ( P @ Y5 )
% 0.32/0.50                     => ( ord_less_eq_num @ Y5 @ X3 ) )
% 0.32/0.50                 => ( Q @ X3 ) ) )
% 0.32/0.50           => ( Q @ ( order_Greatest_num @ P ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % GreatestI2_order
% 0.32/0.50  thf(fact_190_GreatestI2__order,axiom,
% 0.32/0.50      ! [P: int > $o,X2: int,Q: int > $o] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: int] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_int @ Y2 @ X2 ) )
% 0.32/0.50         => ( ! [X3: int] :
% 0.32/0.50                ( ( P @ X3 )
% 0.32/0.50               => ( ! [Y5: int] :
% 0.32/0.50                      ( ( P @ Y5 )
% 0.32/0.50                     => ( ord_less_eq_int @ Y5 @ X3 ) )
% 0.32/0.50                 => ( Q @ X3 ) ) )
% 0.32/0.50           => ( Q @ ( order_Greatest_int @ P ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % GreatestI2_order
% 0.32/0.50  thf(fact_191_GreatestI2__order,axiom,
% 0.32/0.50      ! [P: nat > $o,X2: nat,Q: nat > $o] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [Y2: nat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_nat @ Y2 @ X2 ) )
% 0.32/0.50         => ( ! [X3: nat] :
% 0.32/0.50                ( ( P @ X3 )
% 0.32/0.50               => ( ! [Y5: nat] :
% 0.32/0.50                      ( ( P @ Y5 )
% 0.32/0.50                     => ( ord_less_eq_nat @ Y5 @ X3 ) )
% 0.32/0.50                 => ( Q @ X3 ) ) )
% 0.32/0.50           => ( Q @ ( order_Greatest_nat @ P ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % GreatestI2_order
% 0.32/0.50  thf(fact_192_TBOUND__assert_H__bind,axiom,
% 0.32/0.50      ! [P: $o,P2: $o,M: heap_Time_Heap_a,T: nat] :
% 0.32/0.50        ( ( time_EQ_o @ P @ P2 )
% 0.32/0.50       => ( ( P
% 0.32/0.50           => ( time_TBOUND_a @ M @ T ) )
% 0.32/0.50         => ( time_TBOUND_a
% 0.32/0.50            @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ P )
% 0.32/0.50              @ ^ [Uu: product_unit] : M )
% 0.32/0.50            @ ( if_nat @ P2 @ T @ zero_zero_nat ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_assert'_bind
% 0.32/0.50  thf(fact_193_TBOUND__assert_H__bind,axiom,
% 0.32/0.50      ! [P: $o,P2: $o,M: heap_T5738788834812785303t_unit,T: nat] :
% 0.32/0.50        ( ( time_EQ_o @ P @ P2 )
% 0.32/0.50       => ( ( P
% 0.32/0.50           => ( time_T7469515765551943773t_unit @ M @ T ) )
% 0.32/0.50         => ( time_T7469515765551943773t_unit
% 0.32/0.50            @ ( heap_T2633723481742716231t_unit @ ( refine_Imp_assert @ P )
% 0.32/0.50              @ ^ [Uu: product_unit] : M )
% 0.32/0.50            @ ( if_nat @ P2 @ T @ zero_zero_nat ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_assert'_bind
% 0.32/0.50  thf(fact_194_bounded__Max__nat,axiom,
% 0.32/0.50      ! [P: nat > $o,X2: nat,M3: nat] :
% 0.32/0.50        ( ( P @ X2 )
% 0.32/0.50       => ( ! [X3: nat] :
% 0.32/0.50              ( ( P @ X3 )
% 0.32/0.50             => ( ord_less_eq_nat @ X3 @ M3 ) )
% 0.32/0.50         => ~ ! [M4: nat] :
% 0.32/0.50                ( ( P @ M4 )
% 0.32/0.50               => ~ ! [X4: nat] :
% 0.32/0.50                      ( ( P @ X4 )
% 0.32/0.50                     => ( ord_less_eq_nat @ X4 @ M4 ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % bounded_Max_nat
% 0.32/0.50  thf(fact_195_le__rel__bool__arg__iff,axiom,
% 0.32/0.50      ( ord_le7022414076629706543et_nat
% 0.32/0.50      = ( ^ [X5: $o > set_nat,Y6: $o > set_nat] :
% 0.32/0.50            ( ( ord_less_eq_set_nat @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 0.32/0.50            & ( ord_less_eq_set_nat @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_rel_bool_arg_iff
% 0.32/0.50  thf(fact_196_le__rel__bool__arg__iff,axiom,
% 0.32/0.50      ( ord_less_eq_o_rat
% 0.32/0.50      = ( ^ [X5: $o > rat,Y6: $o > rat] :
% 0.32/0.50            ( ( ord_less_eq_rat @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 0.32/0.50            & ( ord_less_eq_rat @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_rel_bool_arg_iff
% 0.32/0.50  thf(fact_197_le__rel__bool__arg__iff,axiom,
% 0.32/0.50      ( ord_less_eq_o_num
% 0.32/0.50      = ( ^ [X5: $o > num,Y6: $o > num] :
% 0.32/0.50            ( ( ord_less_eq_num @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 0.32/0.50            & ( ord_less_eq_num @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_rel_bool_arg_iff
% 0.32/0.50  thf(fact_198_le__rel__bool__arg__iff,axiom,
% 0.32/0.50      ( ord_less_eq_o_nat
% 0.32/0.50      = ( ^ [X5: $o > nat,Y6: $o > nat] :
% 0.32/0.50            ( ( ord_less_eq_nat @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 0.32/0.50            & ( ord_less_eq_nat @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_rel_bool_arg_iff
% 0.32/0.50  thf(fact_199_le__rel__bool__arg__iff,axiom,
% 0.32/0.50      ( ord_less_eq_o_int
% 0.32/0.50      = ( ^ [X5: $o > int,Y6: $o > int] :
% 0.32/0.50            ( ( ord_less_eq_int @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 0.32/0.50            & ( ord_less_eq_int @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_rel_bool_arg_iff
% 0.32/0.50  thf(fact_200_verit__la__disequality,axiom,
% 0.32/0.50      ! [A: rat,B: rat] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50        | ~ ( ord_less_eq_rat @ A @ B )
% 0.32/0.50        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % verit_la_disequality
% 0.32/0.50  thf(fact_201_verit__la__disequality,axiom,
% 0.32/0.50      ! [A: num,B: num] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50        | ~ ( ord_less_eq_num @ A @ B )
% 0.32/0.50        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % verit_la_disequality
% 0.32/0.50  thf(fact_202_verit__la__disequality,axiom,
% 0.32/0.50      ! [A: nat,B: nat] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50        | ~ ( ord_less_eq_nat @ A @ B )
% 0.32/0.50        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % verit_la_disequality
% 0.32/0.50  thf(fact_203_verit__la__disequality,axiom,
% 0.32/0.50      ! [A: int,B: int] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50        | ~ ( ord_less_eq_int @ A @ B )
% 0.32/0.50        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % verit_la_disequality
% 0.32/0.50  thf(fact_204_ord__eq__le__eq__trans,axiom,
% 0.32/0.50      ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.32/0.50         => ( ( C = D )
% 0.32/0.50           => ( ord_less_eq_set_nat @ A @ D ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_eq_trans
% 0.32/0.50  thf(fact_205_ord__eq__le__eq__trans,axiom,
% 0.32/0.50      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.50         => ( ( C = D )
% 0.32/0.50           => ( ord_less_eq_rat @ A @ D ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_eq_trans
% 0.32/0.50  thf(fact_206_ord__eq__le__eq__trans,axiom,
% 0.32/0.50      ! [A: num,B: num,C: num,D: num] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.50         => ( ( C = D )
% 0.32/0.50           => ( ord_less_eq_num @ A @ D ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_eq_trans
% 0.32/0.50  thf(fact_207_ord__eq__le__eq__trans,axiom,
% 0.32/0.50      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.50         => ( ( C = D )
% 0.32/0.50           => ( ord_less_eq_nat @ A @ D ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_eq_trans
% 0.32/0.50  thf(fact_208_ord__eq__le__eq__trans,axiom,
% 0.32/0.50      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.50        ( ( A = B )
% 0.32/0.50       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.50         => ( ( C = D )
% 0.32/0.50           => ( ord_less_eq_int @ A @ D ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ord_eq_le_eq_trans
% 0.32/0.50  thf(fact_209_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.50      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % verit_comp_simplify1(2)
% 0.32/0.50  thf(fact_210_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.50      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % verit_comp_simplify1(2)
% 0.32/0.50  thf(fact_211_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.50      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % verit_comp_simplify1(2)
% 0.32/0.50  thf(fact_212_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.50      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % verit_comp_simplify1(2)
% 0.32/0.50  thf(fact_213_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.50      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % verit_comp_simplify1(2)
% 0.32/0.50  thf(fact_214_refines__assert_H__bind,axiom,
% 0.32/0.50      ! [P3: heap_Time_Heap_a,Q2: heap_Time_Heap_a,Phi: $o] :
% 0.32/0.50        ( ( refine_Imp_refines_a @ P3 @ Q2 )
% 0.32/0.50       => ( refine_Imp_refines_a @ P3
% 0.32/0.50          @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ Phi )
% 0.32/0.50            @ ^ [Uu: product_unit] : Q2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % refines_assert'_bind
% 0.32/0.50  thf(fact_215_refines__assert_H__bind,axiom,
% 0.32/0.50      ! [P3: heap_T5738788834812785303t_unit,Q2: heap_T5738788834812785303t_unit,Phi: $o] :
% 0.32/0.50        ( ( refine451278484176762712t_unit @ P3 @ Q2 )
% 0.32/0.50       => ( refine451278484176762712t_unit @ P3
% 0.32/0.50          @ ( heap_T2633723481742716231t_unit @ ( refine_Imp_assert @ Phi )
% 0.32/0.50            @ ^ [Uu: product_unit] : Q2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % refines_assert'_bind
% 0.32/0.50  thf(fact_216_ureturn__bind,axiom,
% 0.32/0.50      ! [X2: a,F: a > heap_Time_Heap_a] :
% 0.32/0.50        ( ( heap_Time_bind_a_a @ ( heap_Time_ureturn_a @ X2 ) @ F )
% 0.32/0.50        = ( F @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ureturn_bind
% 0.32/0.50  thf(fact_217_ureturn__bind,axiom,
% 0.32/0.50      ! [X2: product_unit,F: product_unit > heap_Time_Heap_a] :
% 0.32/0.50        ( ( heap_T757603679106148408unit_a @ ( heap_T4284346855313245393t_unit @ X2 ) @ F )
% 0.32/0.50        = ( F @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ureturn_bind
% 0.32/0.50  thf(fact_218_ureturn__bind,axiom,
% 0.32/0.50      ! [X2: product_unit,F: product_unit > heap_T5738788834812785303t_unit] :
% 0.32/0.50        ( ( heap_T2633723481742716231t_unit @ ( heap_T4284346855313245393t_unit @ X2 ) @ F )
% 0.32/0.50        = ( F @ X2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % ureturn_bind
% 0.32/0.50  thf(fact_219_bot__nat__0_Oextremum,axiom,
% 0.32/0.50      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.32/0.50  
% 0.32/0.50  % bot_nat_0.extremum
% 0.32/0.50  thf(fact_220_le0,axiom,
% 0.32/0.50      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.32/0.50  
% 0.32/0.50  % le0
% 0.32/0.50  thf(fact_221_refines__refl,axiom,
% 0.32/0.50      ! [P3: heap_T5738788834812785303t_unit] : ( refine451278484176762712t_unit @ P3 @ P3 ) ).
% 0.32/0.50  
% 0.32/0.50  % refines_refl
% 0.32/0.50  thf(fact_222_refines__If,axiom,
% 0.32/0.50      ! [B: $o,T: heap_T5738788834812785303t_unit,T3: heap_T5738788834812785303t_unit,E: heap_T5738788834812785303t_unit,E2: heap_T5738788834812785303t_unit] :
% 0.32/0.50        ( ( B
% 0.32/0.50         => ( refine451278484176762712t_unit @ T @ T3 ) )
% 0.32/0.50       => ( ( ~ B
% 0.32/0.50           => ( refine451278484176762712t_unit @ E @ E2 ) )
% 0.32/0.50         => ( refine451278484176762712t_unit @ ( if_Hea8138950348631371857t_unit @ B @ T @ E ) @ ( if_Hea8138950348631371857t_unit @ B @ T3 @ E2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % refines_If
% 0.32/0.50  thf(fact_223_time__raise,axiom,
% 0.32/0.50      ! [Msg: list_char,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_time_a @ ( heap_Time_raise_a @ Msg ) @ H )
% 0.32/0.50        = zero_zero_nat ) ).
% 0.32/0.50  
% 0.32/0.50  % time_raise
% 0.32/0.50  thf(fact_224_time__raise,axiom,
% 0.32/0.50      ! [Msg: list_char,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_t4224138285095624986t_unit @ ( heap_T2927564422264180874t_unit @ Msg ) @ H )
% 0.32/0.50        = zero_zero_nat ) ).
% 0.32/0.50  
% 0.32/0.50  % time_raise
% 0.32/0.50  thf(fact_225_refines__bind,axiom,
% 0.32/0.50      ! [M: heap_Time_Heap_a,M5: heap_Time_Heap_a,F: a > heap_Time_Heap_a,F2: a > heap_Time_Heap_a] :
% 0.32/0.50        ( ( refine_Imp_refines_a @ M @ M5 )
% 0.32/0.50       => ( ! [X3: a] : ( refine_Imp_refines_a @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 0.32/0.50         => ( refine_Imp_refines_a @ ( heap_Time_bind_a_a @ M @ F ) @ ( heap_Time_bind_a_a @ M5 @ F2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % refines_bind
% 0.32/0.50  thf(fact_226_refines__bind,axiom,
% 0.32/0.50      ! [M: heap_T5738788834812785303t_unit,M5: heap_T5738788834812785303t_unit,F: product_unit > heap_Time_Heap_a,F2: product_unit > heap_Time_Heap_a] :
% 0.32/0.50        ( ( refine451278484176762712t_unit @ M @ M5 )
% 0.32/0.50       => ( ! [X3: product_unit] : ( refine_Imp_refines_a @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 0.32/0.50         => ( refine_Imp_refines_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ ( heap_T757603679106148408unit_a @ M5 @ F2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % refines_bind
% 0.32/0.50  thf(fact_227_refines__bind,axiom,
% 0.32/0.50      ! [M: heap_T5738788834812785303t_unit,M5: heap_T5738788834812785303t_unit,F: product_unit > heap_T5738788834812785303t_unit,F2: product_unit > heap_T5738788834812785303t_unit] :
% 0.32/0.50        ( ( refine451278484176762712t_unit @ M @ M5 )
% 0.32/0.50       => ( ! [X3: product_unit] : ( refine451278484176762712t_unit @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 0.32/0.50         => ( refine451278484176762712t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ ( heap_T2633723481742716231t_unit @ M5 @ F2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % refines_bind
% 0.32/0.50  thf(fact_228_less__eq__nat_Osimps_I1_J,axiom,
% 0.32/0.50      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.32/0.50  
% 0.32/0.50  % less_eq_nat.simps(1)
% 0.32/0.50  thf(fact_229_bot__nat__0_Oextremum__unique,axiom,
% 0.32/0.50      ! [A: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.32/0.50        = ( A = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % bot_nat_0.extremum_unique
% 0.32/0.50  thf(fact_230_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.32/0.50      ! [A: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.32/0.50       => ( A = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % bot_nat_0.extremum_uniqueI
% 0.32/0.50  thf(fact_231_le__0__eq,axiom,
% 0.32/0.50      ! [N: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.32/0.50        = ( N = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_0_eq
% 0.32/0.50  thf(fact_232_time__assert_H,axiom,
% 0.32/0.50      ! [P: $o,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_t4224138285095624986t_unit @ ( refine_Imp_assert @ P ) @ H )
% 0.32/0.50        = zero_zero_nat ) ).
% 0.32/0.50  
% 0.32/0.50  % time_assert'
% 0.32/0.50  thf(fact_233_TBOUND__refines,axiom,
% 0.32/0.50      ! [C: heap_Time_Heap_a,T: nat,D: heap_Time_Heap_a] :
% 0.32/0.50        ( ( time_TBOUND_a @ C @ T )
% 0.32/0.50       => ( ( refine_Imp_refines_a @ C @ D )
% 0.32/0.50         => ( time_TBOUND_a @ D @ T ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_refines
% 0.32/0.50  thf(fact_234_TBOUND__refines,axiom,
% 0.32/0.50      ! [C: heap_T5738788834812785303t_unit,T: nat,D: heap_T5738788834812785303t_unit] :
% 0.32/0.50        ( ( time_T7469515765551943773t_unit @ C @ T )
% 0.32/0.50       => ( ( refine451278484176762712t_unit @ C @ D )
% 0.32/0.50         => ( time_T7469515765551943773t_unit @ D @ T ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_refines
% 0.32/0.50  thf(fact_235_GreatestI__nat,axiom,
% 0.32/0.50      ! [P: nat > $o,K: nat,B: nat] :
% 0.32/0.50        ( ( P @ K )
% 0.32/0.50       => ( ! [Y2: nat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.32/0.50         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % GreatestI_nat
% 0.32/0.50  thf(fact_236_Greatest__le__nat,axiom,
% 0.32/0.50      ! [P: nat > $o,K: nat,B: nat] :
% 0.32/0.50        ( ( P @ K )
% 0.32/0.50       => ( ! [Y2: nat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.32/0.50         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % Greatest_le_nat
% 0.32/0.50  thf(fact_237_GreatestI__ex__nat,axiom,
% 0.32/0.50      ! [P: nat > $o,B: nat] :
% 0.32/0.50        ( ? [X_1: nat] : ( P @ X_1 )
% 0.32/0.50       => ( ! [Y2: nat] :
% 0.32/0.50              ( ( P @ Y2 )
% 0.32/0.50             => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.32/0.50         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % GreatestI_ex_nat
% 0.32/0.50  thf(fact_238_bind__ureturn,axiom,
% 0.32/0.50      ! [F: heap_Time_Heap_a] :
% 0.32/0.50        ( ( heap_Time_bind_a_a @ F @ heap_Time_ureturn_a )
% 0.32/0.50        = F ) ).
% 0.32/0.50  
% 0.32/0.50  % bind_ureturn
% 0.32/0.50  thf(fact_239_bind__ureturn,axiom,
% 0.32/0.50      ! [F: heap_T5738788834812785303t_unit] :
% 0.32/0.50        ( ( heap_T2633723481742716231t_unit @ F @ heap_T4284346855313245393t_unit )
% 0.32/0.50        = F ) ).
% 0.32/0.50  
% 0.32/0.50  % bind_ureturn
% 0.32/0.50  thf(fact_240_le__zero__eq,axiom,
% 0.32/0.50      ! [N: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.32/0.50        = ( N = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_zero_eq
% 0.32/0.50  thf(fact_241_le__numeral__extra_I3_J,axiom,
% 0.32/0.50      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 0.32/0.50  
% 0.32/0.50  % le_numeral_extra(3)
% 0.32/0.50  thf(fact_242_le__numeral__extra_I3_J,axiom,
% 0.32/0.50      ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ zero_z2226904508553997617atural ).
% 0.32/0.50  
% 0.32/0.50  % le_numeral_extra(3)
% 0.32/0.50  thf(fact_243_le__numeral__extra_I3_J,axiom,
% 0.32/0.50      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 0.32/0.50  
% 0.32/0.50  % le_numeral_extra(3)
% 0.32/0.50  thf(fact_244_le__numeral__extra_I3_J,axiom,
% 0.32/0.50      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.32/0.50  
% 0.32/0.50  % le_numeral_extra(3)
% 0.32/0.50  thf(fact_245_le__numeral__extra_I3_J,axiom,
% 0.32/0.50      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.32/0.50  
% 0.32/0.50  % le_numeral_extra(3)
% 0.32/0.50  thf(fact_246_zero__le,axiom,
% 0.32/0.50      ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_le
% 0.32/0.50  thf(fact_247_time__refines,axiom,
% 0.32/0.50      ! [C: heap_Time_Heap_a,C2: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( refine_Imp_refines_a @ C @ C2 )
% 0.32/0.50       => ( ~ ( time_fails_a @ C2 @ H )
% 0.32/0.50         => ( ord_less_eq_nat @ ( time_time_a @ C @ H ) @ ( time_time_a @ C2 @ H ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % time_refines
% 0.32/0.50  thf(fact_248_time__refines,axiom,
% 0.32/0.50      ! [C: heap_T5738788834812785303t_unit,C2: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( refine451278484176762712t_unit @ C @ C2 )
% 0.32/0.50       => ( ~ ( time_f8834461667527620124t_unit @ C2 @ H )
% 0.32/0.50         => ( ord_less_eq_nat @ ( time_t4224138285095624986t_unit @ C @ H ) @ ( time_t4224138285095624986t_unit @ C2 @ H ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % time_refines
% 0.32/0.50  thf(fact_249_of__nat__le__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_0_iff
% 0.32/0.50  thf(fact_250_of__nat__le__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ M ) @ zero_z2226904508553997617atural )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_0_iff
% 0.32/0.50  thf(fact_251_of__nat__le__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_0_iff
% 0.32/0.50  thf(fact_252_of__nat__le__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_0_iff
% 0.32/0.50  thf(fact_253_of__nat__le__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_0_iff
% 0.32/0.50  thf(fact_254_zero__natural_Orsp,axiom,
% 0.32/0.50      zero_zero_nat = zero_zero_nat ).
% 0.32/0.50  
% 0.32/0.50  % zero_natural.rsp
% 0.32/0.50  thf(fact_255_zero__reorient,axiom,
% 0.32/0.50      ! [X2: nat] :
% 0.32/0.50        ( ( zero_zero_nat = X2 )
% 0.32/0.50        = ( X2 = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_reorient
% 0.32/0.50  thf(fact_256_zero__reorient,axiom,
% 0.32/0.50      ! [X2: int] :
% 0.32/0.50        ( ( zero_zero_int = X2 )
% 0.32/0.50        = ( X2 = zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_reorient
% 0.32/0.50  thf(fact_257_zero__reorient,axiom,
% 0.32/0.50      ! [X2: code_integer] :
% 0.32/0.50        ( ( zero_z3403309356797280102nteger = X2 )
% 0.32/0.50        = ( X2 = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_reorient
% 0.32/0.50  thf(fact_258_zero__reorient,axiom,
% 0.32/0.50      ! [X2: rat] :
% 0.32/0.50        ( ( zero_zero_rat = X2 )
% 0.32/0.50        = ( X2 = zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_reorient
% 0.32/0.50  thf(fact_259_zero__reorient,axiom,
% 0.32/0.50      ! [X2: code_natural] :
% 0.32/0.50        ( ( zero_z2226904508553997617atural = X2 )
% 0.32/0.50        = ( X2 = zero_z2226904508553997617atural ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_reorient
% 0.32/0.50  thf(fact_260_of__nat__eq__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ( semiri1314217659103216013at_int @ M )
% 0.32/0.50          = ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.50        = ( M = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_iff
% 0.32/0.50  thf(fact_261_of__nat__eq__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.32/0.50          = ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.50        = ( M = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_iff
% 0.32/0.50  thf(fact_262_of__nat__eq__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ( semiri4939895301339042750nteger @ M )
% 0.32/0.50          = ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.50        = ( M = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_iff
% 0.32/0.50  thf(fact_263_of__nat__eq__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ( semiri681578069525770553at_rat @ M )
% 0.32/0.50          = ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.50        = ( M = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_iff
% 0.32/0.50  thf(fact_264_of__nat__eq__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ( semiri3763490453095760265atural @ M )
% 0.32/0.50          = ( semiri3763490453095760265atural @ N ) )
% 0.32/0.50        = ( M = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_iff
% 0.32/0.50  thf(fact_265_of__nat__eq__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ( semiri1314217659103216013at_int @ M )
% 0.32/0.50          = zero_zero_int )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_0_iff
% 0.32/0.50  thf(fact_266_of__nat__eq__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.32/0.50          = zero_zero_nat )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_0_iff
% 0.32/0.50  thf(fact_267_of__nat__eq__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ( semiri4939895301339042750nteger @ M )
% 0.32/0.50          = zero_z3403309356797280102nteger )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_0_iff
% 0.32/0.50  thf(fact_268_of__nat__eq__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ( semiri681578069525770553at_rat @ M )
% 0.32/0.50          = zero_zero_rat )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_0_iff
% 0.32/0.50  thf(fact_269_of__nat__eq__0__iff,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( ( semiri3763490453095760265atural @ M )
% 0.32/0.50          = zero_z2226904508553997617atural )
% 0.32/0.50        = ( M = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_eq_0_iff
% 0.32/0.50  thf(fact_270_of__nat__0__eq__iff,axiom,
% 0.32/0.50      ! [N: nat] :
% 0.32/0.50        ( ( zero_zero_int
% 0.32/0.50          = ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.50        = ( zero_zero_nat = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_eq_iff
% 0.32/0.50  thf(fact_271_of__nat__0__eq__iff,axiom,
% 0.32/0.50      ! [N: nat] :
% 0.32/0.50        ( ( zero_zero_nat
% 0.32/0.50          = ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.50        = ( zero_zero_nat = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_eq_iff
% 0.32/0.50  thf(fact_272_of__nat__0__eq__iff,axiom,
% 0.32/0.50      ! [N: nat] :
% 0.32/0.50        ( ( zero_z3403309356797280102nteger
% 0.32/0.50          = ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.50        = ( zero_zero_nat = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_eq_iff
% 0.32/0.50  thf(fact_273_of__nat__0__eq__iff,axiom,
% 0.32/0.50      ! [N: nat] :
% 0.32/0.50        ( ( zero_zero_rat
% 0.32/0.50          = ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.50        = ( zero_zero_nat = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_eq_iff
% 0.32/0.50  thf(fact_274_of__nat__0__eq__iff,axiom,
% 0.32/0.50      ! [N: nat] :
% 0.32/0.50        ( ( zero_z2226904508553997617atural
% 0.32/0.50          = ( semiri3763490453095760265atural @ N ) )
% 0.32/0.50        = ( zero_zero_nat = N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_eq_iff
% 0.32/0.50  thf(fact_275_of__nat__0,axiom,
% 0.32/0.50      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.32/0.50      = zero_zero_int ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0
% 0.32/0.50  thf(fact_276_of__nat__0,axiom,
% 0.32/0.50      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 0.32/0.50      = zero_zero_nat ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0
% 0.32/0.50  thf(fact_277_of__nat__0,axiom,
% 0.32/0.50      ( ( semiri4939895301339042750nteger @ zero_zero_nat )
% 0.32/0.50      = zero_z3403309356797280102nteger ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0
% 0.32/0.50  thf(fact_278_of__nat__0,axiom,
% 0.32/0.50      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 0.32/0.50      = zero_zero_rat ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0
% 0.32/0.50  thf(fact_279_of__nat__0,axiom,
% 0.32/0.50      ( ( semiri3763490453095760265atural @ zero_zero_nat )
% 0.32/0.50      = zero_z2226904508553997617atural ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0
% 0.32/0.50  thf(fact_280_of__nat__le__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_iff
% 0.32/0.50  thf(fact_281_of__nat__le__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) )
% 0.32/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_iff
% 0.32/0.50  thf(fact_282_of__nat__le__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_iff
% 0.32/0.50  thf(fact_283_of__nat__le__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_iff
% 0.32/0.50  thf(fact_284_of__nat__le__iff,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_le_iff
% 0.32/0.50  thf(fact_285_int__ops_I1_J,axiom,
% 0.32/0.50      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.32/0.50      = zero_zero_int ) ).
% 0.32/0.50  
% 0.32/0.50  % int_ops(1)
% 0.32/0.50  thf(fact_286_nat__int__comparison_I3_J,axiom,
% 0.32/0.50      ( ord_less_eq_nat
% 0.32/0.50      = ( ^ [A2: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nat_int_comparison(3)
% 0.32/0.50  thf(fact_287_nat__leq__as__int,axiom,
% 0.32/0.50      ( ord_less_eq_nat
% 0.32/0.50      = ( ^ [A2: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nat_leq_as_int
% 0.32/0.50  thf(fact_288_of__nat__0__le__iff,axiom,
% 0.32/0.50      ! [N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_le_iff
% 0.32/0.50  thf(fact_289_of__nat__0__le__iff,axiom,
% 0.32/0.50      ! [N: nat] : ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( semiri3763490453095760265atural @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_le_iff
% 0.32/0.50  thf(fact_290_of__nat__0__le__iff,axiom,
% 0.32/0.50      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_le_iff
% 0.32/0.50  thf(fact_291_of__nat__0__le__iff,axiom,
% 0.32/0.50      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_le_iff
% 0.32/0.50  thf(fact_292_of__nat__0__le__iff,axiom,
% 0.32/0.50      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_0_le_iff
% 0.32/0.50  thf(fact_293_of__nat__mono,axiom,
% 0.32/0.50      ! [I: nat,J: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.50       => ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ I ) @ ( semiri4939895301339042750nteger @ J ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_mono
% 0.32/0.50  thf(fact_294_of__nat__mono,axiom,
% 0.32/0.50      ! [I: nat,J: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.50       => ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ I ) @ ( semiri3763490453095760265atural @ J ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_mono
% 0.32/0.50  thf(fact_295_of__nat__mono,axiom,
% 0.32/0.50      ! [I: nat,J: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.50       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_mono
% 0.32/0.50  thf(fact_296_of__nat__mono,axiom,
% 0.32/0.50      ! [I: nat,J: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.50       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_mono
% 0.32/0.50  thf(fact_297_of__nat__mono,axiom,
% 0.32/0.50      ! [I: nat,J: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.50       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_mono
% 0.32/0.50  thf(fact_298_fails__refines,axiom,
% 0.32/0.50      ! [C: heap_T5738788834812785303t_unit,C2: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( refine451278484176762712t_unit @ C @ C2 )
% 0.32/0.50       => ( ( time_f8834461667527620124t_unit @ C @ H )
% 0.32/0.50         => ( time_f8834461667527620124t_unit @ C2 @ H ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % fails_refines
% 0.32/0.50  thf(fact_299_fails__assert_H,axiom,
% 0.32/0.50      ! [P: $o,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_f8834461667527620124t_unit @ ( refine_Imp_assert @ P ) @ H )
% 0.32/0.50        = ( ~ P ) ) ).
% 0.32/0.50  
% 0.32/0.50  % fails_assert'
% 0.32/0.50  thf(fact_300_real__arch__simple,axiom,
% 0.32/0.50      ! [X2: rat] :
% 0.32/0.50      ? [N2: nat] : ( ord_less_eq_rat @ X2 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.32/0.50  
% 0.32/0.50  % real_arch_simple
% 0.32/0.50  thf(fact_301_time__wait,axiom,
% 0.32/0.50      ! [N: nat,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_t4224138285095624986t_unit @ ( heap_Time_wait @ N ) @ H )
% 0.32/0.50        = N ) ).
% 0.32/0.50  
% 0.32/0.50  % time_wait
% 0.32/0.50  thf(fact_302_zle__int,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zle_int
% 0.32/0.50  thf(fact_303_dbl__simps_I2_J,axiom,
% 0.32/0.50      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 0.32/0.50      = zero_zero_int ) ).
% 0.32/0.50  
% 0.32/0.50  % dbl_simps(2)
% 0.32/0.50  thf(fact_304_dbl__simps_I2_J,axiom,
% 0.32/0.50      ( ( neg_nu8804712462038260780nteger @ zero_z3403309356797280102nteger )
% 0.32/0.50      = zero_z3403309356797280102nteger ) ).
% 0.32/0.50  
% 0.32/0.50  % dbl_simps(2)
% 0.32/0.50  thf(fact_305_dbl__simps_I2_J,axiom,
% 0.32/0.50      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 0.32/0.50      = zero_zero_rat ) ).
% 0.32/0.50  
% 0.32/0.50  % dbl_simps(2)
% 0.32/0.50  thf(fact_306_fails__bind,axiom,
% 0.32/0.50      ! [M: heap_Time_Heap_a,F: a > heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_fails_a @ ( heap_Time_bind_a_a @ M @ F ) @ H )
% 0.32/0.50        = ( ~ ( time_fails_a @ M @ H )
% 0.32/0.50         => ( time_fails_a @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % fails_bind
% 0.32/0.50  thf(fact_307_fails__bind,axiom,
% 0.32/0.50      ! [M: heap_T5738788834812785303t_unit,F: product_unit > heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_fails_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ H )
% 0.32/0.50        = ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 0.32/0.50         => ( time_fails_a @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % fails_bind
% 0.32/0.50  thf(fact_308_fails__bind,axiom,
% 0.32/0.50      ! [M: heap_T5738788834812785303t_unit,F: product_unit > heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 0.32/0.50        ( ( time_f8834461667527620124t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ H )
% 0.32/0.50        = ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 0.32/0.50         => ( time_f8834461667527620124t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % fails_bind
% 0.32/0.50  thf(fact_309_TBOUND__bind,axiom,
% 0.32/0.50      ! [M: heap_Time_Heap_a,T_1: nat,F: a > heap_Time_Heap_a,T_2: nat] :
% 0.32/0.50        ( ( time_TBOUND_a @ M @ T_1 )
% 0.32/0.50       => ( ! [X3: a,H2: heap_e7401611519738050253t_unit] :
% 0.32/0.50              ( ( X3
% 0.32/0.50                = ( time_the_res_a @ M @ H2 ) )
% 0.32/0.50             => ( ~ ( time_fails_a @ M @ H2 )
% 0.32/0.50               => ( time_TBOUND_a @ ( F @ X3 ) @ T_2 ) ) )
% 0.32/0.50         => ( time_TBOUND_a @ ( heap_Time_bind_a_a @ M @ F ) @ ( plus_plus_nat @ T_1 @ T_2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_bind
% 0.32/0.50  thf(fact_310_TBOUND__bind,axiom,
% 0.32/0.50      ! [M: heap_Time_Heap_a,T_1: nat,F: a > heap_T5738788834812785303t_unit,T_2: nat] :
% 0.32/0.50        ( ( time_TBOUND_a @ M @ T_1 )
% 0.32/0.50       => ( ! [X3: a,H2: heap_e7401611519738050253t_unit] :
% 0.32/0.50              ( ( X3
% 0.32/0.50                = ( time_the_res_a @ M @ H2 ) )
% 0.32/0.50             => ( ~ ( time_fails_a @ M @ H2 )
% 0.32/0.50               => ( time_T7469515765551943773t_unit @ ( F @ X3 ) @ T_2 ) ) )
% 0.32/0.50         => ( time_T7469515765551943773t_unit @ ( heap_T8685611227969916822t_unit @ M @ F ) @ ( plus_plus_nat @ T_1 @ T_2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_bind
% 0.32/0.50  thf(fact_311_TBOUND__bind,axiom,
% 0.32/0.50      ! [M: heap_T5738788834812785303t_unit,T_1: nat,F: product_unit > heap_Time_Heap_a,T_2: nat] :
% 0.32/0.50        ( ( time_T7469515765551943773t_unit @ M @ T_1 )
% 0.32/0.50       => ( ! [X3: product_unit,H2: heap_e7401611519738050253t_unit] :
% 0.32/0.50              ( ( X3
% 0.32/0.50                = ( time_t2745601220510131320t_unit @ M @ H2 ) )
% 0.32/0.50             => ( ~ ( time_f8834461667527620124t_unit @ M @ H2 )
% 0.32/0.50               => ( time_TBOUND_a @ ( F @ X3 ) @ T_2 ) ) )
% 0.32/0.50         => ( time_TBOUND_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ ( plus_plus_nat @ T_1 @ T_2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_bind
% 0.32/0.50  thf(fact_312_TBOUND__bind,axiom,
% 0.32/0.50      ! [M: heap_T5738788834812785303t_unit,T_1: nat,F: product_unit > heap_T5738788834812785303t_unit,T_2: nat] :
% 0.32/0.50        ( ( time_T7469515765551943773t_unit @ M @ T_1 )
% 0.32/0.50       => ( ! [X3: product_unit,H2: heap_e7401611519738050253t_unit] :
% 0.32/0.50              ( ( X3
% 0.32/0.50                = ( time_t2745601220510131320t_unit @ M @ H2 ) )
% 0.32/0.50             => ( ~ ( time_f8834461667527620124t_unit @ M @ H2 )
% 0.32/0.50               => ( time_T7469515765551943773t_unit @ ( F @ X3 ) @ T_2 ) ) )
% 0.32/0.50         => ( time_T7469515765551943773t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ ( plus_plus_nat @ T_1 @ T_2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % TBOUND_bind
% 0.32/0.50  thf(fact_313_add__left__cancel,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.50        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ A @ C ) )
% 0.32/0.50        = ( B = C ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_left_cancel
% 0.32/0.50  thf(fact_314_add__left__cancel,axiom,
% 0.32/0.50      ! [A: rat,B: rat,C: rat] :
% 0.32/0.50        ( ( ( plus_plus_rat @ A @ B )
% 0.32/0.50          = ( plus_plus_rat @ A @ C ) )
% 0.32/0.50        = ( B = C ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_left_cancel
% 0.32/0.50  thf(fact_315_add__left__cancel,axiom,
% 0.32/0.50      ! [A: nat,B: nat,C: nat] :
% 0.32/0.50        ( ( ( plus_plus_nat @ A @ B )
% 0.32/0.50          = ( plus_plus_nat @ A @ C ) )
% 0.32/0.50        = ( B = C ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_left_cancel
% 0.32/0.50  thf(fact_316_add__left__cancel,axiom,
% 0.32/0.50      ! [A: int,B: int,C: int] :
% 0.32/0.50        ( ( ( plus_plus_int @ A @ B )
% 0.32/0.50          = ( plus_plus_int @ A @ C ) )
% 0.32/0.50        = ( B = C ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_left_cancel
% 0.32/0.50  thf(fact_317_add__right__cancel,axiom,
% 0.32/0.50      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.50        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ C @ A ) )
% 0.32/0.50        = ( B = C ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_right_cancel
% 0.32/0.50  thf(fact_318_add__right__cancel,axiom,
% 0.32/0.50      ! [B: rat,A: rat,C: rat] :
% 0.32/0.50        ( ( ( plus_plus_rat @ B @ A )
% 0.32/0.50          = ( plus_plus_rat @ C @ A ) )
% 0.32/0.50        = ( B = C ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_right_cancel
% 0.32/0.50  thf(fact_319_add__right__cancel,axiom,
% 0.32/0.50      ! [B: nat,A: nat,C: nat] :
% 0.32/0.50        ( ( ( plus_plus_nat @ B @ A )
% 0.32/0.50          = ( plus_plus_nat @ C @ A ) )
% 0.32/0.50        = ( B = C ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_right_cancel
% 0.32/0.50  thf(fact_320_add__right__cancel,axiom,
% 0.32/0.50      ! [B: int,A: int,C: int] :
% 0.32/0.50        ( ( ( plus_plus_int @ B @ A )
% 0.32/0.50          = ( plus_plus_int @ C @ A ) )
% 0.32/0.50        = ( B = C ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_right_cancel
% 0.32/0.50  thf(fact_321_add__le__cancel__left,axiom,
% 0.32/0.50      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 0.32/0.50        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_cancel_left
% 0.32/0.50  thf(fact_322_add__le__cancel__left,axiom,
% 0.32/0.50      ! [C: rat,A: rat,B: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.32/0.50        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_cancel_left
% 0.32/0.50  thf(fact_323_add__le__cancel__left,axiom,
% 0.32/0.50      ! [C: nat,A: nat,B: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.32/0.50        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_cancel_left
% 0.32/0.50  thf(fact_324_add__le__cancel__left,axiom,
% 0.32/0.50      ! [C: int,A: int,B: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.32/0.50        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_cancel_left
% 0.32/0.50  thf(fact_325_add__le__cancel__right,axiom,
% 0.32/0.50      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.50        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_cancel_right
% 0.32/0.50  thf(fact_326_add__le__cancel__right,axiom,
% 0.32/0.50      ! [A: rat,C: rat,B: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.50        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_cancel_right
% 0.32/0.50  thf(fact_327_add__le__cancel__right,axiom,
% 0.32/0.50      ! [A: nat,C: nat,B: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.50        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_cancel_right
% 0.32/0.50  thf(fact_328_add__le__cancel__right,axiom,
% 0.32/0.50      ! [A: int,C: int,B: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.32/0.50        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_cancel_right
% 0.32/0.50  thf(fact_329_double__eq__0__iff,axiom,
% 0.32/0.50      ! [A: int] :
% 0.32/0.50        ( ( ( plus_plus_int @ A @ A )
% 0.32/0.50          = zero_zero_int )
% 0.32/0.50        = ( A = zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % double_eq_0_iff
% 0.32/0.50  thf(fact_330_double__eq__0__iff,axiom,
% 0.32/0.50      ! [A: code_integer] :
% 0.32/0.50        ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 0.32/0.50          = zero_z3403309356797280102nteger )
% 0.32/0.50        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % double_eq_0_iff
% 0.32/0.50  thf(fact_331_double__eq__0__iff,axiom,
% 0.32/0.50      ! [A: rat] :
% 0.32/0.50        ( ( ( plus_plus_rat @ A @ A )
% 0.32/0.50          = zero_zero_rat )
% 0.32/0.50        = ( A = zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % double_eq_0_iff
% 0.32/0.50  thf(fact_332_add__0,axiom,
% 0.32/0.50      ! [A: nat] :
% 0.32/0.50        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add_0
% 0.32/0.50  thf(fact_333_add__0,axiom,
% 0.32/0.50      ! [A: int] :
% 0.32/0.50        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add_0
% 0.32/0.50  thf(fact_334_add__0,axiom,
% 0.32/0.50      ! [A: code_integer] :
% 0.32/0.50        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add_0
% 0.32/0.50  thf(fact_335_add__0,axiom,
% 0.32/0.50      ! [A: rat] :
% 0.32/0.50        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add_0
% 0.32/0.50  thf(fact_336_add__0,axiom,
% 0.32/0.50      ! [A: code_natural] :
% 0.32/0.50        ( ( plus_p4538020629002901425atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add_0
% 0.32/0.50  thf(fact_337_zero__eq__add__iff__both__eq__0,axiom,
% 0.32/0.50      ! [X2: nat,Y: nat] :
% 0.32/0.50        ( ( zero_zero_nat
% 0.32/0.50          = ( plus_plus_nat @ X2 @ Y ) )
% 0.32/0.50        = ( ( X2 = zero_zero_nat )
% 0.32/0.50          & ( Y = zero_zero_nat ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_eq_add_iff_both_eq_0
% 0.32/0.50  thf(fact_338_add__eq__0__iff__both__eq__0,axiom,
% 0.32/0.50      ! [X2: nat,Y: nat] :
% 0.32/0.50        ( ( ( plus_plus_nat @ X2 @ Y )
% 0.32/0.50          = zero_zero_nat )
% 0.32/0.50        = ( ( X2 = zero_zero_nat )
% 0.32/0.50          & ( Y = zero_zero_nat ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_eq_0_iff_both_eq_0
% 0.32/0.50  thf(fact_339_add__cancel__right__right,axiom,
% 0.32/0.50      ! [A: nat,B: nat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_plus_nat @ A @ B ) )
% 0.32/0.50        = ( B = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_right
% 0.32/0.50  thf(fact_340_add__cancel__right__right,axiom,
% 0.32/0.50      ! [A: int,B: int] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_plus_int @ A @ B ) )
% 0.32/0.50        = ( B = zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_right
% 0.32/0.50  thf(fact_341_add__cancel__right__right,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.50        = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_right
% 0.32/0.50  thf(fact_342_add__cancel__right__right,axiom,
% 0.32/0.50      ! [A: rat,B: rat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_plus_rat @ A @ B ) )
% 0.32/0.50        = ( B = zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_right
% 0.32/0.50  thf(fact_343_add__cancel__right__right,axiom,
% 0.32/0.50      ! [A: code_natural,B: code_natural] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_p4538020629002901425atural @ A @ B ) )
% 0.32/0.50        = ( B = zero_z2226904508553997617atural ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_right
% 0.32/0.50  thf(fact_344_add__cancel__right__left,axiom,
% 0.32/0.50      ! [A: nat,B: nat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_plus_nat @ B @ A ) )
% 0.32/0.50        = ( B = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_left
% 0.32/0.50  thf(fact_345_add__cancel__right__left,axiom,
% 0.32/0.50      ! [A: int,B: int] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_plus_int @ B @ A ) )
% 0.32/0.50        = ( B = zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_left
% 0.32/0.50  thf(fact_346_add__cancel__right__left,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.32/0.50        = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_left
% 0.32/0.50  thf(fact_347_add__cancel__right__left,axiom,
% 0.32/0.50      ! [A: rat,B: rat] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_plus_rat @ B @ A ) )
% 0.32/0.50        = ( B = zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_left
% 0.32/0.50  thf(fact_348_add__cancel__right__left,axiom,
% 0.32/0.50      ! [A: code_natural,B: code_natural] :
% 0.32/0.50        ( ( A
% 0.32/0.50          = ( plus_p4538020629002901425atural @ B @ A ) )
% 0.32/0.50        = ( B = zero_z2226904508553997617atural ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_right_left
% 0.32/0.50  thf(fact_349_add__cancel__left__right,axiom,
% 0.32/0.50      ! [A: nat,B: nat] :
% 0.32/0.50        ( ( ( plus_plus_nat @ A @ B )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_right
% 0.32/0.50  thf(fact_350_add__cancel__left__right,axiom,
% 0.32/0.50      ! [A: int,B: int] :
% 0.32/0.50        ( ( ( plus_plus_int @ A @ B )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_right
% 0.32/0.50  thf(fact_351_add__cancel__left__right,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer] :
% 0.32/0.50        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_right
% 0.32/0.50  thf(fact_352_add__cancel__left__right,axiom,
% 0.32/0.50      ! [A: rat,B: rat] :
% 0.32/0.50        ( ( ( plus_plus_rat @ A @ B )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_right
% 0.32/0.50  thf(fact_353_add__cancel__left__right,axiom,
% 0.32/0.50      ! [A: code_natural,B: code_natural] :
% 0.32/0.50        ( ( ( plus_p4538020629002901425atural @ A @ B )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_z2226904508553997617atural ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_right
% 0.32/0.50  thf(fact_354_add__cancel__left__left,axiom,
% 0.32/0.50      ! [B: nat,A: nat] :
% 0.32/0.50        ( ( ( plus_plus_nat @ B @ A )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_left
% 0.32/0.50  thf(fact_355_add__cancel__left__left,axiom,
% 0.32/0.50      ! [B: int,A: int] :
% 0.32/0.50        ( ( ( plus_plus_int @ B @ A )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_left
% 0.32/0.50  thf(fact_356_add__cancel__left__left,axiom,
% 0.32/0.50      ! [B: code_integer,A: code_integer] :
% 0.32/0.50        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_left
% 0.32/0.50  thf(fact_357_add__cancel__left__left,axiom,
% 0.32/0.50      ! [B: rat,A: rat] :
% 0.32/0.50        ( ( ( plus_plus_rat @ B @ A )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_left
% 0.32/0.50  thf(fact_358_add__cancel__left__left,axiom,
% 0.32/0.50      ! [B: code_natural,A: code_natural] :
% 0.32/0.50        ( ( ( plus_p4538020629002901425atural @ B @ A )
% 0.32/0.50          = A )
% 0.32/0.50        = ( B = zero_z2226904508553997617atural ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_cancel_left_left
% 0.32/0.50  thf(fact_359_double__zero__sym,axiom,
% 0.32/0.50      ! [A: int] :
% 0.32/0.50        ( ( zero_zero_int
% 0.32/0.50          = ( plus_plus_int @ A @ A ) )
% 0.32/0.50        = ( A = zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % double_zero_sym
% 0.32/0.50  thf(fact_360_double__zero__sym,axiom,
% 0.32/0.50      ! [A: code_integer] :
% 0.32/0.50        ( ( zero_z3403309356797280102nteger
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ A @ A ) )
% 0.32/0.50        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % double_zero_sym
% 0.32/0.50  thf(fact_361_double__zero__sym,axiom,
% 0.32/0.50      ! [A: rat] :
% 0.32/0.50        ( ( zero_zero_rat
% 0.32/0.50          = ( plus_plus_rat @ A @ A ) )
% 0.32/0.50        = ( A = zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % double_zero_sym
% 0.32/0.50  thf(fact_362_add_Oright__neutral,axiom,
% 0.32/0.50      ! [A: nat] :
% 0.32/0.50        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add.right_neutral
% 0.32/0.50  thf(fact_363_add_Oright__neutral,axiom,
% 0.32/0.50      ! [A: int] :
% 0.32/0.50        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add.right_neutral
% 0.32/0.50  thf(fact_364_add_Oright__neutral,axiom,
% 0.32/0.50      ! [A: code_integer] :
% 0.32/0.50        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add.right_neutral
% 0.32/0.50  thf(fact_365_add_Oright__neutral,axiom,
% 0.32/0.50      ! [A: rat] :
% 0.32/0.50        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add.right_neutral
% 0.32/0.50  thf(fact_366_add_Oright__neutral,axiom,
% 0.32/0.50      ! [A: code_natural] :
% 0.32/0.50        ( ( plus_p4538020629002901425atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.50        = A ) ).
% 0.32/0.50  
% 0.32/0.50  % add.right_neutral
% 0.32/0.50  thf(fact_367_add__is__0,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( ( plus_plus_nat @ M @ N )
% 0.32/0.50          = zero_zero_nat )
% 0.32/0.50        = ( ( M = zero_zero_nat )
% 0.32/0.50          & ( N = zero_zero_nat ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_is_0
% 0.32/0.50  thf(fact_368_Nat_Oadd__0__right,axiom,
% 0.32/0.50      ! [M: nat] :
% 0.32/0.50        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.32/0.50        = M ) ).
% 0.32/0.50  
% 0.32/0.50  % Nat.add_0_right
% 0.32/0.50  thf(fact_369_nat__add__left__cancel__le,axiom,
% 0.32/0.50      ! [K: nat,M: nat,N: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.32/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nat_add_left_cancel_le
% 0.32/0.50  thf(fact_370_add__le__same__cancel1,axiom,
% 0.32/0.50      ! [B: code_integer,A: code_integer] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.32/0.50        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel1
% 0.32/0.50  thf(fact_371_add__le__same__cancel1,axiom,
% 0.32/0.50      ! [B: code_natural,A: code_natural] :
% 0.32/0.50        ( ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 0.32/0.50        = ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel1
% 0.32/0.50  thf(fact_372_add__le__same__cancel1,axiom,
% 0.32/0.50      ! [B: rat,A: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.32/0.50        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel1
% 0.32/0.50  thf(fact_373_add__le__same__cancel1,axiom,
% 0.32/0.50      ! [B: nat,A: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.32/0.50        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel1
% 0.32/0.50  thf(fact_374_add__le__same__cancel1,axiom,
% 0.32/0.50      ! [B: int,A: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.32/0.50        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel1
% 0.32/0.50  thf(fact_375_add__le__same__cancel2,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.32/0.50        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel2
% 0.32/0.50  thf(fact_376_add__le__same__cancel2,axiom,
% 0.32/0.50      ! [A: code_natural,B: code_natural] :
% 0.32/0.50        ( ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 0.32/0.50        = ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel2
% 0.32/0.50  thf(fact_377_add__le__same__cancel2,axiom,
% 0.32/0.50      ! [A: rat,B: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.32/0.50        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel2
% 0.32/0.50  thf(fact_378_add__le__same__cancel2,axiom,
% 0.32/0.50      ! [A: nat,B: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.32/0.50        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel2
% 0.32/0.50  thf(fact_379_add__le__same__cancel2,axiom,
% 0.32/0.50      ! [A: int,B: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.32/0.50        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_le_same_cancel2
% 0.32/0.50  thf(fact_380_le__add__same__cancel1,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.50        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel1
% 0.32/0.50  thf(fact_381_le__add__same__cancel1,axiom,
% 0.32/0.50      ! [A: code_natural,B: code_natural] :
% 0.32/0.50        ( ( ord_le1926595141338095240atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 0.32/0.50        = ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel1
% 0.32/0.50  thf(fact_382_le__add__same__cancel1,axiom,
% 0.32/0.50      ! [A: rat,B: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.50        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel1
% 0.32/0.50  thf(fact_383_le__add__same__cancel1,axiom,
% 0.32/0.50      ! [A: nat,B: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.32/0.50        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel1
% 0.32/0.50  thf(fact_384_le__add__same__cancel1,axiom,
% 0.32/0.50      ! [A: int,B: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.32/0.50        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel1
% 0.32/0.50  thf(fact_385_le__add__same__cancel2,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.32/0.50        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel2
% 0.32/0.50  thf(fact_386_le__add__same__cancel2,axiom,
% 0.32/0.50      ! [A: code_natural,B: code_natural] :
% 0.32/0.50        ( ( ord_le1926595141338095240atural @ A @ ( plus_p4538020629002901425atural @ B @ A ) )
% 0.32/0.50        = ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel2
% 0.32/0.50  thf(fact_387_le__add__same__cancel2,axiom,
% 0.32/0.50      ! [A: rat,B: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.32/0.50        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel2
% 0.32/0.50  thf(fact_388_le__add__same__cancel2,axiom,
% 0.32/0.50      ! [A: nat,B: nat] :
% 0.32/0.50        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.32/0.50        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel2
% 0.32/0.50  thf(fact_389_le__add__same__cancel2,axiom,
% 0.32/0.50      ! [A: int,B: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.32/0.50        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.32/0.50  
% 0.32/0.50  % le_add_same_cancel2
% 0.32/0.50  thf(fact_390_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.32/0.50      ! [A: code_integer] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 0.32/0.50        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.50  
% 0.32/0.50  % double_add_le_zero_iff_single_add_le_zero
% 0.32/0.50  thf(fact_391_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.32/0.50      ! [A: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.32/0.50        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.50  
% 0.32/0.50  % double_add_le_zero_iff_single_add_le_zero
% 0.32/0.50  thf(fact_392_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.32/0.50      ! [A: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.32/0.50        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.32/0.50  
% 0.32/0.50  % double_add_le_zero_iff_single_add_le_zero
% 0.32/0.50  thf(fact_393_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.32/0.50      ! [A: code_integer] :
% 0.32/0.50        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 0.32/0.50        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_le_double_add_iff_zero_le_single_add
% 0.32/0.50  thf(fact_394_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.32/0.50      ! [A: rat] :
% 0.32/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.32/0.50        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_le_double_add_iff_zero_le_single_add
% 0.32/0.50  thf(fact_395_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.32/0.50      ! [A: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.32/0.50        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_le_double_add_iff_zero_le_single_add
% 0.32/0.50  thf(fact_396_of__nat__add,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.50        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_add
% 0.32/0.50  thf(fact_397_of__nat__add,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.50        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_add
% 0.32/0.50  thf(fact_398_of__nat__add,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.50        = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_add
% 0.32/0.50  thf(fact_399_of__nat__add,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.50        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_add
% 0.32/0.50  thf(fact_400_of__nat__add,axiom,
% 0.32/0.50      ! [M: nat,N: nat] :
% 0.32/0.50        ( ( semiri3763490453095760265atural @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.50        = ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % of_nat_add
% 0.32/0.50  thf(fact_401_less__eq__int__code_I1_J,axiom,
% 0.32/0.50      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.32/0.50  
% 0.32/0.50  % less_eq_int_code(1)
% 0.32/0.50  thf(fact_402_nonneg__int__cases,axiom,
% 0.32/0.50      ! [K: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.50       => ~ ! [N2: nat] :
% 0.32/0.50              ( K
% 0.32/0.50             != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nonneg_int_cases
% 0.32/0.50  thf(fact_403_zero__le__imp__eq__int,axiom,
% 0.32/0.50      ! [K: int] :
% 0.32/0.50        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.50       => ? [N2: nat] :
% 0.32/0.50            ( K
% 0.32/0.50            = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % zero_le_imp_eq_int
% 0.32/0.50  thf(fact_404_int__if,axiom,
% 0.32/0.50      ! [P: $o,A: nat,B: nat] :
% 0.32/0.50        ( ( P
% 0.32/0.50         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 0.32/0.50            = ( semiri1314217659103216013at_int @ A ) ) )
% 0.32/0.50        & ( ~ P
% 0.32/0.50         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 0.32/0.50            = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % int_if
% 0.32/0.50  thf(fact_405_zero__integer_Orsp,axiom,
% 0.32/0.50      zero_zero_int = zero_zero_int ).
% 0.32/0.50  
% 0.32/0.50  % zero_integer.rsp
% 0.32/0.50  thf(fact_406_nat__int__comparison_I1_J,axiom,
% 0.32/0.50      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.32/0.50      = ( ^ [A2: nat,B2: nat] :
% 0.32/0.50            ( ( semiri1314217659103216013at_int @ A2 )
% 0.32/0.50            = ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % nat_int_comparison(1)
% 0.32/0.50  thf(fact_407_is__num__normalize_I1_J,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.50        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.50        = ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % is_num_normalize(1)
% 0.32/0.50  thf(fact_408_is__num__normalize_I1_J,axiom,
% 0.32/0.50      ! [A: rat,B: rat,C: rat] :
% 0.32/0.50        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.32/0.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % is_num_normalize(1)
% 0.32/0.50  thf(fact_409_is__num__normalize_I1_J,axiom,
% 0.32/0.50      ! [A: int,B: int,C: int] :
% 0.32/0.50        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % is_num_normalize(1)
% 0.32/0.50  thf(fact_410_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.32/0.50      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.32/0.50        ( ( ( I = J )
% 0.32/0.50          & ( K = L ) )
% 0.32/0.50       => ( ( plus_p5714425477246183910nteger @ I @ K )
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_mono_thms_linordered_semiring(4)
% 0.32/0.50  thf(fact_411_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.32/0.50      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.32/0.50        ( ( ( I = J )
% 0.32/0.50          & ( K = L ) )
% 0.32/0.50       => ( ( plus_plus_rat @ I @ K )
% 0.32/0.50          = ( plus_plus_rat @ J @ L ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_mono_thms_linordered_semiring(4)
% 0.32/0.50  thf(fact_412_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.32/0.50      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.50        ( ( ( I = J )
% 0.32/0.50          & ( K = L ) )
% 0.32/0.50       => ( ( plus_plus_nat @ I @ K )
% 0.32/0.50          = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_mono_thms_linordered_semiring(4)
% 0.32/0.50  thf(fact_413_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.32/0.50      ! [I: int,J: int,K: int,L: int] :
% 0.32/0.50        ( ( ( I = J )
% 0.32/0.50          & ( K = L ) )
% 0.32/0.50       => ( ( plus_plus_int @ I @ K )
% 0.32/0.50          = ( plus_plus_int @ J @ L ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add_mono_thms_linordered_semiring(4)
% 0.32/0.50  thf(fact_414_group__cancel_Oadd1,axiom,
% 0.32/0.50      ! [A4: code_integer,K: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.50        ( ( A4
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.32/0.50       => ( ( plus_p5714425477246183910nteger @ A4 @ B )
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ K @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % group_cancel.add1
% 0.32/0.50  thf(fact_415_group__cancel_Oadd1,axiom,
% 0.32/0.50      ! [A4: rat,K: rat,A: rat,B: rat] :
% 0.32/0.50        ( ( A4
% 0.32/0.50          = ( plus_plus_rat @ K @ A ) )
% 0.32/0.50       => ( ( plus_plus_rat @ A4 @ B )
% 0.32/0.50          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % group_cancel.add1
% 0.32/0.50  thf(fact_416_group__cancel_Oadd1,axiom,
% 0.32/0.50      ! [A4: nat,K: nat,A: nat,B: nat] :
% 0.32/0.50        ( ( A4
% 0.32/0.50          = ( plus_plus_nat @ K @ A ) )
% 0.32/0.50       => ( ( plus_plus_nat @ A4 @ B )
% 0.32/0.50          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % group_cancel.add1
% 0.32/0.50  thf(fact_417_group__cancel_Oadd1,axiom,
% 0.32/0.50      ! [A4: int,K: int,A: int,B: int] :
% 0.32/0.50        ( ( A4
% 0.32/0.50          = ( plus_plus_int @ K @ A ) )
% 0.32/0.50       => ( ( plus_plus_int @ A4 @ B )
% 0.32/0.50          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % group_cancel.add1
% 0.32/0.50  thf(fact_418_group__cancel_Oadd2,axiom,
% 0.32/0.50      ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.50        ( ( B4
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 0.32/0.50       => ( ( plus_p5714425477246183910nteger @ A @ B4 )
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ K @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % group_cancel.add2
% 0.32/0.50  thf(fact_419_group__cancel_Oadd2,axiom,
% 0.32/0.50      ! [B4: rat,K: rat,B: rat,A: rat] :
% 0.32/0.50        ( ( B4
% 0.32/0.50          = ( plus_plus_rat @ K @ B ) )
% 0.32/0.50       => ( ( plus_plus_rat @ A @ B4 )
% 0.32/0.50          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % group_cancel.add2
% 0.32/0.50  thf(fact_420_group__cancel_Oadd2,axiom,
% 0.32/0.50      ! [B4: nat,K: nat,B: nat,A: nat] :
% 0.32/0.50        ( ( B4
% 0.32/0.50          = ( plus_plus_nat @ K @ B ) )
% 0.32/0.50       => ( ( plus_plus_nat @ A @ B4 )
% 0.32/0.50          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % group_cancel.add2
% 0.32/0.50  thf(fact_421_group__cancel_Oadd2,axiom,
% 0.32/0.50      ! [B4: int,K: int,B: int,A: int] :
% 0.32/0.50        ( ( B4
% 0.32/0.50          = ( plus_plus_int @ K @ B ) )
% 0.32/0.50       => ( ( plus_plus_int @ A @ B4 )
% 0.32/0.50          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % group_cancel.add2
% 0.32/0.50  thf(fact_422_dbl__def,axiom,
% 0.32/0.50      ( neg_nu8804712462038260780nteger
% 0.32/0.50      = ( ^ [X: code_integer] : ( plus_p5714425477246183910nteger @ X @ X ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dbl_def
% 0.32/0.50  thf(fact_423_dbl__def,axiom,
% 0.32/0.50      ( neg_numeral_dbl_rat
% 0.32/0.50      = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dbl_def
% 0.32/0.50  thf(fact_424_dbl__def,axiom,
% 0.32/0.50      ( neg_numeral_dbl_int
% 0.32/0.50      = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % dbl_def
% 0.32/0.50  thf(fact_425_add_Oassoc,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.50        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.50        = ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add.assoc
% 0.32/0.50  thf(fact_426_add_Oassoc,axiom,
% 0.32/0.50      ! [A: rat,B: rat,C: rat] :
% 0.32/0.50        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.32/0.50        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add.assoc
% 0.32/0.50  thf(fact_427_add_Oassoc,axiom,
% 0.32/0.50      ! [A: nat,B: nat,C: nat] :
% 0.32/0.50        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.32/0.50        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add.assoc
% 0.32/0.50  thf(fact_428_add_Oassoc,axiom,
% 0.32/0.50      ! [A: int,B: int,C: int] :
% 0.32/0.50        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.50        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add.assoc
% 0.32/0.50  thf(fact_429_add_Oleft__cancel,axiom,
% 0.32/0.50      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.50        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.50          = ( plus_p5714425477246183910nteger @ A @ C ) )
% 0.32/0.50        = ( B = C ) ) ).
% 0.32/0.50  
% 0.32/0.50  % add.left_cancel
% 0.32/0.50  thf(fact_430_add_Oleft__cancel,axiom,
% 0.32/0.50      ! [A: rat,B: rat,C: rat] :
% 0.32/0.50        ( ( ( plus_plus_rat @ A @ B )
% 0.32/0.50          = ( plus_plus_rat @ A @ C ) )
% 0.32/0.51        = ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add.left_cancel
% 0.32/0.51  thf(fact_431_add_Oleft__cancel,axiom,
% 0.32/0.51      ! [A: int,B: int,C: int] :
% 0.32/0.51        ( ( ( plus_plus_int @ A @ B )
% 0.32/0.51          = ( plus_plus_int @ A @ C ) )
% 0.32/0.51        = ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add.left_cancel
% 0.32/0.51  thf(fact_432_add_Oright__cancel,axiom,
% 0.32/0.51      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.51        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 0.32/0.51          = ( plus_p5714425477246183910nteger @ C @ A ) )
% 0.32/0.51        = ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add.right_cancel
% 0.32/0.51  thf(fact_433_add_Oright__cancel,axiom,
% 0.32/0.51      ! [B: rat,A: rat,C: rat] :
% 0.32/0.51        ( ( ( plus_plus_rat @ B @ A )
% 0.32/0.51          = ( plus_plus_rat @ C @ A ) )
% 0.32/0.51        = ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add.right_cancel
% 0.32/0.51  thf(fact_434_add_Oright__cancel,axiom,
% 0.32/0.51      ! [B: int,A: int,C: int] :
% 0.32/0.51        ( ( ( plus_plus_int @ B @ A )
% 0.32/0.51          = ( plus_plus_int @ C @ A ) )
% 0.32/0.51        = ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add.right_cancel
% 0.32/0.51  thf(fact_435_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.32/0.51      ( plus_p5714425477246183910nteger
% 0.32/0.51      = ( ^ [A2: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ B2 @ A2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ab_semigroup_add_class.add.commute
% 0.32/0.51  thf(fact_436_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.32/0.51      ( plus_plus_rat
% 0.32/0.51      = ( ^ [A2: rat,B2: rat] : ( plus_plus_rat @ B2 @ A2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ab_semigroup_add_class.add.commute
% 0.32/0.51  thf(fact_437_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.32/0.51      ( plus_plus_nat
% 0.32/0.51      = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ab_semigroup_add_class.add.commute
% 0.32/0.51  thf(fact_438_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.32/0.51      ( plus_plus_int
% 0.32/0.51      = ( ^ [A2: int,B2: int] : ( plus_plus_int @ B2 @ A2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ab_semigroup_add_class.add.commute
% 0.32/0.51  thf(fact_439_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.32/0.51      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.51        ( ( plus_p5714425477246183910nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) )
% 0.32/0.51        = ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ab_semigroup_add_class.add.left_commute
% 0.32/0.51  thf(fact_440_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.32/0.51      ! [B: rat,A: rat,C: rat] :
% 0.32/0.51        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 0.32/0.51        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ab_semigroup_add_class.add.left_commute
% 0.32/0.51  thf(fact_441_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.32/0.51      ! [B: nat,A: nat,C: nat] :
% 0.32/0.51        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.32/0.51        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ab_semigroup_add_class.add.left_commute
% 0.32/0.51  thf(fact_442_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.32/0.51      ! [B: int,A: int,C: int] :
% 0.32/0.51        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 0.32/0.51        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ab_semigroup_add_class.add.left_commute
% 0.32/0.51  thf(fact_443_add__left__imp__eq,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.51        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.51          = ( plus_p5714425477246183910nteger @ A @ C ) )
% 0.32/0.51       => ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_left_imp_eq
% 0.32/0.51  thf(fact_444_add__left__imp__eq,axiom,
% 0.32/0.51      ! [A: rat,B: rat,C: rat] :
% 0.32/0.51        ( ( ( plus_plus_rat @ A @ B )
% 0.32/0.51          = ( plus_plus_rat @ A @ C ) )
% 0.32/0.51       => ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_left_imp_eq
% 0.32/0.51  thf(fact_445_add__left__imp__eq,axiom,
% 0.32/0.51      ! [A: nat,B: nat,C: nat] :
% 0.32/0.51        ( ( ( plus_plus_nat @ A @ B )
% 0.32/0.51          = ( plus_plus_nat @ A @ C ) )
% 0.32/0.51       => ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_left_imp_eq
% 0.32/0.51  thf(fact_446_add__left__imp__eq,axiom,
% 0.32/0.51      ! [A: int,B: int,C: int] :
% 0.32/0.51        ( ( ( plus_plus_int @ A @ B )
% 0.32/0.51          = ( plus_plus_int @ A @ C ) )
% 0.32/0.51       => ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_left_imp_eq
% 0.32/0.51  thf(fact_447_add__right__imp__eq,axiom,
% 0.32/0.51      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.51        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 0.32/0.51          = ( plus_p5714425477246183910nteger @ C @ A ) )
% 0.32/0.51       => ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_right_imp_eq
% 0.32/0.51  thf(fact_448_add__right__imp__eq,axiom,
% 0.32/0.51      ! [B: rat,A: rat,C: rat] :
% 0.32/0.51        ( ( ( plus_plus_rat @ B @ A )
% 0.32/0.51          = ( plus_plus_rat @ C @ A ) )
% 0.32/0.51       => ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_right_imp_eq
% 0.32/0.51  thf(fact_449_add__right__imp__eq,axiom,
% 0.32/0.51      ! [B: nat,A: nat,C: nat] :
% 0.32/0.51        ( ( ( plus_plus_nat @ B @ A )
% 0.32/0.51          = ( plus_plus_nat @ C @ A ) )
% 0.32/0.51       => ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_right_imp_eq
% 0.32/0.51  thf(fact_450_add__right__imp__eq,axiom,
% 0.32/0.51      ! [B: int,A: int,C: int] :
% 0.32/0.51        ( ( ( plus_plus_int @ B @ A )
% 0.32/0.51          = ( plus_plus_int @ C @ A ) )
% 0.32/0.51       => ( B = C ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_right_imp_eq
% 0.32/0.51  thf(fact_451_int__int__eq,axiom,
% 0.32/0.51      ! [M: nat,N: nat] :
% 0.32/0.51        ( ( ( semiri1314217659103216013at_int @ M )
% 0.32/0.51          = ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.51        = ( M = N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % int_int_eq
% 0.32/0.51  thf(fact_452_verit__la__generic,axiom,
% 0.32/0.51      ! [A: int,X2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ A @ X2 )
% 0.32/0.51        | ( A = X2 )
% 0.32/0.51        | ( ord_less_eq_int @ X2 @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % verit_la_generic
% 0.32/0.51  thf(fact_453_fails__wait,axiom,
% 0.32/0.51      ! [X2: nat,H: heap_e7401611519738050253t_unit] :
% 0.32/0.51        ~ ( time_f8834461667527620124t_unit @ ( heap_Time_wait @ X2 ) @ H ) ).
% 0.32/0.51  
% 0.32/0.51  % fails_wait
% 0.32/0.51  thf(fact_454_size__neq__size__imp__neq,axiom,
% 0.32/0.51      ! [X2: list_nat,Y: list_nat] :
% 0.32/0.51        ( ( ( size_size_list_nat @ X2 )
% 0.32/0.51         != ( size_size_list_nat @ Y ) )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % size_neq_size_imp_neq
% 0.32/0.51  thf(fact_455_size__neq__size__imp__neq,axiom,
% 0.32/0.51      ! [X2: list_int,Y: list_int] :
% 0.32/0.51        ( ( ( size_size_list_int @ X2 )
% 0.32/0.51         != ( size_size_list_int @ Y ) )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % size_neq_size_imp_neq
% 0.32/0.51  thf(fact_456_size__neq__size__imp__neq,axiom,
% 0.32/0.51      ! [X2: num,Y: num] :
% 0.32/0.51        ( ( ( size_size_num @ X2 )
% 0.32/0.51         != ( size_size_num @ Y ) )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % size_neq_size_imp_neq
% 0.32/0.51  thf(fact_457_size__neq__size__imp__neq,axiom,
% 0.32/0.51      ! [X2: list_o,Y: list_o] :
% 0.32/0.51        ( ( ( size_size_list_o @ X2 )
% 0.32/0.51         != ( size_size_list_o @ Y ) )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % size_neq_size_imp_neq
% 0.32/0.51  thf(fact_458_size__neq__size__imp__neq,axiom,
% 0.32/0.51      ! [X2: char,Y: char] :
% 0.32/0.51        ( ( ( size_size_char @ X2 )
% 0.32/0.51         != ( size_size_char @ Y ) )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % size_neq_size_imp_neq
% 0.32/0.51  thf(fact_459_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.32/0.51      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.32/0.51        ( ( ( ord_le3102999989581377725nteger @ I @ J )
% 0.32/0.51          & ( K = L ) )
% 0.32/0.51       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(3)
% 0.32/0.51  thf(fact_460_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.32/0.51      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.32/0.51        ( ( ( ord_less_eq_rat @ I @ J )
% 0.32/0.51          & ( K = L ) )
% 0.32/0.51       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(3)
% 0.32/0.51  thf(fact_461_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.32/0.51      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.51        ( ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.51          & ( K = L ) )
% 0.32/0.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(3)
% 0.32/0.51  thf(fact_462_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.32/0.51      ! [I: int,J: int,K: int,L: int] :
% 0.32/0.51        ( ( ( ord_less_eq_int @ I @ J )
% 0.32/0.51          & ( K = L ) )
% 0.32/0.51       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(3)
% 0.32/0.51  thf(fact_463_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.32/0.51      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.32/0.51        ( ( ( I = J )
% 0.32/0.51          & ( ord_le3102999989581377725nteger @ K @ L ) )
% 0.32/0.51       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(2)
% 0.32/0.51  thf(fact_464_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.32/0.51      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.32/0.51        ( ( ( I = J )
% 0.32/0.51          & ( ord_less_eq_rat @ K @ L ) )
% 0.32/0.51       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(2)
% 0.32/0.51  thf(fact_465_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.32/0.51      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.51        ( ( ( I = J )
% 0.32/0.51          & ( ord_less_eq_nat @ K @ L ) )
% 0.32/0.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(2)
% 0.32/0.51  thf(fact_466_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.32/0.51      ! [I: int,J: int,K: int,L: int] :
% 0.32/0.51        ( ( ( I = J )
% 0.32/0.51          & ( ord_less_eq_int @ K @ L ) )
% 0.32/0.51       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(2)
% 0.32/0.51  thf(fact_467_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.32/0.51      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.32/0.51        ( ( ( ord_le3102999989581377725nteger @ I @ J )
% 0.32/0.51          & ( ord_le3102999989581377725nteger @ K @ L ) )
% 0.32/0.51       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(1)
% 0.32/0.51  thf(fact_468_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.32/0.51      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.32/0.51        ( ( ( ord_less_eq_rat @ I @ J )
% 0.32/0.51          & ( ord_less_eq_rat @ K @ L ) )
% 0.32/0.51       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(1)
% 0.32/0.51  thf(fact_469_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.32/0.51      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.51        ( ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.51          & ( ord_less_eq_nat @ K @ L ) )
% 0.32/0.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(1)
% 0.32/0.51  thf(fact_470_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.32/0.51      ! [I: int,J: int,K: int,L: int] :
% 0.32/0.51        ( ( ( ord_less_eq_int @ I @ J )
% 0.32/0.51          & ( ord_less_eq_int @ K @ L ) )
% 0.32/0.51       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono_thms_linordered_semiring(1)
% 0.32/0.51  thf(fact_471_add__mono,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.51       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 0.32/0.51         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono
% 0.32/0.51  thf(fact_472_add__mono,axiom,
% 0.32/0.51      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.51       => ( ( ord_less_eq_rat @ C @ D )
% 0.32/0.51         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono
% 0.32/0.51  thf(fact_473_add__mono,axiom,
% 0.32/0.51      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.51       => ( ( ord_less_eq_nat @ C @ D )
% 0.32/0.51         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono
% 0.32/0.51  thf(fact_474_add__mono,axiom,
% 0.32/0.51      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.51       => ( ( ord_less_eq_int @ C @ D )
% 0.32/0.51         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_mono
% 0.32/0.51  thf(fact_475_add__left__mono,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.51       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_left_mono
% 0.32/0.51  thf(fact_476_add__left__mono,axiom,
% 0.32/0.51      ! [A: rat,B: rat,C: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.51       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_left_mono
% 0.32/0.51  thf(fact_477_add__left__mono,axiom,
% 0.32/0.51      ! [A: nat,B: nat,C: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_left_mono
% 0.32/0.51  thf(fact_478_add__left__mono,axiom,
% 0.32/0.51      ! [A: int,B: int,C: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.51       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_left_mono
% 0.32/0.51  thf(fact_479_less__eqE,axiom,
% 0.32/0.51      ! [A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.51       => ~ ! [C3: nat] :
% 0.32/0.51              ( B
% 0.32/0.51             != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_eqE
% 0.32/0.51  thf(fact_480_add__right__mono,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.51       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_right_mono
% 0.32/0.51  thf(fact_481_add__right__mono,axiom,
% 0.32/0.51      ! [A: rat,B: rat,C: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.51       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_right_mono
% 0.32/0.51  thf(fact_482_add__right__mono,axiom,
% 0.32/0.51      ! [A: nat,B: nat,C: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_right_mono
% 0.32/0.51  thf(fact_483_add__right__mono,axiom,
% 0.32/0.51      ! [A: int,B: int,C: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.51       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_right_mono
% 0.32/0.51  thf(fact_484_le__iff__add,axiom,
% 0.32/0.51      ( ord_less_eq_nat
% 0.32/0.51      = ( ^ [A2: nat,B2: nat] :
% 0.32/0.51          ? [C4: nat] :
% 0.32/0.51            ( B2
% 0.32/0.51            = ( plus_plus_nat @ A2 @ C4 ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % le_iff_add
% 0.32/0.51  thf(fact_485_add__le__imp__le__left,axiom,
% 0.32/0.51      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 0.32/0.51       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_imp_le_left
% 0.32/0.51  thf(fact_486_add__le__imp__le__left,axiom,
% 0.32/0.51      ! [C: rat,A: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.32/0.51       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_imp_le_left
% 0.32/0.51  thf(fact_487_add__le__imp__le__left,axiom,
% 0.32/0.51      ! [C: nat,A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.32/0.51       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_imp_le_left
% 0.32/0.51  thf(fact_488_add__le__imp__le__left,axiom,
% 0.32/0.51      ! [C: int,A: int,B: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.32/0.51       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_imp_le_left
% 0.32/0.51  thf(fact_489_add__le__imp__le__right,axiom,
% 0.32/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.51       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_imp_le_right
% 0.32/0.51  thf(fact_490_add__le__imp__le__right,axiom,
% 0.32/0.51      ! [A: rat,C: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.51       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_imp_le_right
% 0.32/0.51  thf(fact_491_add__le__imp__le__right,axiom,
% 0.32/0.51      ! [A: nat,C: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.51       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_imp_le_right
% 0.32/0.51  thf(fact_492_add__le__imp__le__right,axiom,
% 0.32/0.51      ! [A: int,C: int,B: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.32/0.51       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_imp_le_right
% 0.32/0.51  thf(fact_493_verit__sum__simplify,axiom,
% 0.32/0.51      ! [A: nat] :
% 0.32/0.51        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % verit_sum_simplify
% 0.32/0.51  thf(fact_494_verit__sum__simplify,axiom,
% 0.32/0.51      ! [A: int] :
% 0.32/0.51        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % verit_sum_simplify
% 0.32/0.51  thf(fact_495_verit__sum__simplify,axiom,
% 0.32/0.51      ! [A: code_integer] :
% 0.32/0.51        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % verit_sum_simplify
% 0.32/0.51  thf(fact_496_verit__sum__simplify,axiom,
% 0.32/0.51      ! [A: rat] :
% 0.32/0.51        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % verit_sum_simplify
% 0.32/0.51  thf(fact_497_verit__sum__simplify,axiom,
% 0.32/0.51      ! [A: code_natural] :
% 0.32/0.51        ( ( plus_p4538020629002901425atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % verit_sum_simplify
% 0.32/0.51  thf(fact_498_add_Ogroup__left__neutral,axiom,
% 0.32/0.51      ! [A: int] :
% 0.32/0.51        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % add.group_left_neutral
% 0.32/0.51  thf(fact_499_add_Ogroup__left__neutral,axiom,
% 0.32/0.51      ! [A: code_integer] :
% 0.32/0.51        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % add.group_left_neutral
% 0.32/0.51  thf(fact_500_add_Ogroup__left__neutral,axiom,
% 0.32/0.51      ! [A: rat] :
% 0.32/0.51        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % add.group_left_neutral
% 0.32/0.51  thf(fact_501_add_Ocomm__neutral,axiom,
% 0.32/0.51      ! [A: nat] :
% 0.32/0.51        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % add.comm_neutral
% 0.32/0.51  thf(fact_502_add_Ocomm__neutral,axiom,
% 0.32/0.51      ! [A: int] :
% 0.32/0.51        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % add.comm_neutral
% 0.32/0.51  thf(fact_503_add_Ocomm__neutral,axiom,
% 0.32/0.51      ! [A: code_integer] :
% 0.32/0.51        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % add.comm_neutral
% 0.32/0.51  thf(fact_504_add_Ocomm__neutral,axiom,
% 0.32/0.51      ! [A: rat] :
% 0.32/0.51        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % add.comm_neutral
% 0.32/0.51  thf(fact_505_add_Ocomm__neutral,axiom,
% 0.32/0.51      ! [A: code_natural] :
% 0.32/0.51        ( ( plus_p4538020629002901425atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % add.comm_neutral
% 0.32/0.51  thf(fact_506_comm__monoid__add__class_Oadd__0,axiom,
% 0.32/0.51      ! [A: nat] :
% 0.32/0.51        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % comm_monoid_add_class.add_0
% 0.32/0.51  thf(fact_507_comm__monoid__add__class_Oadd__0,axiom,
% 0.32/0.51      ! [A: int] :
% 0.32/0.51        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % comm_monoid_add_class.add_0
% 0.32/0.51  thf(fact_508_comm__monoid__add__class_Oadd__0,axiom,
% 0.32/0.51      ! [A: code_integer] :
% 0.32/0.51        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % comm_monoid_add_class.add_0
% 0.32/0.51  thf(fact_509_comm__monoid__add__class_Oadd__0,axiom,
% 0.32/0.51      ! [A: rat] :
% 0.32/0.51        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % comm_monoid_add_class.add_0
% 0.32/0.51  thf(fact_510_comm__monoid__add__class_Oadd__0,axiom,
% 0.32/0.51      ! [A: code_natural] :
% 0.32/0.51        ( ( plus_p4538020629002901425atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.51        = A ) ).
% 0.32/0.51  
% 0.32/0.51  % comm_monoid_add_class.add_0
% 0.32/0.51  thf(fact_511_plus__nat_Oadd__0,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.32/0.51        = N ) ).
% 0.32/0.51  
% 0.32/0.51  % plus_nat.add_0
% 0.32/0.51  thf(fact_512_add__eq__self__zero,axiom,
% 0.32/0.51      ! [M: nat,N: nat] :
% 0.32/0.51        ( ( ( plus_plus_nat @ M @ N )
% 0.32/0.51          = M )
% 0.32/0.51       => ( N = zero_zero_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_eq_self_zero
% 0.32/0.51  thf(fact_513_add__leE,axiom,
% 0.32/0.51      ! [M: nat,K: nat,N: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.32/0.51       => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.51           => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_leE
% 0.32/0.51  thf(fact_514_le__add1,axiom,
% 0.32/0.51      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.32/0.51  
% 0.32/0.51  % le_add1
% 0.32/0.51  thf(fact_515_le__add2,axiom,
% 0.32/0.51      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % le_add2
% 0.32/0.51  thf(fact_516_add__leD1,axiom,
% 0.32/0.51      ! [M: nat,K: nat,N: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.32/0.51       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_leD1
% 0.32/0.51  thf(fact_517_add__leD2,axiom,
% 0.32/0.51      ! [M: nat,K: nat,N: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.32/0.51       => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_leD2
% 0.32/0.51  thf(fact_518_le__Suc__ex,axiom,
% 0.32/0.51      ! [K: nat,L: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ K @ L )
% 0.32/0.51       => ? [N2: nat] :
% 0.32/0.51            ( L
% 0.32/0.51            = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % le_Suc_ex
% 0.32/0.51  thf(fact_519_add__le__mono,axiom,
% 0.32/0.51      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.51       => ( ( ord_less_eq_nat @ K @ L )
% 0.32/0.51         => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_mono
% 0.32/0.51  thf(fact_520_add__le__mono1,axiom,
% 0.32/0.51      ! [I: nat,J: nat,K: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.51       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_le_mono1
% 0.32/0.51  thf(fact_521_trans__le__add1,axiom,
% 0.32/0.51      ! [I: nat,J: nat,M: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.51       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % trans_le_add1
% 0.32/0.51  thf(fact_522_trans__le__add2,axiom,
% 0.32/0.51      ! [I: nat,J: nat,M: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.51       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % trans_le_add2
% 0.32/0.51  thf(fact_523_nat__le__iff__add,axiom,
% 0.32/0.51      ( ord_less_eq_nat
% 0.32/0.51      = ( ^ [M2: nat,N3: nat] :
% 0.32/0.51          ? [K2: nat] :
% 0.32/0.51            ( N3
% 0.32/0.51            = ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % nat_le_iff_add
% 0.32/0.51  thf(fact_524_add__decreasing,axiom,
% 0.32/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.51       => ( ( ord_le3102999989581377725nteger @ C @ B )
% 0.32/0.51         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing
% 0.32/0.51  thf(fact_525_add__decreasing,axiom,
% 0.32/0.51      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.32/0.51        ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.51       => ( ( ord_le1926595141338095240atural @ C @ B )
% 0.32/0.51         => ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing
% 0.32/0.51  thf(fact_526_add__decreasing,axiom,
% 0.32/0.51      ! [A: rat,C: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.51       => ( ( ord_less_eq_rat @ C @ B )
% 0.32/0.51         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing
% 0.32/0.51  thf(fact_527_add__decreasing,axiom,
% 0.32/0.51      ! [A: nat,C: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.32/0.51       => ( ( ord_less_eq_nat @ C @ B )
% 0.32/0.51         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing
% 0.32/0.51  thf(fact_528_add__decreasing,axiom,
% 0.32/0.51      ! [A: int,C: int,B: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.51       => ( ( ord_less_eq_int @ C @ B )
% 0.32/0.51         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing
% 0.32/0.51  thf(fact_529_add__increasing,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.51       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 0.32/0.51         => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing
% 0.32/0.51  thf(fact_530_add__increasing,axiom,
% 0.32/0.51      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.51        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.51       => ( ( ord_le1926595141338095240atural @ B @ C )
% 0.32/0.51         => ( ord_le1926595141338095240atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing
% 0.32/0.51  thf(fact_531_add__increasing,axiom,
% 0.32/0.51      ! [A: rat,B: rat,C: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.51       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.51         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing
% 0.32/0.51  thf(fact_532_add__increasing,axiom,
% 0.32/0.51      ! [A: nat,B: nat,C: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.51       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.51         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing
% 0.32/0.51  thf(fact_533_add__increasing,axiom,
% 0.32/0.51      ! [A: int,B: int,C: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.51       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.51         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing
% 0.32/0.51  thf(fact_534_add__decreasing2,axiom,
% 0.32/0.51      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.51       => ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.51         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing2
% 0.32/0.51  thf(fact_535_add__decreasing2,axiom,
% 0.32/0.51      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.32/0.51        ( ( ord_le1926595141338095240atural @ C @ zero_z2226904508553997617atural )
% 0.32/0.51       => ( ( ord_le1926595141338095240atural @ A @ B )
% 0.32/0.51         => ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing2
% 0.32/0.51  thf(fact_536_add__decreasing2,axiom,
% 0.32/0.51      ! [C: rat,A: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.51       => ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.51         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing2
% 0.32/0.51  thf(fact_537_add__decreasing2,axiom,
% 0.32/0.51      ! [C: nat,A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 0.32/0.51       => ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.51         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing2
% 0.32/0.51  thf(fact_538_add__decreasing2,axiom,
% 0.32/0.51      ! [C: int,A: int,B: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.32/0.51       => ( ( ord_less_eq_int @ A @ B )
% 0.32/0.51         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_decreasing2
% 0.32/0.51  thf(fact_539_add__increasing2,axiom,
% 0.32/0.51      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.51       => ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.51         => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing2
% 0.32/0.51  thf(fact_540_add__increasing2,axiom,
% 0.32/0.51      ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.32/0.51        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.51       => ( ( ord_le1926595141338095240atural @ B @ A )
% 0.32/0.51         => ( ord_le1926595141338095240atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing2
% 0.32/0.51  thf(fact_541_add__increasing2,axiom,
% 0.32/0.51      ! [C: rat,B: rat,A: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.51       => ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.51         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing2
% 0.32/0.51  thf(fact_542_add__increasing2,axiom,
% 0.32/0.51      ! [C: nat,B: nat,A: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.51       => ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.51         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing2
% 0.32/0.51  thf(fact_543_add__increasing2,axiom,
% 0.32/0.51      ! [C: int,B: int,A: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.51       => ( ( ord_less_eq_int @ B @ A )
% 0.32/0.51         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_increasing2
% 0.32/0.51  thf(fact_544_add__nonneg__nonneg,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.51       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.51         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_nonneg
% 0.32/0.51  thf(fact_545_add__nonneg__nonneg,axiom,
% 0.32/0.51      ! [A: code_natural,B: code_natural] :
% 0.32/0.51        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.51       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.51         => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_nonneg
% 0.32/0.51  thf(fact_546_add__nonneg__nonneg,axiom,
% 0.32/0.51      ! [A: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.51         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_nonneg
% 0.32/0.51  thf(fact_547_add__nonneg__nonneg,axiom,
% 0.32/0.51      ! [A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.51         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_nonneg
% 0.32/0.51  thf(fact_548_add__nonneg__nonneg,axiom,
% 0.32/0.51      ! [A: int,B: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.51         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_nonneg
% 0.32/0.51  thf(fact_549_add__nonpos__nonpos,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.51       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.51         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_nonpos
% 0.32/0.51  thf(fact_550_add__nonpos__nonpos,axiom,
% 0.32/0.51      ! [A: code_natural,B: code_natural] :
% 0.32/0.51        ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.51       => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 0.32/0.51         => ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_nonpos
% 0.32/0.51  thf(fact_551_add__nonpos__nonpos,axiom,
% 0.32/0.51      ! [A: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.51       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.32/0.51         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_nonpos
% 0.32/0.51  thf(fact_552_add__nonpos__nonpos,axiom,
% 0.32/0.51      ! [A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.32/0.51       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.32/0.51         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_nonpos
% 0.32/0.51  thf(fact_553_add__nonpos__nonpos,axiom,
% 0.32/0.51      ! [A: int,B: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.51       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.32/0.51         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_nonpos
% 0.32/0.51  thf(fact_554_add__nonneg__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 0.32/0.51       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.32/0.51         => ( ( ( plus_p5714425477246183910nteger @ X2 @ Y )
% 0.32/0.51              = zero_z3403309356797280102nteger )
% 0.32/0.51            = ( ( X2 = zero_z3403309356797280102nteger )
% 0.32/0.51              & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_eq_0_iff
% 0.32/0.51  thf(fact_555_add__nonneg__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: code_natural,Y: code_natural] :
% 0.32/0.51        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ X2 )
% 0.32/0.51       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ Y )
% 0.32/0.51         => ( ( ( plus_p4538020629002901425atural @ X2 @ Y )
% 0.32/0.51              = zero_z2226904508553997617atural )
% 0.32/0.51            = ( ( X2 = zero_z2226904508553997617atural )
% 0.32/0.51              & ( Y = zero_z2226904508553997617atural ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_eq_0_iff
% 0.32/0.51  thf(fact_556_add__nonneg__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: rat,Y: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.32/0.51         => ( ( ( plus_plus_rat @ X2 @ Y )
% 0.32/0.51              = zero_zero_rat )
% 0.32/0.51            = ( ( X2 = zero_zero_rat )
% 0.32/0.51              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_eq_0_iff
% 0.32/0.51  thf(fact_557_add__nonneg__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: nat,Y: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 0.32/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.32/0.51         => ( ( ( plus_plus_nat @ X2 @ Y )
% 0.32/0.51              = zero_zero_nat )
% 0.32/0.51            = ( ( X2 = zero_zero_nat )
% 0.32/0.51              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_eq_0_iff
% 0.32/0.51  thf(fact_558_add__nonneg__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: int,Y: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.32/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.51         => ( ( ( plus_plus_int @ X2 @ Y )
% 0.32/0.51              = zero_zero_int )
% 0.32/0.51            = ( ( X2 = zero_zero_int )
% 0.32/0.51              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonneg_eq_0_iff
% 0.32/0.51  thf(fact_559_add__nonpos__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ X2 @ zero_z3403309356797280102nteger )
% 0.32/0.51       => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 0.32/0.51         => ( ( ( plus_p5714425477246183910nteger @ X2 @ Y )
% 0.32/0.51              = zero_z3403309356797280102nteger )
% 0.32/0.51            = ( ( X2 = zero_z3403309356797280102nteger )
% 0.32/0.51              & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_eq_0_iff
% 0.32/0.51  thf(fact_560_add__nonpos__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: code_natural,Y: code_natural] :
% 0.32/0.51        ( ( ord_le1926595141338095240atural @ X2 @ zero_z2226904508553997617atural )
% 0.32/0.51       => ( ( ord_le1926595141338095240atural @ Y @ zero_z2226904508553997617atural )
% 0.32/0.51         => ( ( ( plus_p4538020629002901425atural @ X2 @ Y )
% 0.32/0.51              = zero_z2226904508553997617atural )
% 0.32/0.51            = ( ( X2 = zero_z2226904508553997617atural )
% 0.32/0.51              & ( Y = zero_z2226904508553997617atural ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_eq_0_iff
% 0.32/0.51  thf(fact_561_add__nonpos__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: rat,Y: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 0.32/0.51       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.32/0.51         => ( ( ( plus_plus_rat @ X2 @ Y )
% 0.32/0.51              = zero_zero_rat )
% 0.32/0.51            = ( ( X2 = zero_zero_rat )
% 0.32/0.51              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_eq_0_iff
% 0.32/0.51  thf(fact_562_add__nonpos__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: nat,Y: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ X2 @ zero_zero_nat )
% 0.32/0.51       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 0.32/0.51         => ( ( ( plus_plus_nat @ X2 @ Y )
% 0.32/0.51              = zero_zero_nat )
% 0.32/0.51            = ( ( X2 = zero_zero_nat )
% 0.32/0.51              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_eq_0_iff
% 0.32/0.51  thf(fact_563_add__nonpos__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: int,Y: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 0.32/0.51       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.32/0.51         => ( ( ( plus_plus_int @ X2 @ Y )
% 0.32/0.51              = zero_zero_int )
% 0.32/0.51            = ( ( X2 = zero_zero_int )
% 0.32/0.51              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_nonpos_eq_0_iff
% 0.32/0.51  thf(fact_564_time__bind,axiom,
% 0.32/0.51      ! [M: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,F: a > heap_Time_Heap_a] :
% 0.32/0.51        ( ( ( ~ ( time_fails_a @ M @ H )
% 0.32/0.51            & ~ ( time_fails_a @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) )
% 0.32/0.51         => ( ( time_time_a @ ( heap_Time_bind_a_a @ M @ F ) @ H )
% 0.32/0.51            = ( plus_plus_nat @ ( time_time_a @ M @ H ) @ ( time_time_a @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) ) ) )
% 0.32/0.51        & ( ~ ( ~ ( time_fails_a @ M @ H )
% 0.32/0.51              & ~ ( time_fails_a @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) )
% 0.32/0.51         => ( ( time_time_a @ ( heap_Time_bind_a_a @ M @ F ) @ H )
% 0.32/0.51            = zero_zero_nat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % time_bind
% 0.32/0.51  thf(fact_565_time__bind,axiom,
% 0.32/0.51      ! [M: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,F: a > heap_T5738788834812785303t_unit] :
% 0.32/0.51        ( ( ( ~ ( time_fails_a @ M @ H )
% 0.32/0.51            & ~ ( time_f8834461667527620124t_unit @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) )
% 0.32/0.51         => ( ( time_t4224138285095624986t_unit @ ( heap_T8685611227969916822t_unit @ M @ F ) @ H )
% 0.32/0.51            = ( plus_plus_nat @ ( time_time_a @ M @ H ) @ ( time_t4224138285095624986t_unit @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) ) ) )
% 0.32/0.51        & ( ~ ( ~ ( time_fails_a @ M @ H )
% 0.32/0.51              & ~ ( time_f8834461667527620124t_unit @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) )
% 0.32/0.51         => ( ( time_t4224138285095624986t_unit @ ( heap_T8685611227969916822t_unit @ M @ F ) @ H )
% 0.32/0.51            = zero_zero_nat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % time_bind
% 0.32/0.51  thf(fact_566_time__bind,axiom,
% 0.32/0.51      ! [M: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,F: product_unit > heap_Time_Heap_a] :
% 0.32/0.51        ( ( ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 0.32/0.51            & ~ ( time_fails_a @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) )
% 0.32/0.51         => ( ( time_time_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ H )
% 0.32/0.51            = ( plus_plus_nat @ ( time_t4224138285095624986t_unit @ M @ H ) @ ( time_time_a @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) ) ) )
% 0.32/0.51        & ( ~ ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 0.32/0.51              & ~ ( time_fails_a @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) )
% 0.32/0.51         => ( ( time_time_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ H )
% 0.32/0.51            = zero_zero_nat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % time_bind
% 0.32/0.51  thf(fact_567_time__bind,axiom,
% 0.32/0.51      ! [M: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,F: product_unit > heap_T5738788834812785303t_unit] :
% 0.32/0.51        ( ( ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 0.32/0.51            & ~ ( time_f8834461667527620124t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) )
% 0.32/0.51         => ( ( time_t4224138285095624986t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ H )
% 0.32/0.51            = ( plus_plus_nat @ ( time_t4224138285095624986t_unit @ M @ H ) @ ( time_t4224138285095624986t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) ) ) )
% 0.32/0.51        & ( ~ ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 0.32/0.51              & ~ ( time_f8834461667527620124t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) )
% 0.32/0.51         => ( ( time_t4224138285095624986t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ H )
% 0.32/0.51            = zero_zero_nat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % time_bind
% 0.32/0.51  thf(fact_568_imp__le__cong,axiom,
% 0.32/0.51      ! [X2: int,X6: int,P: $o,P2: $o] :
% 0.32/0.51        ( ( X2 = X6 )
% 0.32/0.51       => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 0.32/0.51           => ( P = P2 ) )
% 0.32/0.51         => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.32/0.51             => P )
% 0.32/0.51            = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 0.32/0.51             => P2 ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % imp_le_cong
% 0.32/0.51  thf(fact_569_conj__le__cong,axiom,
% 0.32/0.51      ! [X2: int,X6: int,P: $o,P2: $o] :
% 0.32/0.51        ( ( X2 = X6 )
% 0.32/0.51       => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 0.32/0.51           => ( P = P2 ) )
% 0.32/0.51         => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.32/0.51              & P )
% 0.32/0.51            = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 0.32/0.51              & P2 ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % conj_le_cong
% 0.32/0.51  thf(fact_570_Euclid__induct,axiom,
% 0.32/0.51      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.32/0.51        ( ! [A3: nat,B3: nat] :
% 0.32/0.51            ( ( P @ A3 @ B3 )
% 0.32/0.51            = ( P @ B3 @ A3 ) )
% 0.32/0.51       => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 0.32/0.51         => ( ! [A3: nat,B3: nat] :
% 0.32/0.51                ( ( P @ A3 @ B3 )
% 0.32/0.51               => ( P @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 0.32/0.51           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % Euclid_induct
% 0.32/0.51  thf(fact_571_add__0__iff,axiom,
% 0.32/0.51      ! [B: nat,A: nat] :
% 0.32/0.51        ( ( B
% 0.32/0.51          = ( plus_plus_nat @ B @ A ) )
% 0.32/0.51        = ( A = zero_zero_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_0_iff
% 0.32/0.51  thf(fact_572_add__0__iff,axiom,
% 0.32/0.51      ! [B: int,A: int] :
% 0.32/0.51        ( ( B
% 0.32/0.51          = ( plus_plus_int @ B @ A ) )
% 0.32/0.51        = ( A = zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_0_iff
% 0.32/0.51  thf(fact_573_add__0__iff,axiom,
% 0.32/0.51      ! [B: code_integer,A: code_integer] :
% 0.32/0.51        ( ( B
% 0.32/0.51          = ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.32/0.51        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_0_iff
% 0.32/0.51  thf(fact_574_add__0__iff,axiom,
% 0.32/0.51      ! [B: rat,A: rat] :
% 0.32/0.51        ( ( B
% 0.32/0.51          = ( plus_plus_rat @ B @ A ) )
% 0.32/0.51        = ( A = zero_zero_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_0_iff
% 0.32/0.51  thf(fact_575_of__nat__code,axiom,
% 0.32/0.51      ( semiri1314217659103216013at_int
% 0.32/0.51      = ( ^ [N3: nat] :
% 0.32/0.51            ( semiri8420488043553186161ux_int
% 0.32/0.51            @ ^ [I2: int] : ( plus_plus_int @ I2 @ one_one_int )
% 0.32/0.51            @ N3
% 0.32/0.51            @ zero_zero_int ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_code
% 0.32/0.51  thf(fact_576_of__nat__code,axiom,
% 0.32/0.51      ( semiri1316708129612266289at_nat
% 0.32/0.51      = ( ^ [N3: nat] :
% 0.32/0.51            ( semiri8422978514062236437ux_nat
% 0.32/0.51            @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ one_one_nat )
% 0.32/0.51            @ N3
% 0.32/0.51            @ zero_zero_nat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_code
% 0.32/0.51  thf(fact_577_of__nat__code,axiom,
% 0.32/0.51      ( semiri4939895301339042750nteger
% 0.32/0.51      = ( ^ [N3: nat] :
% 0.32/0.51            ( semiri4055485073559036834nteger
% 0.32/0.51            @ ^ [I2: code_integer] : ( plus_p5714425477246183910nteger @ I2 @ one_one_Code_integer )
% 0.32/0.51            @ N3
% 0.32/0.51            @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_code
% 0.32/0.51  thf(fact_578_of__nat__code,axiom,
% 0.32/0.51      ( semiri681578069525770553at_rat
% 0.32/0.51      = ( ^ [N3: nat] :
% 0.32/0.51            ( semiri7787848453975740701ux_rat
% 0.32/0.51            @ ^ [I2: rat] : ( plus_plus_rat @ I2 @ one_one_rat )
% 0.32/0.51            @ N3
% 0.32/0.51            @ zero_zero_rat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_code
% 0.32/0.51  thf(fact_579_of__nat__code,axiom,
% 0.32/0.51      ( semiri3763490453095760265atural
% 0.32/0.51      = ( ^ [N3: nat] :
% 0.32/0.51            ( semiri2879080225315754349atural
% 0.32/0.51            @ ^ [I2: code_natural] : ( plus_p4538020629002901425atural @ I2 @ one_one_Code_natural )
% 0.32/0.51            @ N3
% 0.32/0.51            @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_code
% 0.32/0.51  thf(fact_580_of__nat__eq__1__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ( semiri1314217659103216013at_int @ N )
% 0.32/0.51          = one_one_int )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_eq_1_iff
% 0.32/0.51  thf(fact_581_of__nat__eq__1__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ( semiri1316708129612266289at_nat @ N )
% 0.32/0.51          = one_one_nat )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_eq_1_iff
% 0.32/0.51  thf(fact_582_of__nat__eq__1__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ( semiri4939895301339042750nteger @ N )
% 0.32/0.51          = one_one_Code_integer )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_eq_1_iff
% 0.32/0.51  thf(fact_583_of__nat__eq__1__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ( semiri681578069525770553at_rat @ N )
% 0.32/0.51          = one_one_rat )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_eq_1_iff
% 0.32/0.51  thf(fact_584_of__nat__eq__1__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ( semiri3763490453095760265atural @ N )
% 0.32/0.51          = one_one_Code_natural )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_eq_1_iff
% 0.32/0.51  thf(fact_585_of__nat__1__eq__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( one_one_int
% 0.32/0.51          = ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1_eq_iff
% 0.32/0.51  thf(fact_586_of__nat__1__eq__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( one_one_nat
% 0.32/0.51          = ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1_eq_iff
% 0.32/0.51  thf(fact_587_of__nat__1__eq__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( one_one_Code_integer
% 0.32/0.51          = ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1_eq_iff
% 0.32/0.51  thf(fact_588_of__nat__1__eq__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( one_one_rat
% 0.32/0.51          = ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1_eq_iff
% 0.32/0.51  thf(fact_589_of__nat__1__eq__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( one_one_Code_natural
% 0.32/0.51          = ( semiri3763490453095760265atural @ N ) )
% 0.32/0.51        = ( N = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1_eq_iff
% 0.32/0.51  thf(fact_590_of__nat__1,axiom,
% 0.32/0.51      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.32/0.51      = one_one_int ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1
% 0.32/0.51  thf(fact_591_of__nat__1,axiom,
% 0.32/0.51      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.32/0.51      = one_one_nat ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1
% 0.32/0.51  thf(fact_592_of__nat__1,axiom,
% 0.32/0.51      ( ( semiri4939895301339042750nteger @ one_one_nat )
% 0.32/0.51      = one_one_Code_integer ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1
% 0.32/0.51  thf(fact_593_of__nat__1,axiom,
% 0.32/0.51      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 0.32/0.51      = one_one_rat ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1
% 0.32/0.51  thf(fact_594_of__nat__1,axiom,
% 0.32/0.51      ( ( semiri3763490453095760265atural @ one_one_nat )
% 0.32/0.51      = one_one_Code_natural ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_1
% 0.32/0.51  thf(fact_595_one__reorient,axiom,
% 0.32/0.51      ! [X2: int] :
% 0.32/0.51        ( ( one_one_int = X2 )
% 0.32/0.51        = ( X2 = one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % one_reorient
% 0.32/0.51  thf(fact_596_one__reorient,axiom,
% 0.32/0.51      ! [X2: nat] :
% 0.32/0.51        ( ( one_one_nat = X2 )
% 0.32/0.51        = ( X2 = one_one_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % one_reorient
% 0.32/0.51  thf(fact_597_one__reorient,axiom,
% 0.32/0.51      ! [X2: code_integer] :
% 0.32/0.51        ( ( one_one_Code_integer = X2 )
% 0.32/0.51        = ( X2 = one_one_Code_integer ) ) ).
% 0.32/0.51  
% 0.32/0.51  % one_reorient
% 0.32/0.51  thf(fact_598_one__reorient,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( one_one_rat = X2 )
% 0.32/0.51        = ( X2 = one_one_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % one_reorient
% 0.32/0.51  thf(fact_599_one__reorient,axiom,
% 0.32/0.51      ! [X2: code_natural] :
% 0.32/0.51        ( ( one_one_Code_natural = X2 )
% 0.32/0.51        = ( X2 = one_one_Code_natural ) ) ).
% 0.32/0.51  
% 0.32/0.51  % one_reorient
% 0.32/0.51  thf(fact_600_odd__nonzero,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 )
% 0.32/0.51       != zero_zero_int ) ).
% 0.32/0.51  
% 0.32/0.51  % odd_nonzero
% 0.32/0.51  thf(fact_601_int__ge__induct,axiom,
% 0.32/0.51      ! [K: int,I: int,P: int > $o] :
% 0.32/0.51        ( ( ord_less_eq_int @ K @ I )
% 0.32/0.51       => ( ( P @ K )
% 0.32/0.51         => ( ! [I3: int] :
% 0.32/0.51                ( ( ord_less_eq_int @ K @ I3 )
% 0.32/0.51               => ( ( P @ I3 )
% 0.32/0.51                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 0.32/0.51           => ( P @ I ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % int_ge_induct
% 0.32/0.51  thf(fact_602_int__ops_I2_J,axiom,
% 0.32/0.51      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.32/0.51      = one_one_int ) ).
% 0.32/0.51  
% 0.32/0.51  % int_ops(2)
% 0.32/0.51  thf(fact_603_plus__int__code_I2_J,axiom,
% 0.32/0.51      ! [L: int] :
% 0.32/0.51        ( ( plus_plus_int @ zero_zero_int @ L )
% 0.32/0.51        = L ) ).
% 0.32/0.51  
% 0.32/0.51  % plus_int_code(2)
% 0.32/0.51  thf(fact_604_plus__int__code_I1_J,axiom,
% 0.32/0.51      ! [K: int] :
% 0.32/0.51        ( ( plus_plus_int @ K @ zero_zero_int )
% 0.32/0.51        = K ) ).
% 0.32/0.51  
% 0.32/0.51  % plus_int_code(1)
% 0.32/0.51  thf(fact_605_le__numeral__extra_I4_J,axiom,
% 0.32/0.51      ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 0.32/0.51  
% 0.32/0.51  % le_numeral_extra(4)
% 0.32/0.51  thf(fact_606_le__numeral__extra_I4_J,axiom,
% 0.32/0.51      ord_le1926595141338095240atural @ one_one_Code_natural @ one_one_Code_natural ).
% 0.32/0.51  
% 0.32/0.51  % le_numeral_extra(4)
% 0.32/0.51  thf(fact_607_le__numeral__extra_I4_J,axiom,
% 0.32/0.51      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.32/0.51  
% 0.32/0.51  % le_numeral_extra(4)
% 0.32/0.51  thf(fact_608_le__numeral__extra_I4_J,axiom,
% 0.32/0.51      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.32/0.51  
% 0.32/0.51  % le_numeral_extra(4)
% 0.32/0.51  thf(fact_609_le__numeral__extra_I4_J,axiom,
% 0.32/0.51      ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.32/0.51  
% 0.32/0.51  % le_numeral_extra(4)
% 0.32/0.51  thf(fact_610_zadd__int__left,axiom,
% 0.32/0.51      ! [M: nat,N: nat,Z2: int] :
% 0.32/0.51        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z2 ) )
% 0.32/0.51        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zadd_int_left
% 0.32/0.51  thf(fact_611_int__ops_I5_J,axiom,
% 0.32/0.51      ! [A: nat,B: nat] :
% 0.32/0.51        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 0.32/0.51        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % int_ops(5)
% 0.32/0.51  thf(fact_612_int__plus,axiom,
% 0.32/0.51      ! [N: nat,M: nat] :
% 0.32/0.51        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 0.32/0.51        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % int_plus
% 0.32/0.51  thf(fact_613_zle__iff__zadd,axiom,
% 0.32/0.51      ( ord_less_eq_int
% 0.32/0.51      = ( ^ [W: int,Z3: int] :
% 0.32/0.51          ? [N3: nat] :
% 0.32/0.51            ( Z3
% 0.32/0.51            = ( plus_plus_int @ W @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zle_iff_zadd
% 0.32/0.51  thf(fact_614_nat__geq__1__eq__neqz,axiom,
% 0.32/0.51      ! [X2: nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ one_one_nat @ X2 )
% 0.32/0.51        = ( X2 != zero_zero_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % nat_geq_1_eq_neqz
% 0.32/0.51  thf(fact_615_someI2__bex,axiom,
% 0.32/0.51      ! [A4: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.32/0.51        ( ? [X4: product_prod_nat_nat] :
% 0.32/0.51            ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 0.32/0.51            & ( P @ X4 ) )
% 0.32/0.51       => ( ! [X3: product_prod_nat_nat] :
% 0.32/0.51              ( ( ( member8440522571783428010at_nat @ X3 @ A4 )
% 0.32/0.51                & ( P @ X3 ) )
% 0.32/0.51             => ( Q @ X3 ) )
% 0.32/0.51         => ( Q
% 0.32/0.51            @ ( fChoic6978938873391328853at_nat
% 0.32/0.51              @ ^ [X: product_prod_nat_nat] :
% 0.32/0.51                  ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.32/0.51                  & ( P @ X ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % someI2_bex
% 0.32/0.51  thf(fact_616_someI2__bex,axiom,
% 0.32/0.51      ! [A4: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o,Q: set_Pr958786334691620121nt_int > $o] :
% 0.32/0.51        ( ? [X4: set_Pr958786334691620121nt_int] :
% 0.32/0.51            ( ( member2340774599025711042nt_int @ X4 @ A4 )
% 0.32/0.51            & ( P @ X4 ) )
% 0.32/0.51       => ( ! [X3: set_Pr958786334691620121nt_int] :
% 0.32/0.51              ( ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 0.32/0.51                & ( P @ X3 ) )
% 0.32/0.51             => ( Q @ X3 ) )
% 0.32/0.51         => ( Q
% 0.32/0.51            @ ( fChoic2749331249758569069nt_int
% 0.32/0.51              @ ^ [X: set_Pr958786334691620121nt_int] :
% 0.32/0.51                  ( ( member2340774599025711042nt_int @ X @ A4 )
% 0.32/0.51                  & ( P @ X ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % someI2_bex
% 0.32/0.51  thf(fact_617_someI2__bex,axiom,
% 0.32/0.51      ! [A4: set_set_nat,P: set_nat > $o,Q: set_nat > $o] :
% 0.32/0.51        ( ? [X4: set_nat] :
% 0.32/0.51            ( ( member_set_nat @ X4 @ A4 )
% 0.32/0.51            & ( P @ X4 ) )
% 0.32/0.51       => ( ! [X3: set_nat] :
% 0.32/0.51              ( ( ( member_set_nat @ X3 @ A4 )
% 0.32/0.51                & ( P @ X3 ) )
% 0.32/0.51             => ( Q @ X3 ) )
% 0.32/0.51         => ( Q
% 0.32/0.51            @ ( fChoice_set_nat
% 0.32/0.51              @ ^ [X: set_nat] :
% 0.32/0.51                  ( ( member_set_nat @ X @ A4 )
% 0.32/0.51                  & ( P @ X ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % someI2_bex
% 0.32/0.51  thf(fact_618_someI2__bex,axiom,
% 0.32/0.51      ! [A4: set_nat,P: nat > $o,Q: nat > $o] :
% 0.32/0.51        ( ? [X4: nat] :
% 0.32/0.51            ( ( member_nat @ X4 @ A4 )
% 0.32/0.51            & ( P @ X4 ) )
% 0.32/0.51       => ( ! [X3: nat] :
% 0.32/0.51              ( ( ( member_nat @ X3 @ A4 )
% 0.32/0.51                & ( P @ X3 ) )
% 0.32/0.51             => ( Q @ X3 ) )
% 0.32/0.51         => ( Q
% 0.32/0.51            @ ( fChoice_nat
% 0.32/0.51              @ ^ [X: nat] :
% 0.32/0.51                  ( ( member_nat @ X @ A4 )
% 0.32/0.51                  & ( P @ X ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % someI2_bex
% 0.32/0.51  thf(fact_619_someI2__bex,axiom,
% 0.32/0.51      ! [A4: set_int,P: int > $o,Q: int > $o] :
% 0.32/0.51        ( ? [X4: int] :
% 0.32/0.51            ( ( member_int @ X4 @ A4 )
% 0.32/0.51            & ( P @ X4 ) )
% 0.32/0.51       => ( ! [X3: int] :
% 0.32/0.51              ( ( ( member_int @ X3 @ A4 )
% 0.32/0.51                & ( P @ X3 ) )
% 0.32/0.51             => ( Q @ X3 ) )
% 0.32/0.51         => ( Q
% 0.32/0.51            @ ( fChoice_int
% 0.32/0.51              @ ^ [X: int] :
% 0.32/0.51                  ( ( member_int @ X @ A4 )
% 0.32/0.51                  & ( P @ X ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % someI2_bex
% 0.32/0.51  thf(fact_620_not__one__le__zero,axiom,
% 0.32/0.51      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 0.32/0.51  
% 0.32/0.51  % not_one_le_zero
% 0.32/0.51  thf(fact_621_not__one__le__zero,axiom,
% 0.32/0.51      ~ ( ord_le1926595141338095240atural @ one_one_Code_natural @ zero_z2226904508553997617atural ) ).
% 0.32/0.51  
% 0.32/0.51  % not_one_le_zero
% 0.32/0.51  thf(fact_622_not__one__le__zero,axiom,
% 0.32/0.51      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.32/0.51  
% 0.32/0.51  % not_one_le_zero
% 0.32/0.51  thf(fact_623_not__one__le__zero,axiom,
% 0.32/0.51      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.32/0.51  
% 0.32/0.51  % not_one_le_zero
% 0.32/0.51  thf(fact_624_not__one__le__zero,axiom,
% 0.32/0.51      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.32/0.51  
% 0.32/0.51  % not_one_le_zero
% 0.32/0.51  thf(fact_625_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.32/0.51  
% 0.32/0.51  % linordered_nonzero_semiring_class.zero_le_one
% 0.32/0.51  thf(fact_626_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 0.32/0.51  
% 0.32/0.51  % linordered_nonzero_semiring_class.zero_le_one
% 0.32/0.51  thf(fact_627_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.32/0.51  
% 0.32/0.51  % linordered_nonzero_semiring_class.zero_le_one
% 0.32/0.51  thf(fact_628_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.32/0.51  
% 0.32/0.51  % linordered_nonzero_semiring_class.zero_le_one
% 0.32/0.51  thf(fact_629_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.32/0.51  
% 0.32/0.51  % linordered_nonzero_semiring_class.zero_le_one
% 0.32/0.51  thf(fact_630_zero__less__one__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_one_class.zero_le_one
% 0.32/0.51  thf(fact_631_zero__less__one__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_one_class.zero_le_one
% 0.32/0.51  thf(fact_632_zero__less__one__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_one_class.zero_le_one
% 0.32/0.51  thf(fact_633_zero__less__one__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_one_class.zero_le_one
% 0.32/0.51  thf(fact_634_zero__less__one__class_Ozero__le__one,axiom,
% 0.32/0.51      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_one_class.zero_le_one
% 0.32/0.51  thf(fact_635_zero__neq__one,axiom,
% 0.32/0.51      zero_zero_nat != one_one_nat ).
% 0.32/0.51  
% 0.32/0.51  % zero_neq_one
% 0.32/0.51  thf(fact_636_zero__neq__one,axiom,
% 0.32/0.51      zero_zero_int != one_one_int ).
% 0.32/0.51  
% 0.32/0.51  % zero_neq_one
% 0.32/0.51  thf(fact_637_zero__neq__one,axiom,
% 0.32/0.51      zero_z3403309356797280102nteger != one_one_Code_integer ).
% 0.32/0.51  
% 0.32/0.51  % zero_neq_one
% 0.32/0.51  thf(fact_638_zero__neq__one,axiom,
% 0.32/0.51      zero_zero_rat != one_one_rat ).
% 0.32/0.51  
% 0.32/0.51  % zero_neq_one
% 0.32/0.51  thf(fact_639_zero__neq__one,axiom,
% 0.32/0.51      zero_z2226904508553997617atural != one_one_Code_natural ).
% 0.32/0.51  
% 0.32/0.51  % zero_neq_one
% 0.32/0.51  thf(fact_640_return__bind,axiom,
% 0.32/0.51      ! [X2: product_unit,F: product_unit > heap_Time_Heap_a] :
% 0.32/0.51        ( ( heap_T757603679106148408unit_a @ ( heap_T7507251653302230130t_unit @ X2 ) @ F )
% 0.32/0.51        = ( heap_T757603679106148408unit_a @ ( heap_Time_wait @ one_one_nat )
% 0.32/0.51          @ ^ [Uu: product_unit] : ( F @ X2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % return_bind
% 0.32/0.51  thf(fact_641_return__bind,axiom,
% 0.32/0.51      ! [X2: product_unit,F: product_unit > heap_T5738788834812785303t_unit] :
% 0.32/0.51        ( ( heap_T2633723481742716231t_unit @ ( heap_T7507251653302230130t_unit @ X2 ) @ F )
% 0.32/0.51        = ( heap_T2633723481742716231t_unit @ ( heap_Time_wait @ one_one_nat )
% 0.32/0.51          @ ^ [Uu: product_unit] : ( F @ X2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % return_bind
% 0.32/0.51  thf(fact_642_return__bind,axiom,
% 0.32/0.51      ! [X2: a,F: a > heap_Time_Heap_a] :
% 0.32/0.51        ( ( heap_Time_bind_a_a @ ( heap_Time_return_a @ X2 ) @ F )
% 0.32/0.51        = ( heap_T757603679106148408unit_a @ ( heap_Time_wait @ one_one_nat )
% 0.32/0.51          @ ^ [Uu: product_unit] : ( F @ X2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % return_bind
% 0.32/0.51  thf(fact_643_bind__return,axiom,
% 0.32/0.51      ! [F: heap_T5738788834812785303t_unit] :
% 0.32/0.51        ( ( heap_T2633723481742716231t_unit @ F @ heap_T7507251653302230130t_unit )
% 0.32/0.51        = ( heap_T2633723481742716231t_unit @ ( heap_Time_wait @ one_one_nat )
% 0.32/0.51          @ ^ [Uu: product_unit] : F ) ) ).
% 0.32/0.51  
% 0.32/0.51  % bind_return
% 0.32/0.51  thf(fact_644_bind__return,axiom,
% 0.32/0.51      ! [F: heap_Time_Heap_a] :
% 0.32/0.51        ( ( heap_Time_bind_a_a @ F @ heap_Time_return_a )
% 0.32/0.51        = ( heap_T757603679106148408unit_a @ ( heap_Time_wait @ one_one_nat )
% 0.32/0.51          @ ^ [Uu: product_unit] : F ) ) ).
% 0.32/0.51  
% 0.32/0.51  % bind_return
% 0.32/0.51  thf(fact_645_time__array__nth,axiom,
% 0.32/0.51      ! [P3: array_Product_unit,I: nat,H: heap_e7401611519738050253t_unit] :
% 0.32/0.51        ( ( ( time_f8834461667527620124t_unit @ ( array_7872002506669749220t_unit @ P3 @ I ) @ H )
% 0.32/0.51         => ( ( time_t4224138285095624986t_unit @ ( array_7872002506669749220t_unit @ P3 @ I ) @ H )
% 0.32/0.51            = zero_zero_nat ) )
% 0.32/0.51        & ( ~ ( time_f8834461667527620124t_unit @ ( array_7872002506669749220t_unit @ P3 @ I ) @ H )
% 0.32/0.51         => ( ( time_t4224138285095624986t_unit @ ( array_7872002506669749220t_unit @ P3 @ I ) @ H )
% 0.32/0.51            = one_one_nat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % time_array_nth
% 0.32/0.51  thf(fact_646_dbl__inc__simps_I2_J,axiom,
% 0.32/0.51      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.32/0.51      = one_one_int ) ).
% 0.32/0.51  
% 0.32/0.51  % dbl_inc_simps(2)
% 0.32/0.51  thf(fact_647_dbl__inc__simps_I2_J,axiom,
% 0.32/0.51      ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 0.32/0.51      = one_one_Code_integer ) ).
% 0.32/0.51  
% 0.32/0.51  % dbl_inc_simps(2)
% 0.32/0.51  thf(fact_648_dbl__inc__simps_I2_J,axiom,
% 0.32/0.51      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.32/0.51      = one_one_rat ) ).
% 0.32/0.51  
% 0.32/0.51  % dbl_inc_simps(2)
% 0.32/0.51  thf(fact_649_one__natural_Orsp,axiom,
% 0.32/0.51      one_one_nat = one_one_nat ).
% 0.32/0.51  
% 0.32/0.51  % one_natural.rsp
% 0.32/0.51  thf(fact_650_one__integer_Orsp,axiom,
% 0.32/0.51      one_one_int = one_one_int ).
% 0.32/0.51  
% 0.32/0.51  % one_integer.rsp
% 0.32/0.51  thf(fact_651_time__return,axiom,
% 0.32/0.51      ! [X2: a,H: heap_e7401611519738050253t_unit] :
% 0.32/0.51        ( ( time_time_a @ ( heap_Time_return_a @ X2 ) @ H )
% 0.32/0.51        = one_one_nat ) ).
% 0.32/0.51  
% 0.32/0.51  % time_return
% 0.32/0.51  thf(fact_652_time__return,axiom,
% 0.32/0.51      ! [X2: product_unit,H: heap_e7401611519738050253t_unit] :
% 0.32/0.51        ( ( time_t4224138285095624986t_unit @ ( heap_T7507251653302230130t_unit @ X2 ) @ H )
% 0.32/0.51        = one_one_nat ) ).
% 0.32/0.51  
% 0.32/0.51  % time_return
% 0.32/0.51  thf(fact_653_fails__return,axiom,
% 0.32/0.51      ! [X2: product_unit,H: heap_e7401611519738050253t_unit] :
% 0.32/0.51        ~ ( time_f8834461667527620124t_unit @ ( heap_T7507251653302230130t_unit @ X2 ) @ H ) ).
% 0.32/0.51  
% 0.32/0.51  % fails_return
% 0.32/0.51  thf(fact_654_dbl__inc__def,axiom,
% 0.32/0.51      ( neg_nu5831290666863070958nteger
% 0.32/0.51      = ( ^ [X: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X @ X ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % dbl_inc_def
% 0.32/0.51  thf(fact_655_dbl__inc__def,axiom,
% 0.32/0.51      ( neg_nu5219082963157363817nc_rat
% 0.32/0.51      = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % dbl_inc_def
% 0.32/0.51  thf(fact_656_dbl__inc__def,axiom,
% 0.32/0.51      ( neg_nu5851722552734809277nc_int
% 0.32/0.51      = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % dbl_inc_def
% 0.32/0.51  thf(fact_657_bind__lift,axiom,
% 0.32/0.51      ! [F: heap_T5738788834812785303t_unit,G: product_unit > a] :
% 0.32/0.51        ( ( heap_T757603679106148408unit_a @ F @ ( heap_T6901581777565460678unit_a @ G ) )
% 0.32/0.51        = ( heap_T757603679106148408unit_a @ F
% 0.32/0.51          @ ^ [X: product_unit] : ( heap_Time_return_a @ ( G @ X ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % bind_lift
% 0.32/0.51  thf(fact_658_bind__lift,axiom,
% 0.32/0.51      ! [F: heap_T5738788834812785303t_unit,G: product_unit > product_unit] :
% 0.32/0.51        ( ( heap_T2633723481742716231t_unit @ F @ ( heap_T7011250591035762645t_unit @ G ) )
% 0.32/0.51        = ( heap_T2633723481742716231t_unit @ F
% 0.32/0.51          @ ^ [X: product_unit] : ( heap_T7507251653302230130t_unit @ ( G @ X ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % bind_lift
% 0.32/0.51  thf(fact_659_bind__lift,axiom,
% 0.32/0.51      ! [F: heap_Time_Heap_a,G: a > a] :
% 0.32/0.51        ( ( heap_Time_bind_a_a @ F @ ( heap_Time_lift_a_a @ G ) )
% 0.32/0.51        = ( heap_Time_bind_a_a @ F
% 0.32/0.51          @ ^ [X: a] : ( heap_Time_return_a @ ( G @ X ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % bind_lift
% 0.32/0.51  thf(fact_660_lookup__chain,axiom,
% 0.32/0.51      ! [R: ref_Product_unit,F: heap_Time_Heap_a] :
% 0.32/0.51        ( ( heap_T757603679106148408unit_a @ ( ref_lo7930775386976318366t_unit @ R )
% 0.32/0.51          @ ^ [Uu: product_unit] : F )
% 0.32/0.51        = ( heap_T757603679106148408unit_a @ ( heap_Time_wait @ one_one_nat )
% 0.32/0.51          @ ^ [Uu: product_unit] : F ) ) ).
% 0.32/0.51  
% 0.32/0.51  % lookup_chain
% 0.32/0.51  thf(fact_661_lookup__chain,axiom,
% 0.32/0.51      ! [R: ref_Product_unit,F: heap_T5738788834812785303t_unit] :
% 0.32/0.51        ( ( heap_T2633723481742716231t_unit @ ( ref_lo7930775386976318366t_unit @ R )
% 0.32/0.51          @ ^ [Uu: product_unit] : F )
% 0.32/0.51        = ( heap_T2633723481742716231t_unit @ ( heap_Time_wait @ one_one_nat )
% 0.32/0.51          @ ^ [Uu: product_unit] : F ) ) ).
% 0.32/0.51  
% 0.32/0.51  % lookup_chain
% 0.32/0.51  thf(fact_662_ceiling__add__one,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 0.32/0.51        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_add_one
% 0.32/0.51  thf(fact_663_ceiling__le__one,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 0.32/0.51        = ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_le_one
% 0.32/0.51  thf(fact_664_ceiling__le__zero,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 0.32/0.51        = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_le_zero
% 0.32/0.51  thf(fact_665_of__int__le__1__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ one_one_Code_integer )
% 0.32/0.51        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_le_1_iff
% 0.32/0.51  thf(fact_666_of__int__le__1__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 0.32/0.51        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_le_1_iff
% 0.32/0.51  thf(fact_667_of__int__le__1__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 0.32/0.51        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_le_1_iff
% 0.32/0.51  thf(fact_668_of__int__1__le__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.32/0.51        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_1_le_iff
% 0.32/0.51  thf(fact_669_of__int__1__le__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_1_le_iff
% 0.32/0.51  thf(fact_670_of__int__1__le__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.32/0.51        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_1_le_iff
% 0.32/0.51  thf(fact_671_of__int__eq__iff,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ( ring_18347121197199848620nteger @ W2 )
% 0.32/0.51          = ( ring_18347121197199848620nteger @ Z2 ) )
% 0.32/0.51        = ( W2 = Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_eq_iff
% 0.32/0.51  thf(fact_672_of__int__eq__iff,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ( ring_1_of_int_rat @ W2 )
% 0.32/0.51          = ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = ( W2 = Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_eq_iff
% 0.32/0.51  thf(fact_673_of__int__eq__iff,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ( ring_1_of_int_int @ W2 )
% 0.32/0.51          = ( ring_1_of_int_int @ Z2 ) )
% 0.32/0.51        = ( W2 = Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_eq_iff
% 0.32/0.51  thf(fact_674_ceiling__of__int,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( archim2889992004027027881ng_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = Z2 ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_of_int
% 0.32/0.51  thf(fact_675_of__int__0,axiom,
% 0.32/0.51      ( ( ring_18347121197199848620nteger @ zero_zero_int )
% 0.32/0.51      = zero_z3403309356797280102nteger ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0
% 0.32/0.51  thf(fact_676_of__int__0,axiom,
% 0.32/0.51      ( ( ring_1_of_int_rat @ zero_zero_int )
% 0.32/0.51      = zero_zero_rat ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0
% 0.32/0.51  thf(fact_677_of__int__0,axiom,
% 0.32/0.51      ( ( ring_1_of_int_int @ zero_zero_int )
% 0.32/0.51      = zero_zero_int ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0
% 0.32/0.51  thf(fact_678_of__int__0__eq__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( zero_z3403309356797280102nteger
% 0.32/0.51          = ( ring_18347121197199848620nteger @ Z2 ) )
% 0.32/0.51        = ( Z2 = zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0_eq_iff
% 0.32/0.51  thf(fact_679_of__int__0__eq__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( zero_zero_rat
% 0.32/0.51          = ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = ( Z2 = zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0_eq_iff
% 0.32/0.51  thf(fact_680_of__int__0__eq__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( zero_zero_int
% 0.32/0.51          = ( ring_1_of_int_int @ Z2 ) )
% 0.32/0.51        = ( Z2 = zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0_eq_iff
% 0.32/0.51  thf(fact_681_of__int__eq__0__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ( ring_18347121197199848620nteger @ Z2 )
% 0.32/0.51          = zero_z3403309356797280102nteger )
% 0.32/0.51        = ( Z2 = zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_eq_0_iff
% 0.32/0.51  thf(fact_682_of__int__eq__0__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ( ring_1_of_int_rat @ Z2 )
% 0.32/0.51          = zero_zero_rat )
% 0.32/0.51        = ( Z2 = zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_eq_0_iff
% 0.32/0.51  thf(fact_683_of__int__eq__0__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ( ring_1_of_int_int @ Z2 )
% 0.32/0.51          = zero_zero_int )
% 0.32/0.51        = ( Z2 = zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_eq_0_iff
% 0.32/0.51  thf(fact_684_of__int__le__iff,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.32/0.51        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_le_iff
% 0.32/0.51  thf(fact_685_of__int__le__iff,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_le_iff
% 0.32/0.51  thf(fact_686_of__int__le__iff,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.32/0.51        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_le_iff
% 0.32/0.51  thf(fact_687_of__int__eq__1__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ( ring_18347121197199848620nteger @ Z2 )
% 0.32/0.51          = one_one_Code_integer )
% 0.32/0.51        = ( Z2 = one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_eq_1_iff
% 0.32/0.51  thf(fact_688_of__int__eq__1__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ( ring_1_of_int_rat @ Z2 )
% 0.32/0.51          = one_one_rat )
% 0.32/0.51        = ( Z2 = one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_eq_1_iff
% 0.32/0.51  thf(fact_689_of__int__eq__1__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ( ring_1_of_int_int @ Z2 )
% 0.32/0.51          = one_one_int )
% 0.32/0.51        = ( Z2 = one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_eq_1_iff
% 0.32/0.51  thf(fact_690_of__int__1,axiom,
% 0.32/0.51      ( ( ring_18347121197199848620nteger @ one_one_int )
% 0.32/0.51      = one_one_Code_integer ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_1
% 0.32/0.51  thf(fact_691_of__int__1,axiom,
% 0.32/0.51      ( ( ring_1_of_int_rat @ one_one_int )
% 0.32/0.51      = one_one_rat ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_1
% 0.32/0.51  thf(fact_692_of__int__1,axiom,
% 0.32/0.51      ( ( ring_1_of_int_int @ one_one_int )
% 0.32/0.51      = one_one_int ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_1
% 0.32/0.51  thf(fact_693_of__int__add,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ring_18347121197199848620nteger @ ( plus_plus_int @ W2 @ Z2 ) )
% 0.32/0.51        = ( plus_p5714425477246183910nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_add
% 0.32/0.51  thf(fact_694_of__int__add,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W2 @ Z2 ) )
% 0.32/0.51        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_add
% 0.32/0.51  thf(fact_695_of__int__add,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ring_1_of_int_int @ ( plus_plus_int @ W2 @ Z2 ) )
% 0.32/0.51        = ( plus_plus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_add
% 0.32/0.51  thf(fact_696_ceiling__zero,axiom,
% 0.32/0.51      ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 0.32/0.51      = zero_zero_int ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_zero
% 0.32/0.51  thf(fact_697_of__int__of__nat__eq,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_of_nat_eq
% 0.32/0.51  thf(fact_698_of__int__of__nat__eq,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ring_18347121197199848620nteger @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.51        = ( semiri4939895301339042750nteger @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_of_nat_eq
% 0.32/0.51  thf(fact_699_of__int__of__nat__eq,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.51        = ( semiri681578069525770553at_rat @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_of_nat_eq
% 0.32/0.51  thf(fact_700_ceiling__one,axiom,
% 0.32/0.51      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 0.32/0.51      = one_one_int ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_one
% 0.32/0.51  thf(fact_701_ceiling__of__nat,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( archim2889992004027027881ng_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_of_nat
% 0.32/0.51  thf(fact_702_ceiling__add__of__int,axiom,
% 0.32/0.51      ! [X2: rat,Z2: int] :
% 0.32/0.51        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) )
% 0.32/0.51        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_add_of_int
% 0.32/0.51  thf(fact_703_of__int__le__0__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ zero_z3403309356797280102nteger )
% 0.32/0.51        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_le_0_iff
% 0.32/0.51  thf(fact_704_of__int__le__0__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 0.32/0.51        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_le_0_iff
% 0.32/0.51  thf(fact_705_of__int__le__0__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 0.32/0.51        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_le_0_iff
% 0.32/0.51  thf(fact_706_of__int__0__le__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.32/0.51        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0_le_iff
% 0.32/0.51  thf(fact_707_of__int__0__le__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0_le_iff
% 0.32/0.51  thf(fact_708_of__int__0__le__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.32/0.51        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0_le_iff
% 0.32/0.51  thf(fact_709_le__of__int__ceiling,axiom,
% 0.32/0.51      ! [X2: rat] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % le_of_int_ceiling
% 0.32/0.51  thf(fact_710_ceiling__le__iff,axiom,
% 0.32/0.51      ! [X2: rat,Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z2 )
% 0.32/0.51        = ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_le_iff
% 0.32/0.51  thf(fact_711_ex__le__of__int,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51      ? [Z4: int] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ex_le_of_int
% 0.32/0.51  thf(fact_712_ceiling__mono,axiom,
% 0.32/0.51      ! [Y: rat,X2: rat] :
% 0.32/0.51        ( ( ord_less_eq_rat @ Y @ X2 )
% 0.32/0.51       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_mono
% 0.32/0.51  thf(fact_713_ceiling__add__le,axiom,
% 0.32/0.51      ! [X2: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_add_le
% 0.32/0.51  thf(fact_714_of__int__nonneg,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.51       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_nonneg
% 0.32/0.51  thf(fact_715_of__int__nonneg,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.51       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_nonneg
% 0.32/0.51  thf(fact_716_of__int__nonneg,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.51       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_nonneg
% 0.32/0.51  thf(fact_717_change__def,axiom,
% 0.32/0.51      ( ref_ch7259622376331601608t_unit
% 0.32/0.51      = ( ^ [F3: product_unit > product_unit,R2: ref_Product_unit] :
% 0.32/0.51            ( heap_T2633723481742716231t_unit @ ( ref_lo7930775386976318366t_unit @ R2 )
% 0.32/0.51            @ ^ [X: product_unit] :
% 0.32/0.51                ( heap_T2633723481742716231t_unit @ ( ref_up627237114476368303t_unit @ R2 @ ( F3 @ X ) )
% 0.32/0.51                @ ^ [Uu: product_unit] : ( heap_T7507251653302230130t_unit @ ( F3 @ X ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % change_def
% 0.32/0.51  thf(fact_718_one__le__ceiling,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.32/0.51        = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % one_le_ceiling
% 0.32/0.51  thf(fact_719_ceiling__less__one,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 0.32/0.51        = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ceiling_less_one
% 0.32/0.51  thf(fact_720_of__nat__nat,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.51       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 0.32/0.51          = ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_nat
% 0.32/0.51  thf(fact_721_of__nat__nat,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.51       => ( ( semiri4939895301339042750nteger @ ( nat2 @ Z2 ) )
% 0.32/0.51          = ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_nat
% 0.32/0.51  thf(fact_722_of__nat__nat,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.51       => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z2 ) )
% 0.32/0.51          = ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_nat
% 0.32/0.51  thf(fact_723_one__le__floor,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.32/0.51        = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % one_le_floor
% 0.32/0.51  thf(fact_724_power__int__decreasing,axiom,
% 0.32/0.51      ! [N: int,N4: int,A: rat] :
% 0.32/0.51        ( ( ord_less_eq_int @ N @ N4 )
% 0.32/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.51         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.32/0.51           => ( ( ( A != zero_zero_rat )
% 0.32/0.51                | ( N4 != zero_zero_int )
% 0.32/0.51                | ( N = zero_zero_int ) )
% 0.32/0.51             => ( ord_less_eq_rat @ ( power_int_rat @ A @ N4 ) @ ( power_int_rat @ A @ N ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % power_int_decreasing
% 0.32/0.51  thf(fact_725_power__int__le__one,axiom,
% 0.32/0.51      ! [X2: rat,N: int] :
% 0.32/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.32/0.51         => ( ( ord_less_eq_rat @ X2 @ one_one_rat )
% 0.32/0.51           => ( ord_less_eq_rat @ ( power_int_rat @ X2 @ N ) @ one_one_rat ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % power_int_le_one
% 0.32/0.51  thf(fact_726_zero__le__floor,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.32/0.51        = ( ord_less_eq_rat @ zero_zero_rat @ X2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zero_le_floor
% 0.32/0.51  thf(fact_727_rotate1__length01,axiom,
% 0.32/0.51      ! [Xs: list_nat] :
% 0.32/0.51        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 0.32/0.51       => ( ( rotate1_nat @ Xs )
% 0.32/0.51          = Xs ) ) ).
% 0.32/0.51  
% 0.32/0.51  % rotate1_length01
% 0.32/0.51  thf(fact_728_rotate1__length01,axiom,
% 0.32/0.51      ! [Xs: list_int] :
% 0.32/0.51        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 0.32/0.51       => ( ( rotate1_int @ Xs )
% 0.32/0.51          = Xs ) ) ).
% 0.32/0.51  
% 0.32/0.51  % rotate1_length01
% 0.32/0.51  thf(fact_729_rotate1__length01,axiom,
% 0.32/0.51      ! [Xs: list_o] :
% 0.32/0.51        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 0.32/0.51       => ( ( rotate1_o @ Xs )
% 0.32/0.51          = Xs ) ) ).
% 0.32/0.51  
% 0.32/0.51  % rotate1_length01
% 0.32/0.51  thf(fact_730_le__imp__0__less,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.51       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % le_imp_0_less
% 0.32/0.51  thf(fact_731_bot__nat__0_Onot__eq__extremum,axiom,
% 0.32/0.51      ! [A: nat] :
% 0.32/0.51        ( ( A != zero_zero_nat )
% 0.32/0.51        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % bot_nat_0.not_eq_extremum
% 0.32/0.51  thf(fact_732_neq0__conv,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( N != zero_zero_nat )
% 0.32/0.51        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % neq0_conv
% 0.32/0.51  thf(fact_733_less__nat__zero__code,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.32/0.51  
% 0.32/0.51  % less_nat_zero_code
% 0.32/0.51  thf(fact_734_nat__add__left__cancel__less,axiom,
% 0.32/0.51      ! [K: nat,M: nat,N: nat] :
% 0.32/0.51        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.32/0.51        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % nat_add_left_cancel_less
% 0.32/0.51  thf(fact_735_not__gr__zero,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.32/0.51        = ( N = zero_zero_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % not_gr_zero
% 0.32/0.51  thf(fact_736_add__less__cancel__left,axiom,
% 0.32/0.51      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 0.32/0.51        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_cancel_left
% 0.32/0.51  thf(fact_737_add__less__cancel__left,axiom,
% 0.32/0.51      ! [C: rat,A: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.32/0.51        = ( ord_less_rat @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_cancel_left
% 0.32/0.51  thf(fact_738_add__less__cancel__left,axiom,
% 0.32/0.51      ! [C: nat,A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.32/0.51        = ( ord_less_nat @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_cancel_left
% 0.32/0.51  thf(fact_739_add__less__cancel__left,axiom,
% 0.32/0.51      ! [C: int,A: int,B: int] :
% 0.32/0.51        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.32/0.51        = ( ord_less_int @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_cancel_left
% 0.32/0.51  thf(fact_740_add__less__cancel__right,axiom,
% 0.32/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.51        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_cancel_right
% 0.32/0.51  thf(fact_741_add__less__cancel__right,axiom,
% 0.32/0.51      ! [A: rat,C: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.51        = ( ord_less_rat @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_cancel_right
% 0.32/0.51  thf(fact_742_add__less__cancel__right,axiom,
% 0.32/0.51      ! [A: nat,C: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.51        = ( ord_less_nat @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_cancel_right
% 0.32/0.51  thf(fact_743_add__less__cancel__right,axiom,
% 0.32/0.51      ! [A: int,C: int,B: int] :
% 0.32/0.51        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.32/0.51        = ( ord_less_int @ A @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_cancel_right
% 0.32/0.51  thf(fact_744_of__nat__less__iff,axiom,
% 0.32/0.51      ! [M: nat,N: nat] :
% 0.32/0.51        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.51        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_less_iff
% 0.32/0.51  thf(fact_745_of__nat__less__iff,axiom,
% 0.32/0.51      ! [M: nat,N: nat] :
% 0.32/0.51        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.51        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_less_iff
% 0.32/0.51  thf(fact_746_of__nat__less__iff,axiom,
% 0.32/0.51      ! [M: nat,N: nat] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.51        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_less_iff
% 0.32/0.51  thf(fact_747_of__nat__less__iff,axiom,
% 0.32/0.51      ! [M: nat,N: nat] :
% 0.32/0.51        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.51        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_less_iff
% 0.32/0.51  thf(fact_748_of__nat__less__iff,axiom,
% 0.32/0.51      ! [M: nat,N: nat] :
% 0.32/0.51        ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) )
% 0.32/0.51        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_less_iff
% 0.32/0.51  thf(fact_749_add__gr__0,axiom,
% 0.32/0.51      ! [M: nat,N: nat] :
% 0.32/0.51        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.51        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.51          | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_gr_0
% 0.32/0.51  thf(fact_750_less__one,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ord_less_nat @ N @ one_one_nat )
% 0.32/0.51        = ( N = zero_zero_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_one
% 0.32/0.51  thf(fact_751_power__int__1__left,axiom,
% 0.32/0.51      ! [N: int] :
% 0.32/0.51        ( ( power_int_rat @ one_one_rat @ N )
% 0.32/0.51        = one_one_rat ) ).
% 0.32/0.51  
% 0.32/0.51  % power_int_1_left
% 0.32/0.51  thf(fact_752_nat__int,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( nat2 @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.51        = N ) ).
% 0.32/0.51  
% 0.32/0.51  % nat_int
% 0.32/0.51  thf(fact_753_floor__of__int,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( archim3151403230148437115or_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = Z2 ) ).
% 0.32/0.51  
% 0.32/0.51  % floor_of_int
% 0.32/0.51  thf(fact_754_length__rotate1,axiom,
% 0.32/0.51      ! [Xs: list_nat] :
% 0.32/0.51        ( ( size_size_list_nat @ ( rotate1_nat @ Xs ) )
% 0.32/0.51        = ( size_size_list_nat @ Xs ) ) ).
% 0.32/0.51  
% 0.32/0.51  % length_rotate1
% 0.32/0.51  thf(fact_755_length__rotate1,axiom,
% 0.32/0.51      ! [Xs: list_int] :
% 0.32/0.51        ( ( size_size_list_int @ ( rotate1_int @ Xs ) )
% 0.32/0.51        = ( size_size_list_int @ Xs ) ) ).
% 0.32/0.51  
% 0.32/0.51  % length_rotate1
% 0.32/0.51  thf(fact_756_length__rotate1,axiom,
% 0.32/0.51      ! [Xs: list_o] :
% 0.32/0.51        ( ( size_size_list_o @ ( rotate1_o @ Xs ) )
% 0.32/0.51        = ( size_size_list_o @ Xs ) ) ).
% 0.32/0.51  
% 0.32/0.51  % length_rotate1
% 0.32/0.51  thf(fact_757_add__less__same__cancel1,axiom,
% 0.32/0.51      ! [B: code_natural,A: code_natural] :
% 0.32/0.51        ( ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 0.32/0.51        = ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel1
% 0.32/0.51  thf(fact_758_add__less__same__cancel1,axiom,
% 0.32/0.51      ! [B: code_integer,A: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.32/0.51        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel1
% 0.32/0.51  thf(fact_759_add__less__same__cancel1,axiom,
% 0.32/0.51      ! [B: rat,A: rat] :
% 0.32/0.51        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.32/0.51        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel1
% 0.32/0.51  thf(fact_760_add__less__same__cancel1,axiom,
% 0.32/0.51      ! [B: nat,A: nat] :
% 0.32/0.51        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.32/0.51        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel1
% 0.32/0.51  thf(fact_761_add__less__same__cancel1,axiom,
% 0.32/0.51      ! [B: int,A: int] :
% 0.32/0.51        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.32/0.51        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel1
% 0.32/0.51  thf(fact_762_add__less__same__cancel2,axiom,
% 0.32/0.51      ! [A: code_natural,B: code_natural] :
% 0.32/0.51        ( ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 0.32/0.51        = ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel2
% 0.32/0.51  thf(fact_763_add__less__same__cancel2,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.32/0.51        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel2
% 0.32/0.51  thf(fact_764_add__less__same__cancel2,axiom,
% 0.32/0.51      ! [A: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.32/0.51        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel2
% 0.32/0.51  thf(fact_765_add__less__same__cancel2,axiom,
% 0.32/0.51      ! [A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.32/0.51        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel2
% 0.32/0.51  thf(fact_766_add__less__same__cancel2,axiom,
% 0.32/0.51      ! [A: int,B: int] :
% 0.32/0.51        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.32/0.51        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % add_less_same_cancel2
% 0.32/0.51  thf(fact_767_less__add__same__cancel1,axiom,
% 0.32/0.51      ! [A: code_natural,B: code_natural] :
% 0.32/0.51        ( ( ord_le5570908160329646204atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 0.32/0.51        = ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel1
% 0.32/0.51  thf(fact_768_less__add__same__cancel1,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.51        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel1
% 0.32/0.51  thf(fact_769_less__add__same__cancel1,axiom,
% 0.32/0.51      ! [A: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.51        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel1
% 0.32/0.51  thf(fact_770_less__add__same__cancel1,axiom,
% 0.32/0.51      ! [A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.32/0.51        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel1
% 0.32/0.51  thf(fact_771_less__add__same__cancel1,axiom,
% 0.32/0.51      ! [A: int,B: int] :
% 0.32/0.51        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.32/0.51        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel1
% 0.32/0.51  thf(fact_772_less__add__same__cancel2,axiom,
% 0.32/0.51      ! [A: code_natural,B: code_natural] :
% 0.32/0.51        ( ( ord_le5570908160329646204atural @ A @ ( plus_p4538020629002901425atural @ B @ A ) )
% 0.32/0.51        = ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel2
% 0.32/0.51  thf(fact_773_less__add__same__cancel2,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.32/0.51        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel2
% 0.32/0.51  thf(fact_774_less__add__same__cancel2,axiom,
% 0.32/0.51      ! [A: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.32/0.51        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel2
% 0.32/0.51  thf(fact_775_less__add__same__cancel2,axiom,
% 0.32/0.51      ! [A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.32/0.51        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel2
% 0.32/0.51  thf(fact_776_less__add__same__cancel2,axiom,
% 0.32/0.51      ! [A: int,B: int] :
% 0.32/0.51        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.32/0.51        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_add_same_cancel2
% 0.32/0.51  thf(fact_777_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.32/0.51      ! [A: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 0.32/0.51        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.51  
% 0.32/0.51  % double_add_less_zero_iff_single_add_less_zero
% 0.32/0.51  thf(fact_778_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.32/0.51      ! [A: rat] :
% 0.32/0.51        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.32/0.51        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % double_add_less_zero_iff_single_add_less_zero
% 0.32/0.51  thf(fact_779_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.32/0.51      ! [A: int] :
% 0.32/0.51        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.32/0.51        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % double_add_less_zero_iff_single_add_less_zero
% 0.32/0.51  thf(fact_780_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.32/0.51      ! [A: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 0.32/0.51        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_double_add_iff_zero_less_single_add
% 0.32/0.51  thf(fact_781_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.32/0.51      ! [A: rat] :
% 0.32/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.32/0.51        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_double_add_iff_zero_less_single_add
% 0.32/0.51  thf(fact_782_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.32/0.51      ! [A: int] :
% 0.32/0.51        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.32/0.51        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_double_add_iff_zero_less_single_add
% 0.32/0.51  thf(fact_783_of__int__less__iff,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_less_iff
% 0.32/0.51  thf(fact_784_of__int__less__iff,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_less_iff
% 0.32/0.51  thf(fact_785_of__int__less__iff,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_less_iff
% 0.32/0.51  thf(fact_786_power__int__eq__0__iff,axiom,
% 0.32/0.51      ! [X2: rat,N: int] :
% 0.32/0.51        ( ( ( power_int_rat @ X2 @ N )
% 0.32/0.51          = zero_zero_rat )
% 0.32/0.51        = ( ( X2 = zero_zero_rat )
% 0.32/0.51          & ( N != zero_zero_int ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % power_int_eq_0_iff
% 0.32/0.51  thf(fact_787_power__int__0__left,axiom,
% 0.32/0.51      ! [M: int] :
% 0.32/0.51        ( ( M != zero_zero_int )
% 0.32/0.51       => ( ( power_int_rat @ zero_zero_rat @ M )
% 0.32/0.51          = zero_zero_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % power_int_0_left
% 0.32/0.51  thf(fact_788_floor__zero,axiom,
% 0.32/0.51      ( ( archim3151403230148437115or_rat @ zero_zero_rat )
% 0.32/0.51      = zero_zero_int ) ).
% 0.32/0.51  
% 0.32/0.51  % floor_zero
% 0.32/0.51  thf(fact_789_power__int__0__right,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( power_int_rat @ X2 @ zero_zero_int )
% 0.32/0.51        = one_one_rat ) ).
% 0.32/0.51  
% 0.32/0.51  % power_int_0_right
% 0.32/0.51  thf(fact_790_zless__nat__conj,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 0.32/0.51        = ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.32/0.51          & ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zless_nat_conj
% 0.32/0.51  thf(fact_791_floor__one,axiom,
% 0.32/0.51      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 0.32/0.51      = one_one_int ) ).
% 0.32/0.51  
% 0.32/0.51  % floor_one
% 0.32/0.51  thf(fact_792_floor__of__nat,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( archim3151403230148437115or_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.51        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % floor_of_nat
% 0.32/0.51  thf(fact_793_of__nat__0__less__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.51        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_0_less_iff
% 0.32/0.51  thf(fact_794_of__nat__0__less__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.51        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_0_less_iff
% 0.32/0.51  thf(fact_795_of__nat__0__less__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.51        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_0_less_iff
% 0.32/0.51  thf(fact_796_of__nat__0__less__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.51        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_0_less_iff
% 0.32/0.51  thf(fact_797_of__nat__0__less__iff,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( semiri3763490453095760265atural @ N ) )
% 0.32/0.51        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_nat_0_less_iff
% 0.32/0.51  thf(fact_798_nat__0__iff,axiom,
% 0.32/0.51      ! [I: int] :
% 0.32/0.51        ( ( ( nat2 @ I )
% 0.32/0.51          = zero_zero_nat )
% 0.32/0.51        = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % nat_0_iff
% 0.32/0.51  thf(fact_799_nat__le__0,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 0.32/0.51       => ( ( nat2 @ Z2 )
% 0.32/0.51          = zero_zero_nat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % nat_le_0
% 0.32/0.51  thf(fact_800_zero__less__nat__eq,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_nat_eq
% 0.32/0.51  thf(fact_801_zle__add1__eq__le,axiom,
% 0.32/0.51      ! [W2: int,Z2: int] :
% 0.32/0.51        ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 0.32/0.51        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zle_add1_eq_le
% 0.32/0.51  thf(fact_802_int__nat__eq,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.51         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 0.32/0.51            = Z2 ) )
% 0.32/0.51        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.51         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 0.32/0.51            = zero_zero_int ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % int_nat_eq
% 0.32/0.51  thf(fact_803_of__int__less__0__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ zero_z3403309356797280102nteger )
% 0.32/0.51        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_less_0_iff
% 0.32/0.51  thf(fact_804_of__int__less__0__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 0.32/0.51        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_less_0_iff
% 0.32/0.51  thf(fact_805_of__int__less__0__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 0.32/0.51        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_less_0_iff
% 0.32/0.51  thf(fact_806_of__int__0__less__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0_less_iff
% 0.32/0.51  thf(fact_807_of__int__0__less__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0_less_iff
% 0.32/0.51  thf(fact_808_of__int__0__less__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_0_less_iff
% 0.32/0.51  thf(fact_809_power__int__mono__iff,axiom,
% 0.32/0.51      ! [A: rat,B: rat,N: int] :
% 0.32/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.51         => ( ( ord_less_int @ zero_zero_int @ N )
% 0.32/0.51           => ( ( ord_less_eq_rat @ ( power_int_rat @ A @ N ) @ ( power_int_rat @ B @ N ) )
% 0.32/0.51              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % power_int_mono_iff
% 0.32/0.51  thf(fact_810_of__int__less__1__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ one_one_Code_integer )
% 0.32/0.51        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_less_1_iff
% 0.32/0.51  thf(fact_811_of__int__less__1__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 0.32/0.51        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_less_1_iff
% 0.32/0.51  thf(fact_812_of__int__less__1__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 0.32/0.51        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_less_1_iff
% 0.32/0.51  thf(fact_813_of__int__1__less__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_1_less_iff
% 0.32/0.51  thf(fact_814_of__int__1__less__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_1_less_iff
% 0.32/0.51  thf(fact_815_of__int__1__less__iff,axiom,
% 0.32/0.51      ! [Z2: int] :
% 0.32/0.51        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.32/0.51        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % of_int_1_less_iff
% 0.32/0.51  thf(fact_816_floor__less__zero,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 0.32/0.51        = ( ord_less_rat @ X2 @ zero_zero_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % floor_less_zero
% 0.32/0.51  thf(fact_817_zero__less__floor,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.32/0.51        = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_floor
% 0.32/0.51  thf(fact_818_floor__le__zero,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 0.32/0.51        = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % floor_le_zero
% 0.32/0.51  thf(fact_819_zero__less__ceiling,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.32/0.51        = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % zero_less_ceiling
% 0.32/0.51  thf(fact_820_floor__less__one,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 0.32/0.51        = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 0.32/0.51  
% 0.32/0.51  % floor_less_one
% 0.32/0.51  thf(fact_821_one__less__ceiling,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.32/0.51        = ( ord_less_rat @ one_one_rat @ X2 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % one_less_ceiling
% 0.32/0.51  thf(fact_822_neq__if__length__neq,axiom,
% 0.32/0.51      ! [Xs: list_nat,Ys: list_nat] :
% 0.32/0.51        ( ( ( size_size_list_nat @ Xs )
% 0.32/0.51         != ( size_size_list_nat @ Ys ) )
% 0.32/0.51       => ( Xs != Ys ) ) ).
% 0.32/0.51  
% 0.32/0.51  % neq_if_length_neq
% 0.32/0.51  thf(fact_823_neq__if__length__neq,axiom,
% 0.32/0.51      ! [Xs: list_int,Ys: list_int] :
% 0.32/0.51        ( ( ( size_size_list_int @ Xs )
% 0.32/0.51         != ( size_size_list_int @ Ys ) )
% 0.32/0.51       => ( Xs != Ys ) ) ).
% 0.32/0.51  
% 0.32/0.51  % neq_if_length_neq
% 0.32/0.51  thf(fact_824_neq__if__length__neq,axiom,
% 0.32/0.51      ! [Xs: list_o,Ys: list_o] :
% 0.32/0.51        ( ( ( size_size_list_o @ Xs )
% 0.32/0.51         != ( size_size_list_o @ Ys ) )
% 0.32/0.51       => ( Xs != Ys ) ) ).
% 0.32/0.51  
% 0.32/0.51  % neq_if_length_neq
% 0.32/0.51  thf(fact_825_Ex__list__of__length,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51      ? [Xs2: list_nat] :
% 0.32/0.51        ( ( size_size_list_nat @ Xs2 )
% 0.32/0.51        = N ) ).
% 0.32/0.51  
% 0.32/0.51  % Ex_list_of_length
% 0.32/0.51  thf(fact_826_Ex__list__of__length,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51      ? [Xs2: list_int] :
% 0.32/0.51        ( ( size_size_list_int @ Xs2 )
% 0.32/0.51        = N ) ).
% 0.32/0.51  
% 0.32/0.51  % Ex_list_of_length
% 0.32/0.51  thf(fact_827_Ex__list__of__length,axiom,
% 0.32/0.51      ! [N: nat] :
% 0.32/0.51      ? [Xs2: list_o] :
% 0.32/0.51        ( ( size_size_list_o @ Xs2 )
% 0.32/0.51        = N ) ).
% 0.32/0.51  
% 0.32/0.51  % Ex_list_of_length
% 0.32/0.51  thf(fact_828_length__induct,axiom,
% 0.32/0.51      ! [P: list_nat > $o,Xs: list_nat] :
% 0.32/0.51        ( ! [Xs2: list_nat] :
% 0.32/0.51            ( ! [Ys2: list_nat] :
% 0.32/0.51                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 0.32/0.51               => ( P @ Ys2 ) )
% 0.32/0.51           => ( P @ Xs2 ) )
% 0.32/0.51       => ( P @ Xs ) ) ).
% 0.32/0.51  
% 0.32/0.51  % length_induct
% 0.32/0.51  thf(fact_829_length__induct,axiom,
% 0.32/0.51      ! [P: list_int > $o,Xs: list_int] :
% 0.32/0.51        ( ! [Xs2: list_int] :
% 0.32/0.51            ( ! [Ys2: list_int] :
% 0.32/0.51                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 0.32/0.51               => ( P @ Ys2 ) )
% 0.32/0.51           => ( P @ Xs2 ) )
% 0.32/0.51       => ( P @ Xs ) ) ).
% 0.32/0.51  
% 0.32/0.51  % length_induct
% 0.32/0.51  thf(fact_830_length__induct,axiom,
% 0.32/0.51      ! [P: list_o > $o,Xs: list_o] :
% 0.32/0.51        ( ! [Xs2: list_o] :
% 0.32/0.51            ( ! [Ys2: list_o] :
% 0.32/0.51                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs2 ) )
% 0.32/0.51               => ( P @ Ys2 ) )
% 0.32/0.51           => ( P @ Xs2 ) )
% 0.32/0.51       => ( P @ Xs ) ) ).
% 0.32/0.51  
% 0.32/0.51  % length_induct
% 0.32/0.51  thf(fact_831_floor__less__iff,axiom,
% 0.32/0.51      ! [X2: rat,Z2: int] :
% 0.32/0.51        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z2 )
% 0.32/0.51        = ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % floor_less_iff
% 0.32/0.51  thf(fact_832_minf_I7_J,axiom,
% 0.32/0.51      ! [T: code_integer] :
% 0.32/0.51      ? [Z4: code_integer] :
% 0.32/0.51      ! [X4: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 0.32/0.51       => ~ ( ord_le6747313008572928689nteger @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(7)
% 0.32/0.51  thf(fact_833_minf_I7_J,axiom,
% 0.32/0.51      ! [T: rat] :
% 0.32/0.51      ? [Z4: rat] :
% 0.32/0.51      ! [X4: rat] :
% 0.32/0.51        ( ( ord_less_rat @ X4 @ Z4 )
% 0.32/0.51       => ~ ( ord_less_rat @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(7)
% 0.32/0.51  thf(fact_834_minf_I7_J,axiom,
% 0.32/0.51      ! [T: num] :
% 0.32/0.51      ? [Z4: num] :
% 0.32/0.51      ! [X4: num] :
% 0.32/0.51        ( ( ord_less_num @ X4 @ Z4 )
% 0.32/0.51       => ~ ( ord_less_num @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(7)
% 0.32/0.51  thf(fact_835_minf_I7_J,axiom,
% 0.32/0.51      ! [T: nat] :
% 0.32/0.51      ? [Z4: nat] :
% 0.32/0.51      ! [X4: nat] :
% 0.32/0.51        ( ( ord_less_nat @ X4 @ Z4 )
% 0.32/0.51       => ~ ( ord_less_nat @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(7)
% 0.32/0.51  thf(fact_836_minf_I7_J,axiom,
% 0.32/0.51      ! [T: int] :
% 0.32/0.51      ? [Z4: int] :
% 0.32/0.51      ! [X4: int] :
% 0.32/0.51        ( ( ord_less_int @ X4 @ Z4 )
% 0.32/0.51       => ~ ( ord_less_int @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(7)
% 0.32/0.51  thf(fact_837_minf_I5_J,axiom,
% 0.32/0.51      ! [T: code_integer] :
% 0.32/0.51      ? [Z4: code_integer] :
% 0.32/0.51      ! [X4: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 0.32/0.51       => ( ord_le6747313008572928689nteger @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(5)
% 0.32/0.51  thf(fact_838_minf_I5_J,axiom,
% 0.32/0.51      ! [T: rat] :
% 0.32/0.51      ? [Z4: rat] :
% 0.32/0.51      ! [X4: rat] :
% 0.32/0.51        ( ( ord_less_rat @ X4 @ Z4 )
% 0.32/0.51       => ( ord_less_rat @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(5)
% 0.32/0.51  thf(fact_839_minf_I5_J,axiom,
% 0.32/0.51      ! [T: num] :
% 0.32/0.51      ? [Z4: num] :
% 0.32/0.51      ! [X4: num] :
% 0.32/0.51        ( ( ord_less_num @ X4 @ Z4 )
% 0.32/0.51       => ( ord_less_num @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(5)
% 0.32/0.51  thf(fact_840_minf_I5_J,axiom,
% 0.32/0.51      ! [T: nat] :
% 0.32/0.51      ? [Z4: nat] :
% 0.32/0.51      ! [X4: nat] :
% 0.32/0.51        ( ( ord_less_nat @ X4 @ Z4 )
% 0.32/0.51       => ( ord_less_nat @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(5)
% 0.32/0.51  thf(fact_841_minf_I5_J,axiom,
% 0.32/0.51      ! [T: int] :
% 0.32/0.51      ? [Z4: int] :
% 0.32/0.51      ! [X4: int] :
% 0.32/0.51        ( ( ord_less_int @ X4 @ Z4 )
% 0.32/0.51       => ( ord_less_int @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(5)
% 0.32/0.51  thf(fact_842_minf_I4_J,axiom,
% 0.32/0.51      ! [T: code_integer] :
% 0.32/0.51      ? [Z4: code_integer] :
% 0.32/0.51      ! [X4: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(4)
% 0.32/0.51  thf(fact_843_minf_I4_J,axiom,
% 0.32/0.51      ! [T: rat] :
% 0.32/0.51      ? [Z4: rat] :
% 0.32/0.51      ! [X4: rat] :
% 0.32/0.51        ( ( ord_less_rat @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(4)
% 0.32/0.51  thf(fact_844_minf_I4_J,axiom,
% 0.32/0.51      ! [T: num] :
% 0.32/0.51      ? [Z4: num] :
% 0.32/0.51      ! [X4: num] :
% 0.32/0.51        ( ( ord_less_num @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(4)
% 0.32/0.51  thf(fact_845_minf_I4_J,axiom,
% 0.32/0.51      ! [T: nat] :
% 0.32/0.51      ? [Z4: nat] :
% 0.32/0.51      ! [X4: nat] :
% 0.32/0.51        ( ( ord_less_nat @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(4)
% 0.32/0.51  thf(fact_846_minf_I4_J,axiom,
% 0.32/0.51      ! [T: int] :
% 0.32/0.51      ? [Z4: int] :
% 0.32/0.51      ! [X4: int] :
% 0.32/0.51        ( ( ord_less_int @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(4)
% 0.32/0.51  thf(fact_847_minf_I3_J,axiom,
% 0.32/0.51      ! [T: code_integer] :
% 0.32/0.51      ? [Z4: code_integer] :
% 0.32/0.51      ! [X4: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(3)
% 0.32/0.51  thf(fact_848_minf_I3_J,axiom,
% 0.32/0.51      ! [T: rat] :
% 0.32/0.51      ? [Z4: rat] :
% 0.32/0.51      ! [X4: rat] :
% 0.32/0.51        ( ( ord_less_rat @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(3)
% 0.32/0.51  thf(fact_849_minf_I3_J,axiom,
% 0.32/0.51      ! [T: num] :
% 0.32/0.51      ? [Z4: num] :
% 0.32/0.51      ! [X4: num] :
% 0.32/0.51        ( ( ord_less_num @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(3)
% 0.32/0.51  thf(fact_850_minf_I3_J,axiom,
% 0.32/0.51      ! [T: nat] :
% 0.32/0.51      ? [Z4: nat] :
% 0.32/0.51      ! [X4: nat] :
% 0.32/0.51        ( ( ord_less_nat @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(3)
% 0.32/0.51  thf(fact_851_minf_I3_J,axiom,
% 0.32/0.51      ! [T: int] :
% 0.32/0.51      ? [Z4: int] :
% 0.32/0.51      ! [X4: int] :
% 0.32/0.51        ( ( ord_less_int @ X4 @ Z4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(3)
% 0.32/0.51  thf(fact_852_minf_I2_J,axiom,
% 0.32/0.51      ! [P: code_integer > $o,P2: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 0.32/0.51        ( ? [Z5: code_integer] :
% 0.32/0.51          ! [X3: code_integer] :
% 0.32/0.51            ( ( ord_le6747313008572928689nteger @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: code_integer] :
% 0.32/0.51            ! [X3: code_integer] :
% 0.32/0.51              ( ( ord_le6747313008572928689nteger @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: code_integer] :
% 0.32/0.51            ! [X4: code_integer] :
% 0.32/0.51              ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(2)
% 0.32/0.51  thf(fact_853_minf_I2_J,axiom,
% 0.32/0.51      ! [P: rat > $o,P2: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 0.32/0.51        ( ? [Z5: rat] :
% 0.32/0.51          ! [X3: rat] :
% 0.32/0.51            ( ( ord_less_rat @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: rat] :
% 0.32/0.51            ! [X3: rat] :
% 0.32/0.51              ( ( ord_less_rat @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: rat] :
% 0.32/0.51            ! [X4: rat] :
% 0.32/0.51              ( ( ord_less_rat @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(2)
% 0.32/0.51  thf(fact_854_minf_I2_J,axiom,
% 0.32/0.51      ! [P: num > $o,P2: num > $o,Q: num > $o,Q3: num > $o] :
% 0.32/0.51        ( ? [Z5: num] :
% 0.32/0.51          ! [X3: num] :
% 0.32/0.51            ( ( ord_less_num @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: num] :
% 0.32/0.51            ! [X3: num] :
% 0.32/0.51              ( ( ord_less_num @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: num] :
% 0.32/0.51            ! [X4: num] :
% 0.32/0.51              ( ( ord_less_num @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(2)
% 0.32/0.51  thf(fact_855_minf_I2_J,axiom,
% 0.32/0.51      ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 0.32/0.51        ( ? [Z5: nat] :
% 0.32/0.51          ! [X3: nat] :
% 0.32/0.51            ( ( ord_less_nat @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: nat] :
% 0.32/0.51            ! [X3: nat] :
% 0.32/0.51              ( ( ord_less_nat @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: nat] :
% 0.32/0.51            ! [X4: nat] :
% 0.32/0.51              ( ( ord_less_nat @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(2)
% 0.32/0.51  thf(fact_856_minf_I2_J,axiom,
% 0.32/0.51      ! [P: int > $o,P2: int > $o,Q: int > $o,Q3: int > $o] :
% 0.32/0.51        ( ? [Z5: int] :
% 0.32/0.51          ! [X3: int] :
% 0.32/0.51            ( ( ord_less_int @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: int] :
% 0.32/0.51            ! [X3: int] :
% 0.32/0.51              ( ( ord_less_int @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: int] :
% 0.32/0.51            ! [X4: int] :
% 0.32/0.51              ( ( ord_less_int @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(2)
% 0.32/0.51  thf(fact_857_minf_I1_J,axiom,
% 0.32/0.51      ! [P: code_integer > $o,P2: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 0.32/0.51        ( ? [Z5: code_integer] :
% 0.32/0.51          ! [X3: code_integer] :
% 0.32/0.51            ( ( ord_le6747313008572928689nteger @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: code_integer] :
% 0.32/0.51            ! [X3: code_integer] :
% 0.32/0.51              ( ( ord_le6747313008572928689nteger @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: code_integer] :
% 0.32/0.51            ! [X4: code_integer] :
% 0.32/0.51              ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(1)
% 0.32/0.51  thf(fact_858_minf_I1_J,axiom,
% 0.32/0.51      ! [P: rat > $o,P2: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 0.32/0.51        ( ? [Z5: rat] :
% 0.32/0.51          ! [X3: rat] :
% 0.32/0.51            ( ( ord_less_rat @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: rat] :
% 0.32/0.51            ! [X3: rat] :
% 0.32/0.51              ( ( ord_less_rat @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: rat] :
% 0.32/0.51            ! [X4: rat] :
% 0.32/0.51              ( ( ord_less_rat @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(1)
% 0.32/0.51  thf(fact_859_minf_I1_J,axiom,
% 0.32/0.51      ! [P: num > $o,P2: num > $o,Q: num > $o,Q3: num > $o] :
% 0.32/0.51        ( ? [Z5: num] :
% 0.32/0.51          ! [X3: num] :
% 0.32/0.51            ( ( ord_less_num @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: num] :
% 0.32/0.51            ! [X3: num] :
% 0.32/0.51              ( ( ord_less_num @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: num] :
% 0.32/0.51            ! [X4: num] :
% 0.32/0.51              ( ( ord_less_num @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(1)
% 0.32/0.51  thf(fact_860_minf_I1_J,axiom,
% 0.32/0.51      ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 0.32/0.51        ( ? [Z5: nat] :
% 0.32/0.51          ! [X3: nat] :
% 0.32/0.51            ( ( ord_less_nat @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: nat] :
% 0.32/0.51            ! [X3: nat] :
% 0.32/0.51              ( ( ord_less_nat @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: nat] :
% 0.32/0.51            ! [X4: nat] :
% 0.32/0.51              ( ( ord_less_nat @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(1)
% 0.32/0.51  thf(fact_861_minf_I1_J,axiom,
% 0.32/0.51      ! [P: int > $o,P2: int > $o,Q: int > $o,Q3: int > $o] :
% 0.32/0.51        ( ? [Z5: int] :
% 0.32/0.51          ! [X3: int] :
% 0.32/0.51            ( ( ord_less_int @ X3 @ Z5 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: int] :
% 0.32/0.51            ! [X3: int] :
% 0.32/0.51              ( ( ord_less_int @ X3 @ Z5 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: int] :
% 0.32/0.51            ! [X4: int] :
% 0.32/0.51              ( ( ord_less_int @ X4 @ Z4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % minf(1)
% 0.32/0.51  thf(fact_862_pinf_I7_J,axiom,
% 0.32/0.51      ! [T: code_integer] :
% 0.32/0.51      ? [Z4: code_integer] :
% 0.32/0.51      ! [X4: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 0.32/0.51       => ( ord_le6747313008572928689nteger @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(7)
% 0.32/0.51  thf(fact_863_pinf_I7_J,axiom,
% 0.32/0.51      ! [T: rat] :
% 0.32/0.51      ? [Z4: rat] :
% 0.32/0.51      ! [X4: rat] :
% 0.32/0.51        ( ( ord_less_rat @ Z4 @ X4 )
% 0.32/0.51       => ( ord_less_rat @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(7)
% 0.32/0.51  thf(fact_864_pinf_I7_J,axiom,
% 0.32/0.51      ! [T: num] :
% 0.32/0.51      ? [Z4: num] :
% 0.32/0.51      ! [X4: num] :
% 0.32/0.51        ( ( ord_less_num @ Z4 @ X4 )
% 0.32/0.51       => ( ord_less_num @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(7)
% 0.32/0.51  thf(fact_865_pinf_I7_J,axiom,
% 0.32/0.51      ! [T: nat] :
% 0.32/0.51      ? [Z4: nat] :
% 0.32/0.51      ! [X4: nat] :
% 0.32/0.51        ( ( ord_less_nat @ Z4 @ X4 )
% 0.32/0.51       => ( ord_less_nat @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(7)
% 0.32/0.51  thf(fact_866_pinf_I7_J,axiom,
% 0.32/0.51      ! [T: int] :
% 0.32/0.51      ? [Z4: int] :
% 0.32/0.51      ! [X4: int] :
% 0.32/0.51        ( ( ord_less_int @ Z4 @ X4 )
% 0.32/0.51       => ( ord_less_int @ T @ X4 ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(7)
% 0.32/0.51  thf(fact_867_pinf_I5_J,axiom,
% 0.32/0.51      ! [T: code_integer] :
% 0.32/0.51      ? [Z4: code_integer] :
% 0.32/0.51      ! [X4: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 0.32/0.51       => ~ ( ord_le6747313008572928689nteger @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(5)
% 0.32/0.51  thf(fact_868_pinf_I5_J,axiom,
% 0.32/0.51      ! [T: rat] :
% 0.32/0.51      ? [Z4: rat] :
% 0.32/0.51      ! [X4: rat] :
% 0.32/0.51        ( ( ord_less_rat @ Z4 @ X4 )
% 0.32/0.51       => ~ ( ord_less_rat @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(5)
% 0.32/0.51  thf(fact_869_pinf_I5_J,axiom,
% 0.32/0.51      ! [T: num] :
% 0.32/0.51      ? [Z4: num] :
% 0.32/0.51      ! [X4: num] :
% 0.32/0.51        ( ( ord_less_num @ Z4 @ X4 )
% 0.32/0.51       => ~ ( ord_less_num @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(5)
% 0.32/0.51  thf(fact_870_pinf_I5_J,axiom,
% 0.32/0.51      ! [T: nat] :
% 0.32/0.51      ? [Z4: nat] :
% 0.32/0.51      ! [X4: nat] :
% 0.32/0.51        ( ( ord_less_nat @ Z4 @ X4 )
% 0.32/0.51       => ~ ( ord_less_nat @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(5)
% 0.32/0.51  thf(fact_871_pinf_I5_J,axiom,
% 0.32/0.51      ! [T: int] :
% 0.32/0.51      ? [Z4: int] :
% 0.32/0.51      ! [X4: int] :
% 0.32/0.51        ( ( ord_less_int @ Z4 @ X4 )
% 0.32/0.51       => ~ ( ord_less_int @ X4 @ T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(5)
% 0.32/0.51  thf(fact_872_pinf_I4_J,axiom,
% 0.32/0.51      ! [T: code_integer] :
% 0.32/0.51      ? [Z4: code_integer] :
% 0.32/0.51      ! [X4: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(4)
% 0.32/0.51  thf(fact_873_pinf_I4_J,axiom,
% 0.32/0.51      ! [T: rat] :
% 0.32/0.51      ? [Z4: rat] :
% 0.32/0.51      ! [X4: rat] :
% 0.32/0.51        ( ( ord_less_rat @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(4)
% 0.32/0.51  thf(fact_874_pinf_I4_J,axiom,
% 0.32/0.51      ! [T: num] :
% 0.32/0.51      ? [Z4: num] :
% 0.32/0.51      ! [X4: num] :
% 0.32/0.51        ( ( ord_less_num @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(4)
% 0.32/0.51  thf(fact_875_pinf_I4_J,axiom,
% 0.32/0.51      ! [T: nat] :
% 0.32/0.51      ? [Z4: nat] :
% 0.32/0.51      ! [X4: nat] :
% 0.32/0.51        ( ( ord_less_nat @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(4)
% 0.32/0.51  thf(fact_876_pinf_I4_J,axiom,
% 0.32/0.51      ! [T: int] :
% 0.32/0.51      ? [Z4: int] :
% 0.32/0.51      ! [X4: int] :
% 0.32/0.51        ( ( ord_less_int @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(4)
% 0.32/0.51  thf(fact_877_pinf_I3_J,axiom,
% 0.32/0.51      ! [T: code_integer] :
% 0.32/0.51      ? [Z4: code_integer] :
% 0.32/0.51      ! [X4: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(3)
% 0.32/0.51  thf(fact_878_pinf_I3_J,axiom,
% 0.32/0.51      ! [T: rat] :
% 0.32/0.51      ? [Z4: rat] :
% 0.32/0.51      ! [X4: rat] :
% 0.32/0.51        ( ( ord_less_rat @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(3)
% 0.32/0.51  thf(fact_879_pinf_I3_J,axiom,
% 0.32/0.51      ! [T: num] :
% 0.32/0.51      ? [Z4: num] :
% 0.32/0.51      ! [X4: num] :
% 0.32/0.51        ( ( ord_less_num @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(3)
% 0.32/0.51  thf(fact_880_pinf_I3_J,axiom,
% 0.32/0.51      ! [T: nat] :
% 0.32/0.51      ? [Z4: nat] :
% 0.32/0.51      ! [X4: nat] :
% 0.32/0.51        ( ( ord_less_nat @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(3)
% 0.32/0.51  thf(fact_881_pinf_I3_J,axiom,
% 0.32/0.51      ! [T: int] :
% 0.32/0.51      ? [Z4: int] :
% 0.32/0.51      ! [X4: int] :
% 0.32/0.51        ( ( ord_less_int @ Z4 @ X4 )
% 0.32/0.51       => ( X4 != T ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(3)
% 0.32/0.51  thf(fact_882_pinf_I2_J,axiom,
% 0.32/0.51      ! [P: code_integer > $o,P2: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 0.32/0.51        ( ? [Z5: code_integer] :
% 0.32/0.51          ! [X3: code_integer] :
% 0.32/0.51            ( ( ord_le6747313008572928689nteger @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: code_integer] :
% 0.32/0.51            ! [X3: code_integer] :
% 0.32/0.51              ( ( ord_le6747313008572928689nteger @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: code_integer] :
% 0.32/0.51            ! [X4: code_integer] :
% 0.32/0.51              ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(2)
% 0.32/0.51  thf(fact_883_pinf_I2_J,axiom,
% 0.32/0.51      ! [P: rat > $o,P2: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 0.32/0.51        ( ? [Z5: rat] :
% 0.32/0.51          ! [X3: rat] :
% 0.32/0.51            ( ( ord_less_rat @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: rat] :
% 0.32/0.51            ! [X3: rat] :
% 0.32/0.51              ( ( ord_less_rat @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: rat] :
% 0.32/0.51            ! [X4: rat] :
% 0.32/0.51              ( ( ord_less_rat @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(2)
% 0.32/0.51  thf(fact_884_pinf_I2_J,axiom,
% 0.32/0.51      ! [P: num > $o,P2: num > $o,Q: num > $o,Q3: num > $o] :
% 0.32/0.51        ( ? [Z5: num] :
% 0.32/0.51          ! [X3: num] :
% 0.32/0.51            ( ( ord_less_num @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: num] :
% 0.32/0.51            ! [X3: num] :
% 0.32/0.51              ( ( ord_less_num @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: num] :
% 0.32/0.51            ! [X4: num] :
% 0.32/0.51              ( ( ord_less_num @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(2)
% 0.32/0.51  thf(fact_885_pinf_I2_J,axiom,
% 0.32/0.51      ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 0.32/0.51        ( ? [Z5: nat] :
% 0.32/0.51          ! [X3: nat] :
% 0.32/0.51            ( ( ord_less_nat @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: nat] :
% 0.32/0.51            ! [X3: nat] :
% 0.32/0.51              ( ( ord_less_nat @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: nat] :
% 0.32/0.51            ! [X4: nat] :
% 0.32/0.51              ( ( ord_less_nat @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(2)
% 0.32/0.51  thf(fact_886_pinf_I2_J,axiom,
% 0.32/0.51      ! [P: int > $o,P2: int > $o,Q: int > $o,Q3: int > $o] :
% 0.32/0.51        ( ? [Z5: int] :
% 0.32/0.51          ! [X3: int] :
% 0.32/0.51            ( ( ord_less_int @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: int] :
% 0.32/0.51            ! [X3: int] :
% 0.32/0.51              ( ( ord_less_int @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: int] :
% 0.32/0.51            ! [X4: int] :
% 0.32/0.51              ( ( ord_less_int @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  | ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(2)
% 0.32/0.51  thf(fact_887_pinf_I1_J,axiom,
% 0.32/0.51      ! [P: code_integer > $o,P2: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 0.32/0.51        ( ? [Z5: code_integer] :
% 0.32/0.51          ! [X3: code_integer] :
% 0.32/0.51            ( ( ord_le6747313008572928689nteger @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: code_integer] :
% 0.32/0.51            ! [X3: code_integer] :
% 0.32/0.51              ( ( ord_le6747313008572928689nteger @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: code_integer] :
% 0.32/0.51            ! [X4: code_integer] :
% 0.32/0.51              ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(1)
% 0.32/0.51  thf(fact_888_pinf_I1_J,axiom,
% 0.32/0.51      ! [P: rat > $o,P2: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 0.32/0.51        ( ? [Z5: rat] :
% 0.32/0.51          ! [X3: rat] :
% 0.32/0.51            ( ( ord_less_rat @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: rat] :
% 0.32/0.51            ! [X3: rat] :
% 0.32/0.51              ( ( ord_less_rat @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: rat] :
% 0.32/0.51            ! [X4: rat] :
% 0.32/0.51              ( ( ord_less_rat @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(1)
% 0.32/0.51  thf(fact_889_pinf_I1_J,axiom,
% 0.32/0.51      ! [P: num > $o,P2: num > $o,Q: num > $o,Q3: num > $o] :
% 0.32/0.51        ( ? [Z5: num] :
% 0.32/0.51          ! [X3: num] :
% 0.32/0.51            ( ( ord_less_num @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: num] :
% 0.32/0.51            ! [X3: num] :
% 0.32/0.51              ( ( ord_less_num @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: num] :
% 0.32/0.51            ! [X4: num] :
% 0.32/0.51              ( ( ord_less_num @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(1)
% 0.32/0.51  thf(fact_890_pinf_I1_J,axiom,
% 0.32/0.51      ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 0.32/0.51        ( ? [Z5: nat] :
% 0.32/0.51          ! [X3: nat] :
% 0.32/0.51            ( ( ord_less_nat @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: nat] :
% 0.32/0.51            ! [X3: nat] :
% 0.32/0.51              ( ( ord_less_nat @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: nat] :
% 0.32/0.51            ! [X4: nat] :
% 0.32/0.51              ( ( ord_less_nat @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(1)
% 0.32/0.51  thf(fact_891_pinf_I1_J,axiom,
% 0.32/0.51      ! [P: int > $o,P2: int > $o,Q: int > $o,Q3: int > $o] :
% 0.32/0.51        ( ? [Z5: int] :
% 0.32/0.51          ! [X3: int] :
% 0.32/0.51            ( ( ord_less_int @ Z5 @ X3 )
% 0.32/0.51           => ( ( P @ X3 )
% 0.32/0.51              = ( P2 @ X3 ) ) )
% 0.32/0.51       => ( ? [Z5: int] :
% 0.32/0.51            ! [X3: int] :
% 0.32/0.51              ( ( ord_less_int @ Z5 @ X3 )
% 0.32/0.51             => ( ( Q @ X3 )
% 0.32/0.51                = ( Q3 @ X3 ) ) )
% 0.32/0.51         => ? [Z4: int] :
% 0.32/0.51            ! [X4: int] :
% 0.32/0.51              ( ( ord_less_int @ Z4 @ X4 )
% 0.32/0.51             => ( ( ( P @ X4 )
% 0.32/0.51                  & ( Q @ X4 ) )
% 0.32/0.51                = ( ( P2 @ X4 )
% 0.32/0.51                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % pinf(1)
% 0.32/0.51  thf(fact_892_lt__ex,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51      ? [Y2: rat] : ( ord_less_rat @ Y2 @ X2 ) ).
% 0.32/0.51  
% 0.32/0.51  % lt_ex
% 0.32/0.51  thf(fact_893_lt__ex,axiom,
% 0.32/0.51      ! [X2: int] :
% 0.32/0.51      ? [Y2: int] : ( ord_less_int @ Y2 @ X2 ) ).
% 0.32/0.51  
% 0.32/0.51  % lt_ex
% 0.32/0.51  thf(fact_894_gt__ex,axiom,
% 0.32/0.51      ! [X2: rat] :
% 0.32/0.51      ? [X_12: rat] : ( ord_less_rat @ X2 @ X_12 ) ).
% 0.32/0.51  
% 0.32/0.51  % gt_ex
% 0.32/0.51  thf(fact_895_gt__ex,axiom,
% 0.32/0.51      ! [X2: nat] :
% 0.32/0.51      ? [X_12: nat] : ( ord_less_nat @ X2 @ X_12 ) ).
% 0.32/0.51  
% 0.32/0.51  % gt_ex
% 0.32/0.51  thf(fact_896_gt__ex,axiom,
% 0.32/0.51      ! [X2: int] :
% 0.32/0.51      ? [X_12: int] : ( ord_less_int @ X2 @ X_12 ) ).
% 0.32/0.51  
% 0.32/0.51  % gt_ex
% 0.32/0.51  thf(fact_897_dense,axiom,
% 0.32/0.51      ! [X2: rat,Y: rat] :
% 0.32/0.51        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.51       => ? [Z4: rat] :
% 0.32/0.51            ( ( ord_less_rat @ X2 @ Z4 )
% 0.32/0.51            & ( ord_less_rat @ Z4 @ Y ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % dense
% 0.32/0.51  thf(fact_898_less__imp__neq,axiom,
% 0.32/0.51      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_imp_neq
% 0.32/0.51  thf(fact_899_less__imp__neq,axiom,
% 0.32/0.51      ! [X2: rat,Y: rat] :
% 0.32/0.51        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_imp_neq
% 0.32/0.51  thf(fact_900_less__imp__neq,axiom,
% 0.32/0.51      ! [X2: num,Y: num] :
% 0.32/0.51        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_imp_neq
% 0.32/0.51  thf(fact_901_less__imp__neq,axiom,
% 0.32/0.51      ! [X2: nat,Y: nat] :
% 0.32/0.51        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_imp_neq
% 0.32/0.51  thf(fact_902_less__imp__neq,axiom,
% 0.32/0.51      ! [X2: int,Y: int] :
% 0.32/0.51        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.51       => ( X2 != Y ) ) ).
% 0.32/0.51  
% 0.32/0.51  % less_imp_neq
% 0.32/0.51  thf(fact_903_order_Oasym,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer] :
% 0.32/0.51        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.51       => ~ ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % order.asym
% 0.32/0.51  thf(fact_904_order_Oasym,axiom,
% 0.32/0.51      ! [A: rat,B: rat] :
% 0.32/0.51        ( ( ord_less_rat @ A @ B )
% 0.32/0.51       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % order.asym
% 0.32/0.51  thf(fact_905_order_Oasym,axiom,
% 0.32/0.51      ! [A: num,B: num] :
% 0.32/0.51        ( ( ord_less_num @ A @ B )
% 0.32/0.51       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % order.asym
% 0.32/0.51  thf(fact_906_order_Oasym,axiom,
% 0.32/0.51      ! [A: nat,B: nat] :
% 0.32/0.51        ( ( ord_less_nat @ A @ B )
% 0.32/0.51       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % order.asym
% 0.32/0.51  thf(fact_907_order_Oasym,axiom,
% 0.32/0.51      ! [A: int,B: int] :
% 0.32/0.51        ( ( ord_less_int @ A @ B )
% 0.32/0.51       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.32/0.51  
% 0.32/0.51  % order.asym
% 0.32/0.51  thf(fact_908_ord__eq__less__trans,axiom,
% 0.32/0.51      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.51        ( ( A = B )
% 0.32/0.51       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.51         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ord_eq_less_trans
% 0.32/0.51  thf(fact_909_ord__eq__less__trans,axiom,
% 0.32/0.51      ! [A: rat,B: rat,C: rat] :
% 0.32/0.51        ( ( A = B )
% 0.32/0.51       => ( ( ord_less_rat @ B @ C )
% 0.32/0.51         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ord_eq_less_trans
% 0.32/0.51  thf(fact_910_ord__eq__less__trans,axiom,
% 0.32/0.51      ! [A: num,B: num,C: num] :
% 0.32/0.51        ( ( A = B )
% 0.32/0.51       => ( ( ord_less_num @ B @ C )
% 0.32/0.51         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.51  
% 0.32/0.51  % ord_eq_less_trans
% 0.32/0.51  thf(fact_911_ord__eq__less__trans,axiom,
% 0.32/0.51      ! [A: nat,B: nat,C: nat] :
% 0.32/0.51        ( ( A = B )
% 0.32/0.51       => ( ( ord_less_nat @ B @ C )
% 0.32/0.52         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_trans
% 0.32/0.52  thf(fact_912_ord__eq__less__trans,axiom,
% 0.32/0.52      ! [A: int,B: int,C: int] :
% 0.32/0.52        ( ( A = B )
% 0.32/0.52       => ( ( ord_less_int @ B @ C )
% 0.32/0.52         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_trans
% 0.32/0.52  thf(fact_913_ord__less__eq__trans,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( B = C )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_trans
% 0.32/0.52  thf(fact_914_ord__less__eq__trans,axiom,
% 0.32/0.52      ! [A: rat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( B = C )
% 0.32/0.52         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_trans
% 0.32/0.52  thf(fact_915_ord__less__eq__trans,axiom,
% 0.32/0.52      ! [A: num,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_num @ A @ B )
% 0.32/0.52       => ( ( B = C )
% 0.32/0.52         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_trans
% 0.32/0.52  thf(fact_916_ord__less__eq__trans,axiom,
% 0.32/0.52      ! [A: nat,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( ( B = C )
% 0.32/0.52         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_trans
% 0.32/0.52  thf(fact_917_ord__less__eq__trans,axiom,
% 0.32/0.52      ! [A: int,B: int,C: int] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( ( B = C )
% 0.32/0.52         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_trans
% 0.32/0.52  thf(fact_918_less__induct,axiom,
% 0.32/0.52      ! [P: nat > $o,A: nat] :
% 0.32/0.52        ( ! [X3: nat] :
% 0.32/0.52            ( ! [Y5: nat] :
% 0.32/0.52                ( ( ord_less_nat @ Y5 @ X3 )
% 0.32/0.52               => ( P @ Y5 ) )
% 0.32/0.52           => ( P @ X3 ) )
% 0.32/0.52       => ( P @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_induct
% 0.32/0.52  thf(fact_919_antisym__conv3,axiom,
% 0.32/0.52      ! [Y: code_integer,X2: code_integer] :
% 0.32/0.52        ( ~ ( ord_le6747313008572928689nteger @ Y @ X2 )
% 0.32/0.52       => ( ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv3
% 0.32/0.52  thf(fact_920_antisym__conv3,axiom,
% 0.32/0.52      ! [Y: rat,X2: rat] :
% 0.32/0.52        ( ~ ( ord_less_rat @ Y @ X2 )
% 0.32/0.52       => ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv3
% 0.32/0.52  thf(fact_921_antisym__conv3,axiom,
% 0.32/0.52      ! [Y: num,X2: num] :
% 0.32/0.52        ( ~ ( ord_less_num @ Y @ X2 )
% 0.32/0.52       => ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv3
% 0.32/0.52  thf(fact_922_antisym__conv3,axiom,
% 0.32/0.52      ! [Y: nat,X2: nat] :
% 0.32/0.52        ( ~ ( ord_less_nat @ Y @ X2 )
% 0.32/0.52       => ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv3
% 0.32/0.52  thf(fact_923_antisym__conv3,axiom,
% 0.32/0.52      ! [Y: int,X2: int] :
% 0.32/0.52        ( ~ ( ord_less_int @ Y @ X2 )
% 0.32/0.52       => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv3
% 0.32/0.52  thf(fact_924_linorder__cases,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ( ( X2 != Y )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_cases
% 0.32/0.52  thf(fact_925_linorder__cases,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ~ ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( ( X2 != Y )
% 0.32/0.52         => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_cases
% 0.32/0.52  thf(fact_926_linorder__cases,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ~ ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ( ( X2 != Y )
% 0.32/0.52         => ( ord_less_num @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_cases
% 0.32/0.52  thf(fact_927_linorder__cases,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ~ ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ( ( X2 != Y )
% 0.32/0.52         => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_cases
% 0.32/0.52  thf(fact_928_linorder__cases,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ~ ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ( ( X2 != Y )
% 0.32/0.52         => ( ord_less_int @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_cases
% 0.32/0.52  thf(fact_929_dual__order_Oasym,axiom,
% 0.32/0.52      ! [B: code_integer,A: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.52       => ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.asym
% 0.32/0.52  thf(fact_930_dual__order_Oasym,axiom,
% 0.32/0.52      ! [B: rat,A: rat] :
% 0.32/0.52        ( ( ord_less_rat @ B @ A )
% 0.32/0.52       => ~ ( ord_less_rat @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.asym
% 0.32/0.52  thf(fact_931_dual__order_Oasym,axiom,
% 0.32/0.52      ! [B: num,A: num] :
% 0.32/0.52        ( ( ord_less_num @ B @ A )
% 0.32/0.52       => ~ ( ord_less_num @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.asym
% 0.32/0.52  thf(fact_932_dual__order_Oasym,axiom,
% 0.32/0.52      ! [B: nat,A: nat] :
% 0.32/0.52        ( ( ord_less_nat @ B @ A )
% 0.32/0.52       => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.asym
% 0.32/0.52  thf(fact_933_dual__order_Oasym,axiom,
% 0.32/0.52      ! [B: int,A: int] :
% 0.32/0.52        ( ( ord_less_int @ B @ A )
% 0.32/0.52       => ~ ( ord_less_int @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.asym
% 0.32/0.52  thf(fact_934_dual__order_Oirrefl,axiom,
% 0.32/0.52      ! [A: code_integer] :
% 0.32/0.52        ~ ( ord_le6747313008572928689nteger @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.irrefl
% 0.32/0.52  thf(fact_935_dual__order_Oirrefl,axiom,
% 0.32/0.52      ! [A: rat] :
% 0.32/0.52        ~ ( ord_less_rat @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.irrefl
% 0.32/0.52  thf(fact_936_dual__order_Oirrefl,axiom,
% 0.32/0.52      ! [A: num] :
% 0.32/0.52        ~ ( ord_less_num @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.irrefl
% 0.32/0.52  thf(fact_937_dual__order_Oirrefl,axiom,
% 0.32/0.52      ! [A: nat] :
% 0.32/0.52        ~ ( ord_less_nat @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.irrefl
% 0.32/0.52  thf(fact_938_dual__order_Oirrefl,axiom,
% 0.32/0.52      ! [A: int] :
% 0.32/0.52        ~ ( ord_less_int @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.irrefl
% 0.32/0.52  thf(fact_939_exists__least__iff,axiom,
% 0.32/0.52      ( ( ^ [P4: nat > $o] :
% 0.32/0.52          ? [X7: nat] : ( P4 @ X7 ) )
% 0.32/0.52      = ( ^ [P5: nat > $o] :
% 0.32/0.52          ? [N3: nat] :
% 0.32/0.52            ( ( P5 @ N3 )
% 0.32/0.52            & ! [M2: nat] :
% 0.32/0.52                ( ( ord_less_nat @ M2 @ N3 )
% 0.32/0.52               => ~ ( P5 @ M2 ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % exists_least_iff
% 0.32/0.52  thf(fact_940_linorder__less__wlog,axiom,
% 0.32/0.52      ! [P: code_integer > code_integer > $o,A: code_integer,B: code_integer] :
% 0.32/0.52        ( ! [A3: code_integer,B3: code_integer] :
% 0.32/0.52            ( ( ord_le6747313008572928689nteger @ A3 @ B3 )
% 0.32/0.52           => ( P @ A3 @ B3 ) )
% 0.32/0.52       => ( ! [A3: code_integer] : ( P @ A3 @ A3 )
% 0.32/0.52         => ( ! [A3: code_integer,B3: code_integer] :
% 0.32/0.52                ( ( P @ B3 @ A3 )
% 0.32/0.52               => ( P @ A3 @ B3 ) )
% 0.32/0.52           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_wlog
% 0.32/0.52  thf(fact_941_linorder__less__wlog,axiom,
% 0.32/0.52      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.32/0.52        ( ! [A3: rat,B3: rat] :
% 0.32/0.52            ( ( ord_less_rat @ A3 @ B3 )
% 0.32/0.52           => ( P @ A3 @ B3 ) )
% 0.32/0.52       => ( ! [A3: rat] : ( P @ A3 @ A3 )
% 0.32/0.52         => ( ! [A3: rat,B3: rat] :
% 0.32/0.52                ( ( P @ B3 @ A3 )
% 0.32/0.52               => ( P @ A3 @ B3 ) )
% 0.32/0.52           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_wlog
% 0.32/0.52  thf(fact_942_linorder__less__wlog,axiom,
% 0.32/0.52      ! [P: num > num > $o,A: num,B: num] :
% 0.32/0.52        ( ! [A3: num,B3: num] :
% 0.32/0.52            ( ( ord_less_num @ A3 @ B3 )
% 0.32/0.52           => ( P @ A3 @ B3 ) )
% 0.32/0.52       => ( ! [A3: num] : ( P @ A3 @ A3 )
% 0.32/0.52         => ( ! [A3: num,B3: num] :
% 0.32/0.52                ( ( P @ B3 @ A3 )
% 0.32/0.52               => ( P @ A3 @ B3 ) )
% 0.32/0.52           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_wlog
% 0.32/0.52  thf(fact_943_linorder__less__wlog,axiom,
% 0.32/0.52      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.32/0.52        ( ! [A3: nat,B3: nat] :
% 0.32/0.52            ( ( ord_less_nat @ A3 @ B3 )
% 0.32/0.52           => ( P @ A3 @ B3 ) )
% 0.32/0.52       => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 0.32/0.52         => ( ! [A3: nat,B3: nat] :
% 0.32/0.52                ( ( P @ B3 @ A3 )
% 0.32/0.52               => ( P @ A3 @ B3 ) )
% 0.32/0.52           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_wlog
% 0.32/0.52  thf(fact_944_linorder__less__wlog,axiom,
% 0.32/0.52      ! [P: int > int > $o,A: int,B: int] :
% 0.32/0.52        ( ! [A3: int,B3: int] :
% 0.32/0.52            ( ( ord_less_int @ A3 @ B3 )
% 0.32/0.52           => ( P @ A3 @ B3 ) )
% 0.32/0.52       => ( ! [A3: int] : ( P @ A3 @ A3 )
% 0.32/0.52         => ( ! [A3: int,B3: int] :
% 0.32/0.52                ( ( P @ B3 @ A3 )
% 0.32/0.52               => ( P @ A3 @ B3 ) )
% 0.32/0.52           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_wlog
% 0.32/0.52  thf(fact_945_order_Ostrict__trans,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans
% 0.32/0.52  thf(fact_946_order_Ostrict__trans,axiom,
% 0.32/0.52      ! [A: rat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans
% 0.32/0.52  thf(fact_947_order_Ostrict__trans,axiom,
% 0.32/0.52      ! [A: num,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_num @ A @ B )
% 0.32/0.52       => ( ( ord_less_num @ B @ C )
% 0.32/0.52         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans
% 0.32/0.52  thf(fact_948_order_Ostrict__trans,axiom,
% 0.32/0.52      ! [A: nat,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( ( ord_less_nat @ B @ C )
% 0.32/0.52         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans
% 0.32/0.52  thf(fact_949_order_Ostrict__trans,axiom,
% 0.32/0.52      ! [A: int,B: int,C: int] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( ( ord_less_int @ B @ C )
% 0.32/0.52         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans
% 0.32/0.52  thf(fact_950_not__less__iff__gr__or__eq,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) )
% 0.32/0.52        = ( ( ord_le6747313008572928689nteger @ Y @ X2 )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_less_iff_gr_or_eq
% 0.32/0.52  thf(fact_951_not__less__iff__gr__or__eq,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 0.32/0.52        = ( ( ord_less_rat @ Y @ X2 )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_less_iff_gr_or_eq
% 0.32/0.52  thf(fact_952_not__less__iff__gr__or__eq,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 0.32/0.52        = ( ( ord_less_num @ Y @ X2 )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_less_iff_gr_or_eq
% 0.32/0.52  thf(fact_953_not__less__iff__gr__or__eq,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 0.32/0.52        = ( ( ord_less_nat @ Y @ X2 )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_less_iff_gr_or_eq
% 0.32/0.52  thf(fact_954_not__less__iff__gr__or__eq,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 0.32/0.52        = ( ( ord_less_int @ Y @ X2 )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_less_iff_gr_or_eq
% 0.32/0.52  thf(fact_955_dual__order_Ostrict__trans,axiom,
% 0.32/0.52      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ C @ B )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans
% 0.32/0.52  thf(fact_956_dual__order_Ostrict__trans,axiom,
% 0.32/0.52      ! [B: rat,A: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ B @ A )
% 0.32/0.52       => ( ( ord_less_rat @ C @ B )
% 0.32/0.52         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans
% 0.32/0.52  thf(fact_957_dual__order_Ostrict__trans,axiom,
% 0.32/0.52      ! [B: num,A: num,C: num] :
% 0.32/0.52        ( ( ord_less_num @ B @ A )
% 0.32/0.52       => ( ( ord_less_num @ C @ B )
% 0.32/0.52         => ( ord_less_num @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans
% 0.32/0.52  thf(fact_958_dual__order_Ostrict__trans,axiom,
% 0.32/0.52      ! [B: nat,A: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_nat @ B @ A )
% 0.32/0.52       => ( ( ord_less_nat @ C @ B )
% 0.32/0.52         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans
% 0.32/0.52  thf(fact_959_dual__order_Ostrict__trans,axiom,
% 0.32/0.52      ! [B: int,A: int,C: int] :
% 0.32/0.52        ( ( ord_less_int @ B @ A )
% 0.32/0.52       => ( ( ord_less_int @ C @ B )
% 0.32/0.52         => ( ord_less_int @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans
% 0.32/0.52  thf(fact_960_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_not_eq
% 0.32/0.52  thf(fact_961_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [A: rat,B: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_not_eq
% 0.32/0.52  thf(fact_962_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [A: num,B: num] :
% 0.32/0.52        ( ( ord_less_num @ A @ B )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_not_eq
% 0.32/0.52  thf(fact_963_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [A: nat,B: nat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_not_eq
% 0.32/0.52  thf(fact_964_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [A: int,B: int] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_not_eq
% 0.32/0.52  thf(fact_965_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [B: code_integer,A: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_not_eq
% 0.32/0.52  thf(fact_966_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [B: rat,A: rat] :
% 0.32/0.52        ( ( ord_less_rat @ B @ A )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_not_eq
% 0.32/0.52  thf(fact_967_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [B: num,A: num] :
% 0.32/0.52        ( ( ord_less_num @ B @ A )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_not_eq
% 0.32/0.52  thf(fact_968_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [B: nat,A: nat] :
% 0.32/0.52        ( ( ord_less_nat @ B @ A )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_not_eq
% 0.32/0.52  thf(fact_969_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.52      ! [B: int,A: int] :
% 0.32/0.52        ( ( ord_less_int @ B @ A )
% 0.32/0.52       => ( A != B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_not_eq
% 0.32/0.52  thf(fact_970_linorder__neqE,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52       => ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neqE
% 0.32/0.52  thf(fact_971_linorder__neqE,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52       => ( ~ ( ord_less_rat @ X2 @ Y )
% 0.32/0.52         => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neqE
% 0.32/0.52  thf(fact_972_linorder__neqE,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52       => ( ~ ( ord_less_num @ X2 @ Y )
% 0.32/0.52         => ( ord_less_num @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neqE
% 0.32/0.52  thf(fact_973_linorder__neqE,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52       => ( ~ ( ord_less_nat @ X2 @ Y )
% 0.32/0.52         => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neqE
% 0.32/0.52  thf(fact_974_linorder__neqE,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52       => ( ~ ( ord_less_int @ X2 @ Y )
% 0.32/0.52         => ( ord_less_int @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neqE
% 0.32/0.52  thf(fact_975_order__less__asym,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym
% 0.32/0.52  thf(fact_976_order__less__asym,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym
% 0.32/0.52  thf(fact_977_order__less__asym,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym
% 0.32/0.52  thf(fact_978_order__less__asym,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym
% 0.32/0.52  thf(fact_979_order__less__asym,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym
% 0.32/0.52  thf(fact_980_linorder__neq__iff,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52        = ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52          | ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neq_iff
% 0.32/0.52  thf(fact_981_linorder__neq__iff,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52        = ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52          | ( ord_less_rat @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neq_iff
% 0.32/0.52  thf(fact_982_linorder__neq__iff,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52        = ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52          | ( ord_less_num @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neq_iff
% 0.32/0.52  thf(fact_983_linorder__neq__iff,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52        = ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52          | ( ord_less_nat @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neq_iff
% 0.32/0.52  thf(fact_984_linorder__neq__iff,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( X2 != Y )
% 0.32/0.52        = ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52          | ( ord_less_int @ Y @ X2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_neq_iff
% 0.32/0.52  thf(fact_985_order__less__asym_H,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ~ ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym'
% 0.32/0.52  thf(fact_986_order__less__asym_H,axiom,
% 0.32/0.52      ! [A: rat,B: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym'
% 0.32/0.52  thf(fact_987_order__less__asym_H,axiom,
% 0.32/0.52      ! [A: num,B: num] :
% 0.32/0.52        ( ( ord_less_num @ A @ B )
% 0.32/0.52       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym'
% 0.32/0.52  thf(fact_988_order__less__asym_H,axiom,
% 0.32/0.52      ! [A: nat,B: nat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym'
% 0.32/0.52  thf(fact_989_order__less__asym_H,axiom,
% 0.32/0.52      ! [A: int,B: int] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_asym'
% 0.32/0.52  thf(fact_990_order__less__trans,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer,Z2: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ Y @ Z2 )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_trans
% 0.32/0.52  thf(fact_991_order__less__trans,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat,Z2: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_rat @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_rat @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_trans
% 0.32/0.52  thf(fact_992_order__less__trans,axiom,
% 0.32/0.52      ! [X2: num,Y: num,Z2: num] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_num @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_num @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_trans
% 0.32/0.52  thf(fact_993_order__less__trans,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat,Z2: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_nat @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_trans
% 0.32/0.52  thf(fact_994_order__less__trans,axiom,
% 0.32/0.52      ! [X2: int,Y: int,Z2: int] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_int @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_int @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_trans
% 0.32/0.52  thf(fact_995_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: code_integer,F: code_integer > code_integer,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_996_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: rat,F: code_integer > rat,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_997_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: num,F: code_integer > num,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_998_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: nat,F: code_integer > nat,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_999_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: int,F: code_integer > int,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_1000_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_1001_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_1002_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_1003_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_1004_ord__eq__less__subst,axiom,
% 0.32/0.52      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.32/0.52        ( ( A
% 0.32/0.52          = ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_eq_less_subst
% 0.32/0.52  thf(fact_1005_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1006_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > rat,C: rat] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1007_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > num,C: num] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1008_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > nat,C: nat] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1009_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > int,C: int] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1010_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1011_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1012_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1013_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1014_ord__less__eq__subst,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ( F @ B )
% 0.32/0.52            = C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ord_less_eq_subst
% 0.32/0.52  thf(fact_1015_order__less__irrefl,axiom,
% 0.32/0.52      ! [X2: code_integer] :
% 0.32/0.52        ~ ( ord_le6747313008572928689nteger @ X2 @ X2 ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_irrefl
% 0.32/0.52  thf(fact_1016_order__less__irrefl,axiom,
% 0.32/0.52      ! [X2: rat] :
% 0.32/0.52        ~ ( ord_less_rat @ X2 @ X2 ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_irrefl
% 0.32/0.52  thf(fact_1017_order__less__irrefl,axiom,
% 0.32/0.52      ! [X2: num] :
% 0.32/0.52        ~ ( ord_less_num @ X2 @ X2 ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_irrefl
% 0.32/0.52  thf(fact_1018_order__less__irrefl,axiom,
% 0.32/0.52      ! [X2: nat] :
% 0.32/0.52        ~ ( ord_less_nat @ X2 @ X2 ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_irrefl
% 0.32/0.52  thf(fact_1019_order__less__irrefl,axiom,
% 0.32/0.52      ! [X2: int] :
% 0.32/0.52        ~ ( ord_less_int @ X2 @ X2 ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_irrefl
% 0.32/0.52  thf(fact_1020_order__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: code_integer > code_integer,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1021_order__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1022_order__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: num > code_integer,B: num,C: num] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_num @ B @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1023_order__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: nat > code_integer,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_nat @ B @ C )
% 0.32/0.52         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.52                ( ( ord_less_nat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1024_order__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: int > code_integer,B: int,C: int] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_int @ B @ C )
% 0.32/0.52         => ( ! [X3: int,Y2: int] :
% 0.32/0.52                ( ( ord_less_int @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1025_order__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: code_integer > rat,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1026_order__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1027_order__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_num @ B @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1028_order__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_nat @ B @ C )
% 0.32/0.52         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.52                ( ( ord_less_nat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1029_order__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.32/0.52        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_int @ B @ C )
% 0.32/0.52         => ( ! [X3: int,Y2: int] :
% 0.32/0.52                ( ( ord_less_int @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst1
% 0.32/0.52  thf(fact_1030_order__less__subst2,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1031_order__less__subst2,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > rat,C: rat] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1032_order__less__subst2,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > num,C: num] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1033_order__less__subst2,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > nat,C: nat] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1034_order__less__subst2,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > int,C: int] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1035_order__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1036_order__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1037_order__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1038_order__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1039_order__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_subst2
% 0.32/0.52  thf(fact_1040_order__less__not__sym,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_not_sym
% 0.32/0.52  thf(fact_1041_order__less__not__sym,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_not_sym
% 0.32/0.52  thf(fact_1042_order__less__not__sym,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_not_sym
% 0.32/0.52  thf(fact_1043_order__less__not__sym,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_not_sym
% 0.32/0.52  thf(fact_1044_order__less__not__sym,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_not_sym
% 0.32/0.52  thf(fact_1045_order__less__imp__triv,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer,P: $o] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ Y @ X2 )
% 0.32/0.52         => P ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_triv
% 0.32/0.52  thf(fact_1046_order__less__imp__triv,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat,P: $o] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_rat @ Y @ X2 )
% 0.32/0.52         => P ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_triv
% 0.32/0.52  thf(fact_1047_order__less__imp__triv,axiom,
% 0.32/0.52      ! [X2: num,Y: num,P: $o] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_num @ Y @ X2 )
% 0.32/0.52         => P ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_triv
% 0.32/0.52  thf(fact_1048_order__less__imp__triv,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat,P: $o] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_nat @ Y @ X2 )
% 0.32/0.52         => P ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_triv
% 0.32/0.52  thf(fact_1049_order__less__imp__triv,axiom,
% 0.32/0.52      ! [X2: int,Y: int,P: $o] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_int @ Y @ X2 )
% 0.32/0.52         => P ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_triv
% 0.32/0.52  thf(fact_1050_linorder__less__linear,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52        | ( X2 = Y )
% 0.32/0.52        | ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_linear
% 0.32/0.52  thf(fact_1051_linorder__less__linear,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52        | ( X2 = Y )
% 0.32/0.52        | ( ord_less_rat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_linear
% 0.32/0.52  thf(fact_1052_linorder__less__linear,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52        | ( X2 = Y )
% 0.32/0.52        | ( ord_less_num @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_linear
% 0.32/0.52  thf(fact_1053_linorder__less__linear,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52        | ( X2 = Y )
% 0.32/0.52        | ( ord_less_nat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_linear
% 0.32/0.52  thf(fact_1054_linorder__less__linear,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52        | ( X2 = Y )
% 0.32/0.52        | ( ord_less_int @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_less_linear
% 0.32/0.52  thf(fact_1055_order__less__imp__not__eq,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ( X2 != Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq
% 0.32/0.52  thf(fact_1056_order__less__imp__not__eq,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( X2 != Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq
% 0.32/0.52  thf(fact_1057_order__less__imp__not__eq,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ( X2 != Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq
% 0.32/0.52  thf(fact_1058_order__less__imp__not__eq,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ( X2 != Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq
% 0.32/0.52  thf(fact_1059_order__less__imp__not__eq,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ( X2 != Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq
% 0.32/0.52  thf(fact_1060_order__less__imp__not__eq2,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ( Y != X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq2
% 0.32/0.52  thf(fact_1061_order__less__imp__not__eq2,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( Y != X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq2
% 0.32/0.52  thf(fact_1062_order__less__imp__not__eq2,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ( Y != X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq2
% 0.32/0.52  thf(fact_1063_order__less__imp__not__eq2,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ( Y != X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq2
% 0.32/0.52  thf(fact_1064_order__less__imp__not__eq2,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ( Y != X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_eq2
% 0.32/0.52  thf(fact_1065_order__less__imp__not__less,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_less
% 0.32/0.52  thf(fact_1066_order__less__imp__not__less,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_less
% 0.32/0.52  thf(fact_1067_order__less__imp__not__less,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_less
% 0.32/0.52  thf(fact_1068_order__less__imp__not__less,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_less
% 0.32/0.52  thf(fact_1069_order__less__imp__not__less,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_not_less
% 0.32/0.52  thf(fact_1070_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.52      ! [A: code_integer] :
% 0.32/0.52        ~ ( ord_le6747313008572928689nteger @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(1)
% 0.32/0.52  thf(fact_1071_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.52      ! [A: rat] :
% 0.32/0.52        ~ ( ord_less_rat @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(1)
% 0.32/0.52  thf(fact_1072_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.52      ! [A: num] :
% 0.32/0.52        ~ ( ord_less_num @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(1)
% 0.32/0.52  thf(fact_1073_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.52      ! [A: nat] :
% 0.32/0.52        ~ ( ord_less_nat @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(1)
% 0.32/0.52  thf(fact_1074_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.52      ! [A: int] :
% 0.32/0.52        ~ ( ord_less_int @ A @ A ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(1)
% 0.32/0.52  thf(fact_1075_floor__less__cancel,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) )
% 0.32/0.52       => ( ord_less_rat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % floor_less_cancel
% 0.32/0.52  thf(fact_1076_zless__nat__eq__int__zless,axiom,
% 0.32/0.52      ! [M: nat,Z2: int] :
% 0.32/0.52        ( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
% 0.32/0.52        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % zless_nat_eq_int_zless
% 0.32/0.52  thf(fact_1077_nat__mono__iff,axiom,
% 0.32/0.52      ! [Z2: int,W2: int] :
% 0.32/0.52        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.32/0.52       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 0.32/0.52          = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nat_mono_iff
% 0.32/0.52  thf(fact_1078_power__int__strict__increasing,axiom,
% 0.32/0.52      ! [N: int,N4: int,A: rat] :
% 0.32/0.52        ( ( ord_less_int @ N @ N4 )
% 0.32/0.52       => ( ( ord_less_rat @ one_one_rat @ A )
% 0.32/0.52         => ( ord_less_rat @ ( power_int_rat @ A @ N ) @ ( power_int_rat @ A @ N4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % power_int_strict_increasing
% 0.32/0.52  thf(fact_1079_zero__less__power__int,axiom,
% 0.32/0.52      ! [X2: rat,N: int] :
% 0.32/0.52        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 0.32/0.52       => ( ord_less_rat @ zero_zero_rat @ ( power_int_rat @ X2 @ N ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % zero_less_power_int
% 0.32/0.52  thf(fact_1080_less__imp__of__nat__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_nat @ M @ N )
% 0.32/0.52       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_imp_of_nat_less
% 0.32/0.52  thf(fact_1081_less__imp__of__nat__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_nat @ M @ N )
% 0.32/0.52       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_imp_of_nat_less
% 0.32/0.52  thf(fact_1082_less__imp__of__nat__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_nat @ M @ N )
% 0.32/0.52       => ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_imp_of_nat_less
% 0.32/0.52  thf(fact_1083_less__imp__of__nat__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_nat @ M @ N )
% 0.32/0.52       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_imp_of_nat_less
% 0.32/0.52  thf(fact_1084_less__imp__of__nat__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_nat @ M @ N )
% 0.32/0.52       => ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_imp_of_nat_less
% 0.32/0.52  thf(fact_1085_of__nat__less__imp__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.52       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.52  
% 0.32/0.52  % of_nat_less_imp_less
% 0.32/0.52  thf(fact_1086_of__nat__less__imp__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.52       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.52  
% 0.32/0.52  % of_nat_less_imp_less
% 0.32/0.52  thf(fact_1087_of__nat__less__imp__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.52       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.52  
% 0.32/0.52  % of_nat_less_imp_less
% 0.32/0.52  thf(fact_1088_of__nat__less__imp__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.52       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.52  
% 0.32/0.52  % of_nat_less_imp_less
% 0.32/0.52  thf(fact_1089_of__nat__less__imp__less,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) )
% 0.32/0.52       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.52  
% 0.32/0.52  % of_nat_less_imp_less
% 0.32/0.52  thf(fact_1090_nat__int__comparison_I2_J,axiom,
% 0.32/0.52      ( ord_less_nat
% 0.32/0.52      = ( ^ [A2: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nat_int_comparison(2)
% 0.32/0.52  thf(fact_1091_power__int__strict__decreasing,axiom,
% 0.32/0.52      ! [N: int,N4: int,A: rat] :
% 0.32/0.52        ( ( ord_less_int @ N @ N4 )
% 0.32/0.52       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.52         => ( ( ord_less_rat @ A @ one_one_rat )
% 0.32/0.52           => ( ord_less_rat @ ( power_int_rat @ A @ N4 ) @ ( power_int_rat @ A @ N ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % power_int_strict_decreasing
% 0.32/0.52  thf(fact_1092_power__int__strict__antimono,axiom,
% 0.32/0.52      ! [A: rat,B: rat,N: int] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.52         => ( ( ord_less_int @ N @ zero_zero_int )
% 0.32/0.52           => ( ord_less_rat @ ( power_int_rat @ B @ N ) @ ( power_int_rat @ A @ N ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % power_int_strict_antimono
% 0.32/0.52  thf(fact_1093_ceiling__less__cancel,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 0.32/0.52       => ( ord_less_rat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % ceiling_less_cancel
% 0.32/0.52  thf(fact_1094_one__less__power__int,axiom,
% 0.32/0.52      ! [A: rat,N: int] :
% 0.32/0.52        ( ( ord_less_rat @ one_one_rat @ A )
% 0.32/0.52       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.32/0.52         => ( ord_less_rat @ one_one_rat @ ( power_int_rat @ A @ N ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % one_less_power_int
% 0.32/0.52  thf(fact_1095_nat__less__eq__zless,axiom,
% 0.32/0.52      ! [W2: int,Z2: int] :
% 0.32/0.52        ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.32/0.52       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 0.32/0.52          = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nat_less_eq_zless
% 0.32/0.52  thf(fact_1096_nat__less__as__int,axiom,
% 0.32/0.52      ( ord_less_nat
% 0.32/0.52      = ( ^ [A2: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nat_less_as_int
% 0.32/0.52  thf(fact_1097_power__int__antimono,axiom,
% 0.32/0.52      ! [A: rat,B: rat,N: int] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.52         => ( ( ord_less_int @ N @ zero_zero_int )
% 0.32/0.52           => ( ord_less_eq_rat @ ( power_int_rat @ B @ N ) @ ( power_int_rat @ A @ N ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % power_int_antimono
% 0.32/0.52  thf(fact_1098_power__int__strict__mono,axiom,
% 0.32/0.52      ! [A: rat,B: rat,N: int] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.52         => ( ( ord_less_int @ zero_zero_int @ N )
% 0.32/0.52           => ( ord_less_rat @ ( power_int_rat @ A @ N ) @ ( power_int_rat @ B @ N ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % power_int_strict_mono
% 0.32/0.52  thf(fact_1099_power__int__le__imp__less__exp,axiom,
% 0.32/0.52      ! [X2: rat,M: int,N: int] :
% 0.32/0.52        ( ( ord_less_rat @ one_one_rat @ X2 )
% 0.32/0.52       => ( ( ord_less_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ X2 @ N ) )
% 0.32/0.52         => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.32/0.52           => ( ord_less_int @ M @ N ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % power_int_le_imp_less_exp
% 0.32/0.52  thf(fact_1100_nat__less__iff,axiom,
% 0.32/0.52      ! [W2: int,M: nat] :
% 0.32/0.52        ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.32/0.52       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 0.32/0.52          = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nat_less_iff
% 0.32/0.52  thf(fact_1101_less__ceiling__iff,axiom,
% 0.32/0.52      ! [Z2: int,X2: rat] :
% 0.32/0.52        ( ( ord_less_int @ Z2 @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.32/0.52        = ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_ceiling_iff
% 0.32/0.52  thf(fact_1102_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.52      ! [B5: code_integer,A5: code_integer] :
% 0.32/0.52        ( ( ~ ( ord_le3102999989581377725nteger @ B5 @ A5 ) )
% 0.32/0.52        = ( ord_le6747313008572928689nteger @ A5 @ B5 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(3)
% 0.32/0.52  thf(fact_1103_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.52      ! [B5: rat,A5: rat] :
% 0.32/0.52        ( ( ~ ( ord_less_eq_rat @ B5 @ A5 ) )
% 0.32/0.52        = ( ord_less_rat @ A5 @ B5 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(3)
% 0.32/0.52  thf(fact_1104_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.52      ! [B5: num,A5: num] :
% 0.32/0.52        ( ( ~ ( ord_less_eq_num @ B5 @ A5 ) )
% 0.32/0.52        = ( ord_less_num @ A5 @ B5 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(3)
% 0.32/0.52  thf(fact_1105_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.52      ! [B5: nat,A5: nat] :
% 0.32/0.52        ( ( ~ ( ord_less_eq_nat @ B5 @ A5 ) )
% 0.32/0.52        = ( ord_less_nat @ A5 @ B5 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(3)
% 0.32/0.52  thf(fact_1106_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.52      ! [B5: int,A5: int] :
% 0.32/0.52        ( ( ~ ( ord_less_eq_int @ B5 @ A5 ) )
% 0.32/0.52        = ( ord_less_int @ A5 @ B5 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % verit_comp_simplify1(3)
% 0.32/0.52  thf(fact_1107_leD,axiom,
% 0.32/0.52      ! [Y: code_integer,X2: code_integer] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ Y @ X2 )
% 0.32/0.52       => ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leD
% 0.32/0.52  thf(fact_1108_leD,axiom,
% 0.32/0.52      ! [Y: set_nat,X2: set_nat] :
% 0.32/0.52        ( ( ord_less_eq_set_nat @ Y @ X2 )
% 0.32/0.52       => ~ ( ord_less_set_nat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leD
% 0.32/0.52  thf(fact_1109_leD,axiom,
% 0.32/0.52      ! [Y: rat,X2: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ Y @ X2 )
% 0.32/0.52       => ~ ( ord_less_rat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leD
% 0.32/0.52  thf(fact_1110_leD,axiom,
% 0.32/0.52      ! [Y: num,X2: num] :
% 0.32/0.52        ( ( ord_less_eq_num @ Y @ X2 )
% 0.32/0.52       => ~ ( ord_less_num @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leD
% 0.32/0.52  thf(fact_1111_leD,axiom,
% 0.32/0.52      ! [Y: nat,X2: nat] :
% 0.32/0.52        ( ( ord_less_eq_nat @ Y @ X2 )
% 0.32/0.52       => ~ ( ord_less_nat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leD
% 0.32/0.52  thf(fact_1112_leD,axiom,
% 0.32/0.52      ! [Y: int,X2: int] :
% 0.32/0.52        ( ( ord_less_eq_int @ Y @ X2 )
% 0.32/0.52       => ~ ( ord_less_int @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leD
% 0.32/0.52  thf(fact_1113_leI,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ( ord_le3102999989581377725nteger @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leI
% 0.32/0.52  thf(fact_1114_leI,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ~ ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leI
% 0.32/0.52  thf(fact_1115_leI,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ~ ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leI
% 0.32/0.52  thf(fact_1116_leI,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ~ ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leI
% 0.32/0.52  thf(fact_1117_leI,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ~ ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ( ord_less_eq_int @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % leI
% 0.32/0.52  thf(fact_1118_nless__le,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer] :
% 0.32/0.52        ( ( ~ ( ord_le6747313008572928689nteger @ A @ B ) )
% 0.32/0.52        = ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.52          | ( A = B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nless_le
% 0.32/0.52  thf(fact_1119_nless__le,axiom,
% 0.32/0.52      ! [A: set_nat,B: set_nat] :
% 0.32/0.52        ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 0.32/0.52        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.52          | ( A = B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nless_le
% 0.32/0.52  thf(fact_1120_nless__le,axiom,
% 0.32/0.52      ! [A: rat,B: rat] :
% 0.32/0.52        ( ( ~ ( ord_less_rat @ A @ B ) )
% 0.32/0.52        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.32/0.52          | ( A = B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nless_le
% 0.32/0.52  thf(fact_1121_nless__le,axiom,
% 0.32/0.52      ! [A: num,B: num] :
% 0.32/0.52        ( ( ~ ( ord_less_num @ A @ B ) )
% 0.32/0.52        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.32/0.52          | ( A = B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nless_le
% 0.32/0.52  thf(fact_1122_nless__le,axiom,
% 0.32/0.52      ! [A: nat,B: nat] :
% 0.32/0.52        ( ( ~ ( ord_less_nat @ A @ B ) )
% 0.32/0.52        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.32/0.52          | ( A = B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nless_le
% 0.32/0.52  thf(fact_1123_nless__le,axiom,
% 0.32/0.52      ! [A: int,B: int] :
% 0.32/0.52        ( ( ~ ( ord_less_int @ A @ B ) )
% 0.32/0.52        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.32/0.52          | ( A = B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nless_le
% 0.32/0.52  thf(fact_1124_antisym__conv1,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv1
% 0.32/0.52  thf(fact_1125_antisym__conv1,axiom,
% 0.32/0.52      ! [X2: set_nat,Y: set_nat] :
% 0.32/0.52        ( ~ ( ord_less_set_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_set_nat @ X2 @ Y )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv1
% 0.32/0.52  thf(fact_1126_antisym__conv1,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ~ ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv1
% 0.32/0.52  thf(fact_1127_antisym__conv1,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ~ ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv1
% 0.32/0.52  thf(fact_1128_antisym__conv1,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ~ ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv1
% 0.32/0.52  thf(fact_1129_antisym__conv1,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ~ ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv1
% 0.32/0.52  thf(fact_1130_antisym__conv2,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 0.32/0.52       => ( ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv2
% 0.32/0.52  thf(fact_1131_antisym__conv2,axiom,
% 0.32/0.52      ! [X2: set_nat,Y: set_nat] :
% 0.32/0.52        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ~ ( ord_less_set_nat @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv2
% 0.32/0.52  thf(fact_1132_antisym__conv2,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.52       => ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv2
% 0.32/0.52  thf(fact_1133_antisym__conv2,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.52       => ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv2
% 0.32/0.52  thf(fact_1134_antisym__conv2,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv2
% 0.32/0.52  thf(fact_1135_antisym__conv2,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.52       => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 0.32/0.52          = ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % antisym_conv2
% 0.32/0.52  thf(fact_1136_dense__ge,axiom,
% 0.32/0.52      ! [Z2: rat,Y: rat] :
% 0.32/0.52        ( ! [X3: rat] :
% 0.32/0.52            ( ( ord_less_rat @ Z2 @ X3 )
% 0.32/0.52           => ( ord_less_eq_rat @ Y @ X3 ) )
% 0.32/0.52       => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dense_ge
% 0.32/0.52  thf(fact_1137_dense__le,axiom,
% 0.32/0.52      ! [Y: rat,Z2: rat] :
% 0.32/0.52        ( ! [X3: rat] :
% 0.32/0.52            ( ( ord_less_rat @ X3 @ Y )
% 0.32/0.52           => ( ord_less_eq_rat @ X3 @ Z2 ) )
% 0.32/0.52       => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dense_le
% 0.32/0.52  thf(fact_1138_less__le__not__le,axiom,
% 0.32/0.52      ( ord_le6747313008572928689nteger
% 0.32/0.52      = ( ^ [X: code_integer,Y4: code_integer] :
% 0.32/0.52            ( ( ord_le3102999989581377725nteger @ X @ Y4 )
% 0.32/0.52            & ~ ( ord_le3102999989581377725nteger @ Y4 @ X ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_le_not_le
% 0.32/0.52  thf(fact_1139_less__le__not__le,axiom,
% 0.32/0.52      ( ord_less_set_nat
% 0.32/0.52      = ( ^ [X: set_nat,Y4: set_nat] :
% 0.32/0.52            ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.52            & ~ ( ord_less_eq_set_nat @ Y4 @ X ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_le_not_le
% 0.32/0.52  thf(fact_1140_less__le__not__le,axiom,
% 0.32/0.52      ( ord_less_rat
% 0.32/0.52      = ( ^ [X: rat,Y4: rat] :
% 0.32/0.52            ( ( ord_less_eq_rat @ X @ Y4 )
% 0.32/0.52            & ~ ( ord_less_eq_rat @ Y4 @ X ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_le_not_le
% 0.32/0.52  thf(fact_1141_less__le__not__le,axiom,
% 0.32/0.52      ( ord_less_num
% 0.32/0.52      = ( ^ [X: num,Y4: num] :
% 0.32/0.52            ( ( ord_less_eq_num @ X @ Y4 )
% 0.32/0.52            & ~ ( ord_less_eq_num @ Y4 @ X ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_le_not_le
% 0.32/0.52  thf(fact_1142_less__le__not__le,axiom,
% 0.32/0.52      ( ord_less_nat
% 0.32/0.52      = ( ^ [X: nat,Y4: nat] :
% 0.32/0.52            ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.52            & ~ ( ord_less_eq_nat @ Y4 @ X ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_le_not_le
% 0.32/0.52  thf(fact_1143_less__le__not__le,axiom,
% 0.32/0.52      ( ord_less_int
% 0.32/0.52      = ( ^ [X: int,Y4: int] :
% 0.32/0.52            ( ( ord_less_eq_int @ X @ Y4 )
% 0.32/0.52            & ~ ( ord_less_eq_int @ Y4 @ X ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % less_le_not_le
% 0.32/0.52  thf(fact_1144_not__le__imp__less,axiom,
% 0.32/0.52      ! [Y: code_integer,X2: code_integer] :
% 0.32/0.52        ( ~ ( ord_le3102999989581377725nteger @ Y @ X2 )
% 0.32/0.52       => ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_le_imp_less
% 0.32/0.52  thf(fact_1145_not__le__imp__less,axiom,
% 0.32/0.52      ! [Y: rat,X2: rat] :
% 0.32/0.52        ( ~ ( ord_less_eq_rat @ Y @ X2 )
% 0.32/0.52       => ( ord_less_rat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_le_imp_less
% 0.32/0.52  thf(fact_1146_not__le__imp__less,axiom,
% 0.32/0.52      ! [Y: num,X2: num] :
% 0.32/0.52        ( ~ ( ord_less_eq_num @ Y @ X2 )
% 0.32/0.52       => ( ord_less_num @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_le_imp_less
% 0.32/0.52  thf(fact_1147_not__le__imp__less,axiom,
% 0.32/0.52      ! [Y: nat,X2: nat] :
% 0.32/0.52        ( ~ ( ord_less_eq_nat @ Y @ X2 )
% 0.32/0.52       => ( ord_less_nat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_le_imp_less
% 0.32/0.52  thf(fact_1148_not__le__imp__less,axiom,
% 0.32/0.52      ! [Y: int,X2: int] :
% 0.32/0.52        ( ~ ( ord_less_eq_int @ Y @ X2 )
% 0.32/0.52       => ( ord_less_int @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_le_imp_less
% 0.32/0.52  thf(fact_1149_order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_le3102999989581377725nteger
% 0.32/0.52      = ( ^ [A2: code_integer,B2: code_integer] :
% 0.32/0.52            ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.order_iff_strict
% 0.32/0.52  thf(fact_1150_order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_set_nat
% 0.32/0.52      = ( ^ [A2: set_nat,B2: set_nat] :
% 0.32/0.52            ( ( ord_less_set_nat @ A2 @ B2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.order_iff_strict
% 0.32/0.52  thf(fact_1151_order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_rat
% 0.32/0.52      = ( ^ [A2: rat,B2: rat] :
% 0.32/0.52            ( ( ord_less_rat @ A2 @ B2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.order_iff_strict
% 0.32/0.52  thf(fact_1152_order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_num
% 0.32/0.52      = ( ^ [A2: num,B2: num] :
% 0.32/0.52            ( ( ord_less_num @ A2 @ B2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.order_iff_strict
% 0.32/0.52  thf(fact_1153_order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_nat
% 0.32/0.52      = ( ^ [A2: nat,B2: nat] :
% 0.32/0.52            ( ( ord_less_nat @ A2 @ B2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.order_iff_strict
% 0.32/0.52  thf(fact_1154_order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_int
% 0.32/0.52      = ( ^ [A2: int,B2: int] :
% 0.32/0.52            ( ( ord_less_int @ A2 @ B2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.order_iff_strict
% 0.32/0.52  thf(fact_1155_order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_le6747313008572928689nteger
% 0.32/0.52      = ( ^ [A2: code_integer,B2: code_integer] :
% 0.32/0.52            ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_order
% 0.32/0.52  thf(fact_1156_order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_set_nat
% 0.32/0.52      = ( ^ [A2: set_nat,B2: set_nat] :
% 0.32/0.52            ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_order
% 0.32/0.52  thf(fact_1157_order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_rat
% 0.32/0.52      = ( ^ [A2: rat,B2: rat] :
% 0.32/0.52            ( ( ord_less_eq_rat @ A2 @ B2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_order
% 0.32/0.52  thf(fact_1158_order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_num
% 0.32/0.52      = ( ^ [A2: num,B2: num] :
% 0.32/0.52            ( ( ord_less_eq_num @ A2 @ B2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_order
% 0.32/0.52  thf(fact_1159_order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_nat
% 0.32/0.52      = ( ^ [A2: nat,B2: nat] :
% 0.32/0.52            ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_order
% 0.32/0.52  thf(fact_1160_order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_int
% 0.32/0.52      = ( ^ [A2: int,B2: int] :
% 0.32/0.52            ( ( ord_less_eq_int @ A2 @ B2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_order
% 0.32/0.52  thf(fact_1161_order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans1
% 0.32/0.52  thf(fact_1162_order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.32/0.52        ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.52       => ( ( ord_less_set_nat @ B @ C )
% 0.32/0.52         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans1
% 0.32/0.52  thf(fact_1163_order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [A: rat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans1
% 0.32/0.52  thf(fact_1164_order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [A: num,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.52       => ( ( ord_less_num @ B @ C )
% 0.32/0.52         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans1
% 0.32/0.52  thf(fact_1165_order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [A: nat,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.52       => ( ( ord_less_nat @ B @ C )
% 0.32/0.52         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans1
% 0.32/0.52  thf(fact_1166_order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [A: int,B: int,C: int] :
% 0.32/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.52       => ( ( ord_less_int @ B @ C )
% 0.32/0.52         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans1
% 0.32/0.52  thf(fact_1167_order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans2
% 0.32/0.52  thf(fact_1168_order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.32/0.52        ( ( ord_less_set_nat @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.32/0.52         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans2
% 0.32/0.52  thf(fact_1169_order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.52         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans2
% 0.32/0.52  thf(fact_1170_order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [A: num,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_num @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.52         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans2
% 0.32/0.52  thf(fact_1171_order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [A: nat,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.52         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans2
% 0.32/0.52  thf(fact_1172_order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [A: int,B: int,C: int] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.52         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_trans2
% 0.32/0.52  thf(fact_1173_order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_le6747313008572928689nteger
% 0.32/0.52      = ( ^ [A2: code_integer,B2: code_integer] :
% 0.32/0.52            ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 0.32/0.52            & ~ ( ord_le3102999989581377725nteger @ B2 @ A2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_not
% 0.32/0.52  thf(fact_1174_order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_set_nat
% 0.32/0.52      = ( ^ [A2: set_nat,B2: set_nat] :
% 0.32/0.52            ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.52            & ~ ( ord_less_eq_set_nat @ B2 @ A2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_not
% 0.32/0.52  thf(fact_1175_order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_rat
% 0.32/0.52      = ( ^ [A2: rat,B2: rat] :
% 0.32/0.52            ( ( ord_less_eq_rat @ A2 @ B2 )
% 0.32/0.52            & ~ ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_not
% 0.32/0.52  thf(fact_1176_order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_num
% 0.32/0.52      = ( ^ [A2: num,B2: num] :
% 0.32/0.52            ( ( ord_less_eq_num @ A2 @ B2 )
% 0.32/0.52            & ~ ( ord_less_eq_num @ B2 @ A2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_not
% 0.32/0.52  thf(fact_1177_order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_nat
% 0.32/0.52      = ( ^ [A2: nat,B2: nat] :
% 0.32/0.52            ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.52            & ~ ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_not
% 0.32/0.52  thf(fact_1178_order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_int
% 0.32/0.52      = ( ^ [A2: int,B2: int] :
% 0.32/0.52            ( ( ord_less_eq_int @ A2 @ B2 )
% 0.32/0.52            & ~ ( ord_less_eq_int @ B2 @ A2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_iff_not
% 0.32/0.52  thf(fact_1179_dense__ge__bounded,axiom,
% 0.32/0.52      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_rat @ Z2 @ X2 )
% 0.32/0.52       => ( ! [W3: rat] :
% 0.32/0.52              ( ( ord_less_rat @ Z2 @ W3 )
% 0.32/0.52             => ( ( ord_less_rat @ W3 @ X2 )
% 0.32/0.52               => ( ord_less_eq_rat @ Y @ W3 ) ) )
% 0.32/0.52         => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dense_ge_bounded
% 0.32/0.52  thf(fact_1180_dense__le__bounded,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat,Z2: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( ! [W3: rat] :
% 0.32/0.52              ( ( ord_less_rat @ X2 @ W3 )
% 0.32/0.52             => ( ( ord_less_rat @ W3 @ Y )
% 0.32/0.52               => ( ord_less_eq_rat @ W3 @ Z2 ) ) )
% 0.32/0.52         => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dense_le_bounded
% 0.32/0.52  thf(fact_1181_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_le3102999989581377725nteger
% 0.32/0.52      = ( ^ [B2: code_integer,A2: code_integer] :
% 0.32/0.52            ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.order_iff_strict
% 0.32/0.52  thf(fact_1182_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_set_nat
% 0.32/0.52      = ( ^ [B2: set_nat,A2: set_nat] :
% 0.32/0.52            ( ( ord_less_set_nat @ B2 @ A2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.order_iff_strict
% 0.32/0.52  thf(fact_1183_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_rat
% 0.32/0.52      = ( ^ [B2: rat,A2: rat] :
% 0.32/0.52            ( ( ord_less_rat @ B2 @ A2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.order_iff_strict
% 0.32/0.52  thf(fact_1184_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_num
% 0.32/0.52      = ( ^ [B2: num,A2: num] :
% 0.32/0.52            ( ( ord_less_num @ B2 @ A2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.order_iff_strict
% 0.32/0.52  thf(fact_1185_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_nat
% 0.32/0.52      = ( ^ [B2: nat,A2: nat] :
% 0.32/0.52            ( ( ord_less_nat @ B2 @ A2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.order_iff_strict
% 0.32/0.52  thf(fact_1186_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.52      ( ord_less_eq_int
% 0.32/0.52      = ( ^ [B2: int,A2: int] :
% 0.32/0.52            ( ( ord_less_int @ B2 @ A2 )
% 0.32/0.52            | ( A2 = B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.order_iff_strict
% 0.32/0.52  thf(fact_1187_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_le6747313008572928689nteger
% 0.32/0.52      = ( ^ [B2: code_integer,A2: code_integer] :
% 0.32/0.52            ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_order
% 0.32/0.52  thf(fact_1188_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_set_nat
% 0.32/0.52      = ( ^ [B2: set_nat,A2: set_nat] :
% 0.32/0.52            ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_order
% 0.32/0.52  thf(fact_1189_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_rat
% 0.32/0.52      = ( ^ [B2: rat,A2: rat] :
% 0.32/0.52            ( ( ord_less_eq_rat @ B2 @ A2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_order
% 0.32/0.52  thf(fact_1190_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_num
% 0.32/0.52      = ( ^ [B2: num,A2: num] :
% 0.32/0.52            ( ( ord_less_eq_num @ B2 @ A2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_order
% 0.32/0.52  thf(fact_1191_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_nat
% 0.32/0.52      = ( ^ [B2: nat,A2: nat] :
% 0.32/0.52            ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_order
% 0.32/0.52  thf(fact_1192_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.52      ( ord_less_int
% 0.32/0.52      = ( ^ [B2: int,A2: int] :
% 0.32/0.52            ( ( ord_less_eq_int @ B2 @ A2 )
% 0.32/0.52            & ( A2 != B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_order
% 0.32/0.52  thf(fact_1193_dual__order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ C @ B )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans1
% 0.32/0.52  thf(fact_1194_dual__order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.32/0.52        ( ( ord_less_eq_set_nat @ B @ A )
% 0.32/0.52       => ( ( ord_less_set_nat @ C @ B )
% 0.32/0.52         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans1
% 0.32/0.52  thf(fact_1195_dual__order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [B: rat,A: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.52       => ( ( ord_less_rat @ C @ B )
% 0.32/0.52         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans1
% 0.32/0.52  thf(fact_1196_dual__order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [B: num,A: num,C: num] :
% 0.32/0.52        ( ( ord_less_eq_num @ B @ A )
% 0.32/0.52       => ( ( ord_less_num @ C @ B )
% 0.32/0.52         => ( ord_less_num @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans1
% 0.32/0.52  thf(fact_1197_dual__order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [B: nat,A: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.52       => ( ( ord_less_nat @ C @ B )
% 0.32/0.52         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans1
% 0.32/0.52  thf(fact_1198_dual__order_Ostrict__trans1,axiom,
% 0.32/0.52      ! [B: int,A: int,C: int] :
% 0.32/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.52       => ( ( ord_less_int @ C @ B )
% 0.32/0.52         => ( ord_less_int @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans1
% 0.32/0.52  thf(fact_1199_dual__order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ C @ B )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans2
% 0.32/0.52  thf(fact_1200_dual__order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.32/0.52        ( ( ord_less_set_nat @ B @ A )
% 0.32/0.52       => ( ( ord_less_eq_set_nat @ C @ B )
% 0.32/0.52         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans2
% 0.32/0.52  thf(fact_1201_dual__order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [B: rat,A: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ B @ A )
% 0.32/0.52       => ( ( ord_less_eq_rat @ C @ B )
% 0.32/0.52         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans2
% 0.32/0.52  thf(fact_1202_dual__order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [B: num,A: num,C: num] :
% 0.32/0.52        ( ( ord_less_num @ B @ A )
% 0.32/0.52       => ( ( ord_less_eq_num @ C @ B )
% 0.32/0.52         => ( ord_less_num @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans2
% 0.32/0.52  thf(fact_1203_dual__order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [B: nat,A: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_nat @ B @ A )
% 0.32/0.52       => ( ( ord_less_eq_nat @ C @ B )
% 0.32/0.52         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans2
% 0.32/0.52  thf(fact_1204_dual__order_Ostrict__trans2,axiom,
% 0.32/0.52      ! [B: int,A: int,C: int] :
% 0.32/0.52        ( ( ord_less_int @ B @ A )
% 0.32/0.52       => ( ( ord_less_eq_int @ C @ B )
% 0.32/0.52         => ( ord_less_int @ C @ A ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_trans2
% 0.32/0.52  thf(fact_1205_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_le6747313008572928689nteger
% 0.32/0.52      = ( ^ [B2: code_integer,A2: code_integer] :
% 0.32/0.52            ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 0.32/0.52            & ~ ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_not
% 0.32/0.52  thf(fact_1206_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_set_nat
% 0.32/0.52      = ( ^ [B2: set_nat,A2: set_nat] :
% 0.32/0.52            ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.32/0.52            & ~ ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_not
% 0.32/0.52  thf(fact_1207_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_rat
% 0.32/0.52      = ( ^ [B2: rat,A2: rat] :
% 0.32/0.52            ( ( ord_less_eq_rat @ B2 @ A2 )
% 0.32/0.52            & ~ ( ord_less_eq_rat @ A2 @ B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_not
% 0.32/0.52  thf(fact_1208_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_num
% 0.32/0.52      = ( ^ [B2: num,A2: num] :
% 0.32/0.52            ( ( ord_less_eq_num @ B2 @ A2 )
% 0.32/0.52            & ~ ( ord_less_eq_num @ A2 @ B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_not
% 0.32/0.52  thf(fact_1209_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_nat
% 0.32/0.52      = ( ^ [B2: nat,A2: nat] :
% 0.32/0.52            ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.32/0.52            & ~ ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_not
% 0.32/0.52  thf(fact_1210_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.52      ( ord_less_int
% 0.32/0.52      = ( ^ [B2: int,A2: int] :
% 0.32/0.52            ( ( ord_less_eq_int @ B2 @ A2 )
% 0.32/0.52            & ~ ( ord_less_eq_int @ A2 @ B2 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_iff_not
% 0.32/0.52  thf(fact_1211_order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_order
% 0.32/0.52  thf(fact_1212_order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [A: set_nat,B: set_nat] :
% 0.32/0.52        ( ( ord_less_set_nat @ A @ B )
% 0.32/0.52       => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_order
% 0.32/0.52  thf(fact_1213_order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [A: rat,B: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_order
% 0.32/0.52  thf(fact_1214_order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [A: num,B: num] :
% 0.32/0.52        ( ( ord_less_num @ A @ B )
% 0.32/0.52       => ( ord_less_eq_num @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_order
% 0.32/0.52  thf(fact_1215_order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [A: nat,B: nat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_order
% 0.32/0.52  thf(fact_1216_order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [A: int,B: int] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order.strict_implies_order
% 0.32/0.52  thf(fact_1217_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [B: code_integer,A: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.52       => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_order
% 0.32/0.52  thf(fact_1218_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [B: set_nat,A: set_nat] :
% 0.32/0.52        ( ( ord_less_set_nat @ B @ A )
% 0.32/0.52       => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_order
% 0.32/0.52  thf(fact_1219_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [B: rat,A: rat] :
% 0.32/0.52        ( ( ord_less_rat @ B @ A )
% 0.32/0.52       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_order
% 0.32/0.52  thf(fact_1220_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [B: num,A: num] :
% 0.32/0.52        ( ( ord_less_num @ B @ A )
% 0.32/0.52       => ( ord_less_eq_num @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_order
% 0.32/0.52  thf(fact_1221_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [B: nat,A: nat] :
% 0.32/0.52        ( ( ord_less_nat @ B @ A )
% 0.32/0.52       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_order
% 0.32/0.52  thf(fact_1222_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.52      ! [B: int,A: int] :
% 0.32/0.52        ( ( ord_less_int @ B @ A )
% 0.32/0.52       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.32/0.52  
% 0.32/0.52  % dual_order.strict_implies_order
% 0.32/0.52  thf(fact_1223_order__le__less,axiom,
% 0.32/0.52      ( ord_le3102999989581377725nteger
% 0.32/0.52      = ( ^ [X: code_integer,Y4: code_integer] :
% 0.32/0.52            ( ( ord_le6747313008572928689nteger @ X @ Y4 )
% 0.32/0.52            | ( X = Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less
% 0.32/0.52  thf(fact_1224_order__le__less,axiom,
% 0.32/0.52      ( ord_less_eq_set_nat
% 0.32/0.52      = ( ^ [X: set_nat,Y4: set_nat] :
% 0.32/0.52            ( ( ord_less_set_nat @ X @ Y4 )
% 0.32/0.52            | ( X = Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less
% 0.32/0.52  thf(fact_1225_order__le__less,axiom,
% 0.32/0.52      ( ord_less_eq_rat
% 0.32/0.52      = ( ^ [X: rat,Y4: rat] :
% 0.32/0.52            ( ( ord_less_rat @ X @ Y4 )
% 0.32/0.52            | ( X = Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less
% 0.32/0.52  thf(fact_1226_order__le__less,axiom,
% 0.32/0.52      ( ord_less_eq_num
% 0.32/0.52      = ( ^ [X: num,Y4: num] :
% 0.32/0.52            ( ( ord_less_num @ X @ Y4 )
% 0.32/0.52            | ( X = Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less
% 0.32/0.52  thf(fact_1227_order__le__less,axiom,
% 0.32/0.52      ( ord_less_eq_nat
% 0.32/0.52      = ( ^ [X: nat,Y4: nat] :
% 0.32/0.52            ( ( ord_less_nat @ X @ Y4 )
% 0.32/0.52            | ( X = Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less
% 0.32/0.52  thf(fact_1228_order__le__less,axiom,
% 0.32/0.52      ( ord_less_eq_int
% 0.32/0.52      = ( ^ [X: int,Y4: int] :
% 0.32/0.52            ( ( ord_less_int @ X @ Y4 )
% 0.32/0.52            | ( X = Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less
% 0.32/0.52  thf(fact_1229_order__less__le,axiom,
% 0.32/0.52      ( ord_le6747313008572928689nteger
% 0.32/0.52      = ( ^ [X: code_integer,Y4: code_integer] :
% 0.32/0.52            ( ( ord_le3102999989581377725nteger @ X @ Y4 )
% 0.32/0.52            & ( X != Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le
% 0.32/0.52  thf(fact_1230_order__less__le,axiom,
% 0.32/0.52      ( ord_less_set_nat
% 0.32/0.52      = ( ^ [X: set_nat,Y4: set_nat] :
% 0.32/0.52            ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.52            & ( X != Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le
% 0.32/0.52  thf(fact_1231_order__less__le,axiom,
% 0.32/0.52      ( ord_less_rat
% 0.32/0.52      = ( ^ [X: rat,Y4: rat] :
% 0.32/0.52            ( ( ord_less_eq_rat @ X @ Y4 )
% 0.32/0.52            & ( X != Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le
% 0.32/0.52  thf(fact_1232_order__less__le,axiom,
% 0.32/0.52      ( ord_less_num
% 0.32/0.52      = ( ^ [X: num,Y4: num] :
% 0.32/0.52            ( ( ord_less_eq_num @ X @ Y4 )
% 0.32/0.52            & ( X != Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le
% 0.32/0.52  thf(fact_1233_order__less__le,axiom,
% 0.32/0.52      ( ord_less_nat
% 0.32/0.52      = ( ^ [X: nat,Y4: nat] :
% 0.32/0.52            ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.52            & ( X != Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le
% 0.32/0.52  thf(fact_1234_order__less__le,axiom,
% 0.32/0.52      ( ord_less_int
% 0.32/0.52      = ( ^ [X: int,Y4: int] :
% 0.32/0.52            ( ( ord_less_eq_int @ X @ Y4 )
% 0.32/0.52            & ( X != Y4 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le
% 0.32/0.52  thf(fact_1235_linorder__not__le,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ~ ( ord_le3102999989581377725nteger @ X2 @ Y ) )
% 0.32/0.52        = ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_le
% 0.32/0.52  thf(fact_1236_linorder__not__le,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ~ ( ord_less_eq_rat @ X2 @ Y ) )
% 0.32/0.52        = ( ord_less_rat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_le
% 0.32/0.52  thf(fact_1237_linorder__not__le,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ~ ( ord_less_eq_num @ X2 @ Y ) )
% 0.32/0.52        = ( ord_less_num @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_le
% 0.32/0.52  thf(fact_1238_linorder__not__le,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ~ ( ord_less_eq_nat @ X2 @ Y ) )
% 0.32/0.52        = ( ord_less_nat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_le
% 0.32/0.52  thf(fact_1239_linorder__not__le,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ~ ( ord_less_eq_int @ X2 @ Y ) )
% 0.32/0.52        = ( ord_less_int @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_le
% 0.32/0.52  thf(fact_1240_linorder__not__less,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) )
% 0.32/0.52        = ( ord_le3102999989581377725nteger @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_less
% 0.32/0.52  thf(fact_1241_linorder__not__less,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 0.32/0.52        = ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_less
% 0.32/0.52  thf(fact_1242_linorder__not__less,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 0.32/0.52        = ( ord_less_eq_num @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_less
% 0.32/0.52  thf(fact_1243_linorder__not__less,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 0.32/0.52        = ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_less
% 0.32/0.52  thf(fact_1244_linorder__not__less,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 0.32/0.52        = ( ord_less_eq_int @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_not_less
% 0.32/0.52  thf(fact_1245_order__less__imp__le,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ( ord_le3102999989581377725nteger @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_le
% 0.32/0.52  thf(fact_1246_order__less__imp__le,axiom,
% 0.32/0.52      ! [X2: set_nat,Y: set_nat] :
% 0.32/0.52        ( ( ord_less_set_nat @ X2 @ Y )
% 0.32/0.52       => ( ord_less_eq_set_nat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_le
% 0.32/0.52  thf(fact_1247_order__less__imp__le,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_le
% 0.32/0.52  thf(fact_1248_order__less__imp__le,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_le
% 0.32/0.52  thf(fact_1249_order__less__imp__le,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_le
% 0.32/0.52  thf(fact_1250_order__less__imp__le,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ( ord_less_eq_int @ X2 @ Y ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_imp_le
% 0.32/0.52  thf(fact_1251_order__le__neq__trans,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.52       => ( ( A != B )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_neq_trans
% 0.32/0.52  thf(fact_1252_order__le__neq__trans,axiom,
% 0.32/0.52      ! [A: set_nat,B: set_nat] :
% 0.32/0.52        ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.52       => ( ( A != B )
% 0.32/0.52         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_neq_trans
% 0.32/0.52  thf(fact_1253_order__le__neq__trans,axiom,
% 0.32/0.52      ! [A: rat,B: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.52       => ( ( A != B )
% 0.32/0.52         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_neq_trans
% 0.32/0.52  thf(fact_1254_order__le__neq__trans,axiom,
% 0.32/0.52      ! [A: num,B: num] :
% 0.32/0.52        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.52       => ( ( A != B )
% 0.32/0.52         => ( ord_less_num @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_neq_trans
% 0.32/0.52  thf(fact_1255_order__le__neq__trans,axiom,
% 0.32/0.52      ! [A: nat,B: nat] :
% 0.32/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.52       => ( ( A != B )
% 0.32/0.52         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_neq_trans
% 0.32/0.52  thf(fact_1256_order__le__neq__trans,axiom,
% 0.32/0.52      ! [A: int,B: int] :
% 0.32/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.52       => ( ( A != B )
% 0.32/0.52         => ( ord_less_int @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_neq_trans
% 0.32/0.52  thf(fact_1257_order__neq__le__trans,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer] :
% 0.32/0.52        ( ( A != B )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_neq_le_trans
% 0.32/0.52  thf(fact_1258_order__neq__le__trans,axiom,
% 0.32/0.52      ! [A: set_nat,B: set_nat] :
% 0.32/0.52        ( ( A != B )
% 0.32/0.52       => ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.52         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_neq_le_trans
% 0.32/0.52  thf(fact_1259_order__neq__le__trans,axiom,
% 0.32/0.52      ! [A: rat,B: rat] :
% 0.32/0.52        ( ( A != B )
% 0.32/0.52       => ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.52         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_neq_le_trans
% 0.32/0.52  thf(fact_1260_order__neq__le__trans,axiom,
% 0.32/0.52      ! [A: num,B: num] :
% 0.32/0.52        ( ( A != B )
% 0.32/0.52       => ( ( ord_less_eq_num @ A @ B )
% 0.32/0.52         => ( ord_less_num @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_neq_le_trans
% 0.32/0.52  thf(fact_1261_order__neq__le__trans,axiom,
% 0.32/0.52      ! [A: nat,B: nat] :
% 0.32/0.52        ( ( A != B )
% 0.32/0.52       => ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.52         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_neq_le_trans
% 0.32/0.52  thf(fact_1262_order__neq__le__trans,axiom,
% 0.32/0.52      ! [A: int,B: int] :
% 0.32/0.52        ( ( A != B )
% 0.32/0.52       => ( ( ord_less_eq_int @ A @ B )
% 0.32/0.52         => ( ord_less_int @ A @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_neq_le_trans
% 0.32/0.52  thf(fact_1263_order__le__less__trans,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer,Z2: code_integer] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ Y @ Z2 )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_trans
% 0.32/0.52  thf(fact_1264_order__le__less__trans,axiom,
% 0.32/0.52      ! [X2: set_nat,Y: set_nat,Z2: set_nat] :
% 0.32/0.52        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_set_nat @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_set_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_trans
% 0.32/0.52  thf(fact_1265_order__le__less__trans,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat,Z2: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_rat @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_rat @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_trans
% 0.32/0.52  thf(fact_1266_order__le__less__trans,axiom,
% 0.32/0.52      ! [X2: num,Y: num,Z2: num] :
% 0.32/0.52        ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_num @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_num @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_trans
% 0.32/0.52  thf(fact_1267_order__le__less__trans,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat,Z2: nat] :
% 0.32/0.52        ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_nat @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_trans
% 0.32/0.52  thf(fact_1268_order__le__less__trans,axiom,
% 0.32/0.52      ! [X2: int,Y: int,Z2: int] :
% 0.32/0.52        ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_int @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_int @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_trans
% 0.32/0.52  thf(fact_1269_order__less__le__trans,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer,Z2: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ Y @ Z2 )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_trans
% 0.32/0.52  thf(fact_1270_order__less__le__trans,axiom,
% 0.32/0.52      ! [X2: set_nat,Y: set_nat,Z2: set_nat] :
% 0.32/0.52        ( ( ord_less_set_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_set_nat @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_set_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_trans
% 0.32/0.52  thf(fact_1271_order__less__le__trans,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat,Z2: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_rat @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_rat @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_trans
% 0.32/0.52  thf(fact_1272_order__less__le__trans,axiom,
% 0.32/0.52      ! [X2: num,Y: num,Z2: num] :
% 0.32/0.52        ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_num @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_num @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_trans
% 0.32/0.52  thf(fact_1273_order__less__le__trans,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat,Z2: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_nat @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_trans
% 0.32/0.52  thf(fact_1274_order__less__le__trans,axiom,
% 0.32/0.52      ! [X2: int,Y: int,Z2: int] :
% 0.32/0.52        ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_eq_int @ Y @ Z2 )
% 0.32/0.52         => ( ord_less_int @ X2 @ Z2 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_trans
% 0.32/0.52  thf(fact_1275_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: code_integer > code_integer,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1276_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1277_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: num > code_integer,B: num,C: num] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_num @ B @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1278_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: nat > code_integer,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_nat @ B @ C )
% 0.32/0.52         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.52                ( ( ord_less_nat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1279_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: int > code_integer,B: int,C: int] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_int @ B @ C )
% 0.32/0.52         => ( ! [X3: int,Y2: int] :
% 0.32/0.52                ( ( ord_less_int @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1280_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: code_integer > rat,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1281_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1282_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_num @ B @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1283_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_nat @ B @ C )
% 0.32/0.52         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.52                ( ( ord_less_nat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1284_order__le__less__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_int @ B @ C )
% 0.32/0.52         => ( ! [X3: int,Y2: int] :
% 0.32/0.52                ( ( ord_less_int @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst1
% 0.32/0.52  thf(fact_1285_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1286_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1287_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1288_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1289_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1290_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: num,B: num,F: num > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1291_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.32/0.52        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.52       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1292_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: num,B: num,F: num > num,C: num] :
% 0.32/0.52        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.52       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1293_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.32/0.52        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.52       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1294_order__le__less__subst2,axiom,
% 0.32/0.52      ! [A: num,B: num,F: num > int,C: int] :
% 0.32/0.52        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.52       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_less_subst2
% 0.32/0.52  thf(fact_1295_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1296_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1297_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1298_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1299_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1300_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: code_integer,F: num > code_integer,B: num,C: num] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1301_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1302_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: num,F: num > num,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1303_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1304_order__less__le__subst1,axiom,
% 0.32/0.52      ! [A: int,F: num > int,B: num,C: num] :
% 0.32/0.52        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.32/0.52       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_eq_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst1
% 0.32/0.52  thf(fact_1305_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1306_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1307_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: num,B: num,F: num > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_num @ A @ B )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1308_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: nat,B: nat,F: nat > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.52                ( ( ord_less_nat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1309_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: int,B: int,F: int > code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: int,Y2: int] :
% 0.32/0.52                ( ( ord_less_int @ X3 @ Y2 )
% 0.32/0.52               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1310_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,F: code_integer > rat,C: rat] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: code_integer,Y2: code_integer] :
% 0.32/0.52                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1311_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: rat,Y2: rat] :
% 0.32/0.52                ( ( ord_less_rat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1312_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.32/0.52        ( ( ord_less_num @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: num,Y2: num] :
% 0.32/0.52                ( ( ord_less_num @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1313_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.52                ( ( ord_less_nat @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1314_order__less__le__subst2,axiom,
% 0.32/0.52      ! [A: int,B: int,F: int > rat,C: rat] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.52         => ( ! [X3: int,Y2: int] :
% 0.32/0.52                ( ( ord_less_int @ X3 @ Y2 )
% 0.32/0.52               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.32/0.52           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_less_le_subst2
% 0.32/0.52  thf(fact_1315_linorder__le__less__linear,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 0.32/0.52        | ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_le_less_linear
% 0.32/0.52  thf(fact_1316_linorder__le__less__linear,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.52        | ( ord_less_rat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_le_less_linear
% 0.32/0.52  thf(fact_1317_linorder__le__less__linear,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.52        | ( ord_less_num @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_le_less_linear
% 0.32/0.52  thf(fact_1318_linorder__le__less__linear,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.52        | ( ord_less_nat @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_le_less_linear
% 0.32/0.52  thf(fact_1319_linorder__le__less__linear,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.52        | ( ord_less_int @ Y @ X2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % linorder_le_less_linear
% 0.32/0.52  thf(fact_1320_order__le__imp__less__or__eq,axiom,
% 0.32/0.52      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.52        ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_imp_less_or_eq
% 0.32/0.52  thf(fact_1321_order__le__imp__less__or__eq,axiom,
% 0.32/0.52      ! [X2: set_nat,Y: set_nat] :
% 0.32/0.52        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_set_nat @ X2 @ Y )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_imp_less_or_eq
% 0.32/0.52  thf(fact_1322_order__le__imp__less__or__eq,axiom,
% 0.32/0.52      ! [X2: rat,Y: rat] :
% 0.32/0.52        ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_imp_less_or_eq
% 0.32/0.52  thf(fact_1323_order__le__imp__less__or__eq,axiom,
% 0.32/0.52      ! [X2: num,Y: num] :
% 0.32/0.52        ( ( ord_less_eq_num @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_num @ X2 @ Y )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_imp_less_or_eq
% 0.32/0.52  thf(fact_1324_order__le__imp__less__or__eq,axiom,
% 0.32/0.52      ! [X2: nat,Y: nat] :
% 0.32/0.52        ( ( ord_less_eq_nat @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_imp_less_or_eq
% 0.32/0.52  thf(fact_1325_order__le__imp__less__or__eq,axiom,
% 0.32/0.52      ! [X2: int,Y: int] :
% 0.32/0.52        ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.52       => ( ( ord_less_int @ X2 @ Y )
% 0.32/0.52          | ( X2 = Y ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % order_le_imp_less_or_eq
% 0.32/0.52  thf(fact_1326_minf_I8_J,axiom,
% 0.32/0.52      ! [T: code_integer] :
% 0.32/0.52      ? [Z4: code_integer] :
% 0.32/0.52      ! [X4: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 0.32/0.52       => ~ ( ord_le3102999989581377725nteger @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(8)
% 0.32/0.52  thf(fact_1327_minf_I8_J,axiom,
% 0.32/0.52      ! [T: rat] :
% 0.32/0.52      ? [Z4: rat] :
% 0.32/0.52      ! [X4: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X4 @ Z4 )
% 0.32/0.52       => ~ ( ord_less_eq_rat @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(8)
% 0.32/0.52  thf(fact_1328_minf_I8_J,axiom,
% 0.32/0.52      ! [T: num] :
% 0.32/0.52      ? [Z4: num] :
% 0.32/0.52      ! [X4: num] :
% 0.32/0.52        ( ( ord_less_num @ X4 @ Z4 )
% 0.32/0.52       => ~ ( ord_less_eq_num @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(8)
% 0.32/0.52  thf(fact_1329_minf_I8_J,axiom,
% 0.32/0.52      ! [T: nat] :
% 0.32/0.52      ? [Z4: nat] :
% 0.32/0.52      ! [X4: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X4 @ Z4 )
% 0.32/0.52       => ~ ( ord_less_eq_nat @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(8)
% 0.32/0.52  thf(fact_1330_minf_I8_J,axiom,
% 0.32/0.52      ! [T: int] :
% 0.32/0.52      ? [Z4: int] :
% 0.32/0.52      ! [X4: int] :
% 0.32/0.52        ( ( ord_less_int @ X4 @ Z4 )
% 0.32/0.52       => ~ ( ord_less_eq_int @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(8)
% 0.32/0.52  thf(fact_1331_minf_I6_J,axiom,
% 0.32/0.52      ! [T: code_integer] :
% 0.32/0.52      ? [Z4: code_integer] :
% 0.32/0.52      ! [X4: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 0.32/0.52       => ( ord_le3102999989581377725nteger @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(6)
% 0.32/0.52  thf(fact_1332_minf_I6_J,axiom,
% 0.32/0.52      ! [T: rat] :
% 0.32/0.52      ? [Z4: rat] :
% 0.32/0.52      ! [X4: rat] :
% 0.32/0.52        ( ( ord_less_rat @ X4 @ Z4 )
% 0.32/0.52       => ( ord_less_eq_rat @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(6)
% 0.32/0.52  thf(fact_1333_minf_I6_J,axiom,
% 0.32/0.52      ! [T: num] :
% 0.32/0.52      ? [Z4: num] :
% 0.32/0.52      ! [X4: num] :
% 0.32/0.52        ( ( ord_less_num @ X4 @ Z4 )
% 0.32/0.52       => ( ord_less_eq_num @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(6)
% 0.32/0.52  thf(fact_1334_minf_I6_J,axiom,
% 0.32/0.52      ! [T: nat] :
% 0.32/0.52      ? [Z4: nat] :
% 0.32/0.52      ! [X4: nat] :
% 0.32/0.52        ( ( ord_less_nat @ X4 @ Z4 )
% 0.32/0.52       => ( ord_less_eq_nat @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(6)
% 0.32/0.52  thf(fact_1335_minf_I6_J,axiom,
% 0.32/0.52      ! [T: int] :
% 0.32/0.52      ? [Z4: int] :
% 0.32/0.52      ! [X4: int] :
% 0.32/0.52        ( ( ord_less_int @ X4 @ Z4 )
% 0.32/0.52       => ( ord_less_eq_int @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % minf(6)
% 0.32/0.52  thf(fact_1336_pinf_I8_J,axiom,
% 0.32/0.52      ! [T: code_integer] :
% 0.32/0.52      ? [Z4: code_integer] :
% 0.32/0.52      ! [X4: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 0.32/0.52       => ( ord_le3102999989581377725nteger @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(8)
% 0.32/0.52  thf(fact_1337_pinf_I8_J,axiom,
% 0.32/0.52      ! [T: rat] :
% 0.32/0.52      ? [Z4: rat] :
% 0.32/0.52      ! [X4: rat] :
% 0.32/0.52        ( ( ord_less_rat @ Z4 @ X4 )
% 0.32/0.52       => ( ord_less_eq_rat @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(8)
% 0.32/0.52  thf(fact_1338_pinf_I8_J,axiom,
% 0.32/0.52      ! [T: num] :
% 0.32/0.52      ? [Z4: num] :
% 0.32/0.52      ! [X4: num] :
% 0.32/0.52        ( ( ord_less_num @ Z4 @ X4 )
% 0.32/0.52       => ( ord_less_eq_num @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(8)
% 0.32/0.52  thf(fact_1339_pinf_I8_J,axiom,
% 0.32/0.52      ! [T: nat] :
% 0.32/0.52      ? [Z4: nat] :
% 0.32/0.52      ! [X4: nat] :
% 0.32/0.52        ( ( ord_less_nat @ Z4 @ X4 )
% 0.32/0.52       => ( ord_less_eq_nat @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(8)
% 0.32/0.52  thf(fact_1340_pinf_I8_J,axiom,
% 0.32/0.52      ! [T: int] :
% 0.32/0.52      ? [Z4: int] :
% 0.32/0.52      ! [X4: int] :
% 0.32/0.52        ( ( ord_less_int @ Z4 @ X4 )
% 0.32/0.52       => ( ord_less_eq_int @ T @ X4 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(8)
% 0.32/0.52  thf(fact_1341_pinf_I6_J,axiom,
% 0.32/0.52      ! [T: code_integer] :
% 0.32/0.52      ? [Z4: code_integer] :
% 0.32/0.52      ! [X4: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 0.32/0.52       => ~ ( ord_le3102999989581377725nteger @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(6)
% 0.32/0.52  thf(fact_1342_pinf_I6_J,axiom,
% 0.32/0.52      ! [T: rat] :
% 0.32/0.52      ? [Z4: rat] :
% 0.32/0.52      ! [X4: rat] :
% 0.32/0.52        ( ( ord_less_rat @ Z4 @ X4 )
% 0.32/0.52       => ~ ( ord_less_eq_rat @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(6)
% 0.32/0.52  thf(fact_1343_pinf_I6_J,axiom,
% 0.32/0.52      ! [T: num] :
% 0.32/0.52      ? [Z4: num] :
% 0.32/0.52      ! [X4: num] :
% 0.32/0.52        ( ( ord_less_num @ Z4 @ X4 )
% 0.32/0.52       => ~ ( ord_less_eq_num @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(6)
% 0.32/0.52  thf(fact_1344_pinf_I6_J,axiom,
% 0.32/0.52      ! [T: nat] :
% 0.32/0.52      ? [Z4: nat] :
% 0.32/0.52      ! [X4: nat] :
% 0.32/0.52        ( ( ord_less_nat @ Z4 @ X4 )
% 0.32/0.52       => ~ ( ord_less_eq_nat @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(6)
% 0.32/0.52  thf(fact_1345_pinf_I6_J,axiom,
% 0.32/0.52      ! [T: int] :
% 0.32/0.52      ? [Z4: int] :
% 0.32/0.52      ! [X4: int] :
% 0.32/0.52        ( ( ord_less_int @ Z4 @ X4 )
% 0.32/0.52       => ~ ( ord_less_eq_int @ X4 @ T ) ) ).
% 0.32/0.52  
% 0.32/0.52  % pinf(6)
% 0.32/0.52  thf(fact_1346_zero__less__iff__neq__zero,axiom,
% 0.32/0.52      ! [N: nat] :
% 0.32/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.52        = ( N != zero_zero_nat ) ) ).
% 0.32/0.52  
% 0.32/0.52  % zero_less_iff_neq_zero
% 0.32/0.52  thf(fact_1347_gr__implies__not__zero,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_nat @ M @ N )
% 0.32/0.52       => ( N != zero_zero_nat ) ) ).
% 0.32/0.52  
% 0.32/0.52  % gr_implies_not_zero
% 0.32/0.52  thf(fact_1348_not__less__zero,axiom,
% 0.32/0.52      ! [N: nat] :
% 0.32/0.52        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.32/0.52  
% 0.32/0.52  % not_less_zero
% 0.32/0.52  thf(fact_1349_gr__zeroI,axiom,
% 0.32/0.52      ! [N: nat] :
% 0.32/0.52        ( ( N != zero_zero_nat )
% 0.32/0.52       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.52  
% 0.32/0.52  % gr_zeroI
% 0.32/0.52  thf(fact_1350_less__numeral__extra_I3_J,axiom,
% 0.32/0.52      ~ ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ zero_z2226904508553997617atural ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(3)
% 0.32/0.52  thf(fact_1351_less__numeral__extra_I3_J,axiom,
% 0.32/0.52      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(3)
% 0.32/0.52  thf(fact_1352_less__numeral__extra_I3_J,axiom,
% 0.32/0.52      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(3)
% 0.32/0.52  thf(fact_1353_less__numeral__extra_I3_J,axiom,
% 0.32/0.52      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(3)
% 0.32/0.52  thf(fact_1354_less__numeral__extra_I3_J,axiom,
% 0.32/0.52      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(3)
% 0.32/0.52  thf(fact_1355_add__mono__thms__linordered__field_I5_J,axiom,
% 0.32/0.52      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.32/0.52        ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 0.32/0.52          & ( ord_le6747313008572928689nteger @ K @ L ) )
% 0.32/0.52       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(5)
% 0.32/0.52  thf(fact_1356_add__mono__thms__linordered__field_I5_J,axiom,
% 0.32/0.52      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.32/0.52        ( ( ( ord_less_rat @ I @ J )
% 0.32/0.52          & ( ord_less_rat @ K @ L ) )
% 0.32/0.52       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(5)
% 0.32/0.52  thf(fact_1357_add__mono__thms__linordered__field_I5_J,axiom,
% 0.32/0.52      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.52        ( ( ( ord_less_nat @ I @ J )
% 0.32/0.52          & ( ord_less_nat @ K @ L ) )
% 0.32/0.52       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(5)
% 0.32/0.52  thf(fact_1358_add__mono__thms__linordered__field_I5_J,axiom,
% 0.32/0.52      ! [I: int,J: int,K: int,L: int] :
% 0.32/0.52        ( ( ( ord_less_int @ I @ J )
% 0.32/0.52          & ( ord_less_int @ K @ L ) )
% 0.32/0.52       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(5)
% 0.32/0.52  thf(fact_1359_add__mono__thms__linordered__field_I2_J,axiom,
% 0.32/0.52      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.32/0.52        ( ( ( I = J )
% 0.32/0.52          & ( ord_le6747313008572928689nteger @ K @ L ) )
% 0.32/0.52       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(2)
% 0.32/0.52  thf(fact_1360_add__mono__thms__linordered__field_I2_J,axiom,
% 0.32/0.52      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.32/0.52        ( ( ( I = J )
% 0.32/0.52          & ( ord_less_rat @ K @ L ) )
% 0.32/0.52       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(2)
% 0.32/0.52  thf(fact_1361_add__mono__thms__linordered__field_I2_J,axiom,
% 0.32/0.52      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.52        ( ( ( I = J )
% 0.32/0.52          & ( ord_less_nat @ K @ L ) )
% 0.32/0.52       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(2)
% 0.32/0.52  thf(fact_1362_add__mono__thms__linordered__field_I2_J,axiom,
% 0.32/0.52      ! [I: int,J: int,K: int,L: int] :
% 0.32/0.52        ( ( ( I = J )
% 0.32/0.52          & ( ord_less_int @ K @ L ) )
% 0.32/0.52       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(2)
% 0.32/0.52  thf(fact_1363_add__mono__thms__linordered__field_I1_J,axiom,
% 0.32/0.52      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.32/0.52        ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 0.32/0.52          & ( K = L ) )
% 0.32/0.52       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(1)
% 0.32/0.52  thf(fact_1364_add__mono__thms__linordered__field_I1_J,axiom,
% 0.32/0.52      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.32/0.52        ( ( ( ord_less_rat @ I @ J )
% 0.32/0.52          & ( K = L ) )
% 0.32/0.52       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(1)
% 0.32/0.52  thf(fact_1365_add__mono__thms__linordered__field_I1_J,axiom,
% 0.32/0.52      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.52        ( ( ( ord_less_nat @ I @ J )
% 0.32/0.52          & ( K = L ) )
% 0.32/0.52       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(1)
% 0.32/0.52  thf(fact_1366_add__mono__thms__linordered__field_I1_J,axiom,
% 0.32/0.52      ! [I: int,J: int,K: int,L: int] :
% 0.32/0.52        ( ( ( ord_less_int @ I @ J )
% 0.32/0.52          & ( K = L ) )
% 0.32/0.52       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_mono_thms_linordered_field(1)
% 0.32/0.52  thf(fact_1367_add__strict__mono,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 0.32/0.52         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_mono
% 0.32/0.52  thf(fact_1368_add__strict__mono,axiom,
% 0.32/0.52      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ( ord_less_rat @ C @ D )
% 0.32/0.52         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_mono
% 0.32/0.52  thf(fact_1369_add__strict__mono,axiom,
% 0.32/0.52      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( ( ord_less_nat @ C @ D )
% 0.32/0.52         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_mono
% 0.32/0.52  thf(fact_1370_add__strict__mono,axiom,
% 0.32/0.52      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( ( ord_less_int @ C @ D )
% 0.32/0.52         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_mono
% 0.32/0.52  thf(fact_1371_add__strict__left__mono,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_left_mono
% 0.32/0.52  thf(fact_1372_add__strict__left__mono,axiom,
% 0.32/0.52      ! [A: rat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_left_mono
% 0.32/0.52  thf(fact_1373_add__strict__left__mono,axiom,
% 0.32/0.52      ! [A: nat,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_left_mono
% 0.32/0.52  thf(fact_1374_add__strict__left__mono,axiom,
% 0.32/0.52      ! [A: int,B: int,C: int] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_left_mono
% 0.32/0.52  thf(fact_1375_add__strict__right__mono,axiom,
% 0.32/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.52       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_right_mono
% 0.32/0.52  thf(fact_1376_add__strict__right__mono,axiom,
% 0.32/0.52      ! [A: rat,B: rat,C: rat] :
% 0.32/0.52        ( ( ord_less_rat @ A @ B )
% 0.32/0.52       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_right_mono
% 0.32/0.52  thf(fact_1377_add__strict__right__mono,axiom,
% 0.32/0.52      ! [A: nat,B: nat,C: nat] :
% 0.32/0.52        ( ( ord_less_nat @ A @ B )
% 0.32/0.52       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_right_mono
% 0.32/0.52  thf(fact_1378_add__strict__right__mono,axiom,
% 0.32/0.52      ! [A: int,B: int,C: int] :
% 0.32/0.52        ( ( ord_less_int @ A @ B )
% 0.32/0.52       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_strict_right_mono
% 0.32/0.52  thf(fact_1379_add__less__imp__less__left,axiom,
% 0.32/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 0.32/0.52       => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_less_imp_less_left
% 0.32/0.52  thf(fact_1380_add__less__imp__less__left,axiom,
% 0.32/0.52      ! [C: rat,A: rat,B: rat] :
% 0.32/0.52        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.32/0.52       => ( ord_less_rat @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_less_imp_less_left
% 0.32/0.52  thf(fact_1381_add__less__imp__less__left,axiom,
% 0.32/0.52      ! [C: nat,A: nat,B: nat] :
% 0.32/0.52        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.32/0.52       => ( ord_less_nat @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_less_imp_less_left
% 0.32/0.52  thf(fact_1382_add__less__imp__less__left,axiom,
% 0.32/0.52      ! [C: int,A: int,B: int] :
% 0.32/0.52        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.32/0.52       => ( ord_less_int @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_less_imp_less_left
% 0.32/0.52  thf(fact_1383_add__less__imp__less__right,axiom,
% 0.32/0.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.52        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.52       => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_less_imp_less_right
% 0.32/0.52  thf(fact_1384_add__less__imp__less__right,axiom,
% 0.32/0.52      ! [A: rat,C: rat,B: rat] :
% 0.32/0.52        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.52       => ( ord_less_rat @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_less_imp_less_right
% 0.32/0.52  thf(fact_1385_add__less__imp__less__right,axiom,
% 0.32/0.52      ! [A: nat,C: nat,B: nat] :
% 0.32/0.52        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.52       => ( ord_less_nat @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_less_imp_less_right
% 0.32/0.52  thf(fact_1386_add__less__imp__less__right,axiom,
% 0.32/0.52      ! [A: int,C: int,B: int] :
% 0.32/0.52        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.32/0.52       => ( ord_less_int @ A @ B ) ) ).
% 0.32/0.52  
% 0.32/0.52  % add_less_imp_less_right
% 0.32/0.52  thf(fact_1387_less__numeral__extra_I4_J,axiom,
% 0.32/0.52      ~ ( ord_le5570908160329646204atural @ one_one_Code_natural @ one_one_Code_natural ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(4)
% 0.32/0.52  thf(fact_1388_less__numeral__extra_I4_J,axiom,
% 0.32/0.52      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(4)
% 0.32/0.52  thf(fact_1389_less__numeral__extra_I4_J,axiom,
% 0.32/0.52      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(4)
% 0.32/0.52  thf(fact_1390_less__numeral__extra_I4_J,axiom,
% 0.32/0.52      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(4)
% 0.32/0.52  thf(fact_1391_less__numeral__extra_I4_J,axiom,
% 0.32/0.52      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.32/0.52  
% 0.32/0.52  % less_numeral_extra(4)
% 0.32/0.52  thf(fact_1392_bot__nat__0_Oextremum__strict,axiom,
% 0.32/0.52      ! [A: nat] :
% 0.32/0.52        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.32/0.52  
% 0.32/0.52  % bot_nat_0.extremum_strict
% 0.32/0.52  thf(fact_1393_gr0I,axiom,
% 0.32/0.52      ! [N: nat] :
% 0.32/0.52        ( ( N != zero_zero_nat )
% 0.32/0.52       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.52  
% 0.32/0.52  % gr0I
% 0.32/0.52  thf(fact_1394_not__gr0,axiom,
% 0.32/0.52      ! [N: nat] :
% 0.32/0.52        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.32/0.52        = ( N = zero_zero_nat ) ) ).
% 0.32/0.52  
% 0.32/0.52  % not_gr0
% 0.32/0.52  thf(fact_1395_not__less0,axiom,
% 0.32/0.52      ! [N: nat] :
% 0.32/0.52        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.32/0.52  
% 0.32/0.52  % not_less0
% 0.32/0.52  thf(fact_1396_less__zeroE,axiom,
% 0.32/0.52      ! [N: nat] :
% 0.32/0.52        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.32/0.52  
% 0.32/0.52  % less_zeroE
% 0.32/0.52  thf(fact_1397_gr__implies__not0,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.52        ( ( ord_less_nat @ M @ N )
% 0.32/0.52       => ( N != zero_zero_nat ) ) ).
% 0.32/0.52  
% 0.32/0.52  % gr_implies_not0
% 0.32/0.52  thf(fact_1398_infinite__descent0,axiom,
% 0.32/0.52      ! [P: nat > $o,N: nat] :
% 0.32/0.52        ( ( P @ zero_zero_nat )
% 0.32/0.52       => ( ! [N2: nat] :
% 0.32/0.52              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.32/0.52             => ( ~ ( P @ N2 )
% 0.32/0.52               => ? [M6: nat] :
% 0.32/0.52                    ( ( ord_less_nat @ M6 @ N2 )
% 0.32/0.52                    & ~ ( P @ M6 ) ) ) )
% 0.32/0.52         => ( P @ N ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % infinite_descent0
% 0.32/0.52  thf(fact_1399_reals__Archimedean2,axiom,
% 0.32/0.52      ! [X2: rat] :
% 0.32/0.52      ? [N2: nat] : ( ord_less_rat @ X2 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.32/0.52  
% 0.32/0.52  % reals_Archimedean2
% 0.32/0.52  thf(fact_1400_less__int__code_I1_J,axiom,
% 0.32/0.52      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.32/0.52  
% 0.32/0.52  % less_int_code(1)
% 0.32/0.52  thf(fact_1401_exists__leI,axiom,
% 0.32/0.52      ! [N: nat,P: nat > $o] :
% 0.32/0.52        ( ( ! [N5: nat] :
% 0.32/0.52              ( ( ord_less_nat @ N5 @ N )
% 0.32/0.52             => ~ ( P @ N5 ) )
% 0.32/0.52         => ( P @ N ) )
% 0.32/0.52       => ? [N6: nat] :
% 0.32/0.52            ( ( ord_less_eq_nat @ N6 @ N )
% 0.32/0.52            & ( P @ N6 ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % exists_leI
% 0.32/0.52  thf(fact_1402_nat__less__le,axiom,
% 0.32/0.52      ( ord_less_nat
% 0.32/0.52      = ( ^ [M2: nat,N3: nat] :
% 0.32/0.52            ( ( ord_less_eq_nat @ M2 @ N3 )
% 0.32/0.52            & ( M2 != N3 ) ) ) ) ).
% 0.32/0.52  
% 0.32/0.52  % nat_less_le
% 0.32/0.52  thf(fact_1403_less__imp__le__nat,axiom,
% 0.32/0.52      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ N )
% 0.32/0.53       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_imp_le_nat
% 0.32/0.53  thf(fact_1404_le__eq__less__or__eq,axiom,
% 0.32/0.53      ( ord_less_eq_nat
% 0.32/0.53      = ( ^ [M2: nat,N3: nat] :
% 0.32/0.53            ( ( ord_less_nat @ M2 @ N3 )
% 0.32/0.53            | ( M2 = N3 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_eq_less_or_eq
% 0.32/0.53  thf(fact_1405_less__or__eq__imp__le,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ( ord_less_nat @ M @ N )
% 0.32/0.53          | ( M = N ) )
% 0.32/0.53       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_or_eq_imp_le
% 0.32/0.53  thf(fact_1406_le__neq__implies__less,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.53       => ( ( M != N )
% 0.32/0.53         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_neq_implies_less
% 0.32/0.53  thf(fact_1407_less__mono__imp__le__mono,axiom,
% 0.32/0.53      ! [F: nat > nat,I: nat,J: nat] :
% 0.32/0.53        ( ! [I3: nat,J2: nat] :
% 0.32/0.53            ( ( ord_less_nat @ I3 @ J2 )
% 0.32/0.53           => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.53         => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_mono_imp_le_mono
% 0.32/0.53  thf(fact_1408_add__lessD1,axiom,
% 0.32/0.53      ! [I: nat,J: nat,K: nat] :
% 0.32/0.53        ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.32/0.53       => ( ord_less_nat @ I @ K ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_lessD1
% 0.32/0.53  thf(fact_1409_add__less__mono,axiom,
% 0.32/0.53      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.53        ( ( ord_less_nat @ I @ J )
% 0.32/0.53       => ( ( ord_less_nat @ K @ L )
% 0.32/0.53         => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_less_mono
% 0.32/0.53  thf(fact_1410_not__add__less1,axiom,
% 0.32/0.53      ! [I: nat,J: nat] :
% 0.32/0.53        ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.32/0.53  
% 0.32/0.53  % not_add_less1
% 0.32/0.53  thf(fact_1411_not__add__less2,axiom,
% 0.32/0.53      ! [J: nat,I: nat] :
% 0.32/0.53        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.32/0.53  
% 0.32/0.53  % not_add_less2
% 0.32/0.53  thf(fact_1412_add__less__mono1,axiom,
% 0.32/0.53      ! [I: nat,J: nat,K: nat] :
% 0.32/0.53        ( ( ord_less_nat @ I @ J )
% 0.32/0.53       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_less_mono1
% 0.32/0.53  thf(fact_1413_trans__less__add1,axiom,
% 0.32/0.53      ! [I: nat,J: nat,M: nat] :
% 0.32/0.53        ( ( ord_less_nat @ I @ J )
% 0.32/0.53       => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % trans_less_add1
% 0.32/0.53  thf(fact_1414_trans__less__add2,axiom,
% 0.32/0.53      ! [I: nat,J: nat,M: nat] :
% 0.32/0.53        ( ( ord_less_nat @ I @ J )
% 0.32/0.53       => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % trans_less_add2
% 0.32/0.53  thf(fact_1415_less__add__eq__less,axiom,
% 0.32/0.53      ! [K: nat,L: nat,M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ K @ L )
% 0.32/0.53       => ( ( ( plus_plus_nat @ M @ L )
% 0.32/0.53            = ( plus_plus_nat @ K @ N ) )
% 0.32/0.53         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_add_eq_less
% 0.32/0.53  thf(fact_1416_ex__less__of__int,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53      ? [Z4: int] : ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z4 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % ex_less_of_int
% 0.32/0.53  thf(fact_1417_ex__of__int__less,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53      ? [Z4: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z4 ) @ X2 ) ).
% 0.32/0.53  
% 0.32/0.53  % ex_of_int_less
% 0.32/0.53  thf(fact_1418_of__nat__floor,axiom,
% 0.32/0.53      ! [R: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 0.32/0.53       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R ) ) ) @ R ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_floor
% 0.32/0.53  thf(fact_1419_nat__le__eq__zle,axiom,
% 0.32/0.53      ! [W2: int,Z2: int] :
% 0.32/0.53        ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 0.32/0.53          | ( ord_less_eq_int @ zero_zero_int @ Z2 ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 0.32/0.53          = ( ord_less_eq_int @ W2 @ Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_le_eq_zle
% 0.32/0.53  thf(fact_1420_split__nat,axiom,
% 0.32/0.53      ! [P: nat > $o,I: int] :
% 0.32/0.53        ( ( P @ ( nat2 @ I ) )
% 0.32/0.53        = ( ! [N3: nat] :
% 0.32/0.53              ( ( I
% 0.32/0.53                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.32/0.53             => ( P @ N3 ) )
% 0.32/0.53          & ( ( ord_less_int @ I @ zero_zero_int )
% 0.32/0.53           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % split_nat
% 0.32/0.53  thf(fact_1421_of__int__pos,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.32/0.53       => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_pos
% 0.32/0.53  thf(fact_1422_of__int__pos,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.32/0.53       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_pos
% 0.32/0.53  thf(fact_1423_of__int__pos,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.32/0.53       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_pos
% 0.32/0.53  thf(fact_1424_zero__less__imp__eq__int,axiom,
% 0.32/0.53      ! [K: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.53       => ? [N2: nat] :
% 0.32/0.53            ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.32/0.53            & ( K
% 0.32/0.53              = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_imp_eq_int
% 0.32/0.53  thf(fact_1425_pos__int__cases,axiom,
% 0.32/0.53      ! [K: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.53       => ~ ! [N2: nat] :
% 0.32/0.53              ( ( K
% 0.32/0.53                = ( semiri1314217659103216013at_int @ N2 ) )
% 0.32/0.53             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % pos_int_cases
% 0.32/0.53  thf(fact_1426_of__nat__less__of__int__iff,axiom,
% 0.32/0.53      ! [N: nat,X2: int] :
% 0.32/0.53        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X2 ) )
% 0.32/0.53        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_less_of_int_iff
% 0.32/0.53  thf(fact_1427_of__nat__less__of__int__iff,axiom,
% 0.32/0.53      ! [N: nat,X2: int] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N ) @ ( ring_18347121197199848620nteger @ X2 ) )
% 0.32/0.53        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_less_of_int_iff
% 0.32/0.53  thf(fact_1428_of__nat__less__of__int__iff,axiom,
% 0.32/0.53      ! [N: nat,X2: int] :
% 0.32/0.53        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X2 ) )
% 0.32/0.53        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_less_of_int_iff
% 0.32/0.53  thf(fact_1429_zero__le__power__int,axiom,
% 0.32/0.53      ! [X2: rat,N: int] :
% 0.32/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.53       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_int_rat @ X2 @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_le_power_int
% 0.32/0.53  thf(fact_1430_power__int__le__imp__le__exp,axiom,
% 0.32/0.53      ! [X2: rat,M: int,N: int] :
% 0.32/0.53        ( ( ord_less_rat @ one_one_rat @ X2 )
% 0.32/0.53       => ( ( ord_less_eq_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ X2 @ N ) )
% 0.32/0.53         => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.32/0.53           => ( ord_less_eq_int @ M @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % power_int_le_imp_le_exp
% 0.32/0.53  thf(fact_1431_floor__split,axiom,
% 0.32/0.53      ! [P: int > $o,T: rat] :
% 0.32/0.53        ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 0.32/0.53        = ( ! [I2: int] :
% 0.32/0.53              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I2 ) @ T )
% 0.32/0.53                & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) ) )
% 0.32/0.53             => ( P @ I2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_split
% 0.32/0.53  thf(fact_1432_floor__eq__iff,axiom,
% 0.32/0.53      ! [X2: rat,A: int] :
% 0.32/0.53        ( ( ( archim3151403230148437115or_rat @ X2 )
% 0.32/0.53          = A )
% 0.32/0.53        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X2 )
% 0.32/0.53          & ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_eq_iff
% 0.32/0.53  thf(fact_1433_floor__unique,axiom,
% 0.32/0.53      ! [Z2: int,X2: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 )
% 0.32/0.53       => ( ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) )
% 0.32/0.53         => ( ( archim3151403230148437115or_rat @ X2 )
% 0.32/0.53            = Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_unique
% 0.32/0.53  thf(fact_1434_less__floor__iff,axiom,
% 0.32/0.53      ! [Z2: int,X2: rat] :
% 0.32/0.53        ( ( ord_less_int @ Z2 @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.32/0.53        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_floor_iff
% 0.32/0.53  thf(fact_1435_power__int__not__zero,axiom,
% 0.32/0.53      ! [X2: rat,N: int] :
% 0.32/0.53        ( ( ( X2 != zero_zero_rat )
% 0.32/0.53          | ( N = zero_zero_int ) )
% 0.32/0.53       => ( ( power_int_rat @ X2 @ N )
% 0.32/0.53         != zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % power_int_not_zero
% 0.32/0.53  thf(fact_1436_floor__le__iff,axiom,
% 0.32/0.53      ! [X2: rat,Z2: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z2 )
% 0.32/0.53        = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_le_iff
% 0.32/0.53  thf(fact_1437_floor__correct,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 )
% 0.32/0.53        & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_correct
% 0.32/0.53  thf(fact_1438_floor__mono,axiom,
% 0.32/0.53      ! [X2: rat,Y: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.53       => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_mono
% 0.32/0.53  thf(fact_1439_nat__zero__as__int,axiom,
% 0.32/0.53      ( zero_zero_nat
% 0.32/0.53      = ( nat2 @ zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_zero_as_int
% 0.32/0.53  thf(fact_1440_of__int__floor__le,axiom,
% 0.32/0.53      ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_floor_le
% 0.32/0.53  thf(fact_1441_nat__mono,axiom,
% 0.32/0.53      ! [X2: int,Y: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ X2 @ Y )
% 0.32/0.53       => ( ord_less_eq_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_mono
% 0.32/0.53  thf(fact_1442_ex__nat,axiom,
% 0.32/0.53      ( ( ^ [P4: nat > $o] :
% 0.32/0.53          ? [X7: nat] : ( P4 @ X7 ) )
% 0.32/0.53      = ( ^ [P5: nat > $o] :
% 0.32/0.53          ? [X: int] :
% 0.32/0.53            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.53            & ( P5 @ ( nat2 @ X ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % ex_nat
% 0.32/0.53  thf(fact_1443_all__nat,axiom,
% 0.32/0.53      ( ( ^ [P4: nat > $o] :
% 0.32/0.53          ! [X7: nat] : ( P4 @ X7 ) )
% 0.32/0.53      = ( ^ [P5: nat > $o] :
% 0.32/0.53          ! [X: int] :
% 0.32/0.53            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.53           => ( P5 @ ( nat2 @ X ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % all_nat
% 0.32/0.53  thf(fact_1444_eq__nat__nat__iff,axiom,
% 0.32/0.53      ! [Z2: int,Z6: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 0.32/0.53         => ( ( ( nat2 @ Z2 )
% 0.32/0.53              = ( nat2 @ Z6 ) )
% 0.32/0.53            = ( Z2 = Z6 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % eq_nat_nat_iff
% 0.32/0.53  thf(fact_1445_nat__one__as__int,axiom,
% 0.32/0.53      ( one_one_nat
% 0.32/0.53      = ( nat2 @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_one_as_int
% 0.32/0.53  thf(fact_1446_add__less__le__mono,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.53       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_less_le_mono
% 0.32/0.53  thf(fact_1447_add__less__le__mono,axiom,
% 0.32/0.53      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.53        ( ( ord_less_rat @ A @ B )
% 0.32/0.53       => ( ( ord_less_eq_rat @ C @ D )
% 0.32/0.53         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_less_le_mono
% 0.32/0.53  thf(fact_1448_add__less__le__mono,axiom,
% 0.32/0.53      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.53        ( ( ord_less_nat @ A @ B )
% 0.32/0.53       => ( ( ord_less_eq_nat @ C @ D )
% 0.32/0.53         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_less_le_mono
% 0.32/0.53  thf(fact_1449_add__less__le__mono,axiom,
% 0.32/0.53      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.53        ( ( ord_less_int @ A @ B )
% 0.32/0.53       => ( ( ord_less_eq_int @ C @ D )
% 0.32/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_less_le_mono
% 0.32/0.53  thf(fact_1450_add__le__less__mono,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.53       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_le_less_mono
% 0.32/0.53  thf(fact_1451_add__le__less__mono,axiom,
% 0.32/0.53      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.53       => ( ( ord_less_rat @ C @ D )
% 0.32/0.53         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_le_less_mono
% 0.32/0.53  thf(fact_1452_add__le__less__mono,axiom,
% 0.32/0.53      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.53       => ( ( ord_less_nat @ C @ D )
% 0.32/0.53         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_le_less_mono
% 0.32/0.53  thf(fact_1453_add__le__less__mono,axiom,
% 0.32/0.53      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.53       => ( ( ord_less_int @ C @ D )
% 0.32/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_le_less_mono
% 0.32/0.53  thf(fact_1454_add__mono__thms__linordered__field_I3_J,axiom,
% 0.32/0.53      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.32/0.53        ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 0.32/0.53          & ( ord_le3102999989581377725nteger @ K @ L ) )
% 0.32/0.53       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono_thms_linordered_field(3)
% 0.32/0.53  thf(fact_1455_add__mono__thms__linordered__field_I3_J,axiom,
% 0.32/0.53      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.32/0.53        ( ( ( ord_less_rat @ I @ J )
% 0.32/0.53          & ( ord_less_eq_rat @ K @ L ) )
% 0.32/0.53       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono_thms_linordered_field(3)
% 0.32/0.53  thf(fact_1456_add__mono__thms__linordered__field_I3_J,axiom,
% 0.32/0.53      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.53        ( ( ( ord_less_nat @ I @ J )
% 0.32/0.53          & ( ord_less_eq_nat @ K @ L ) )
% 0.32/0.53       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono_thms_linordered_field(3)
% 0.32/0.53  thf(fact_1457_add__mono__thms__linordered__field_I3_J,axiom,
% 0.32/0.53      ! [I: int,J: int,K: int,L: int] :
% 0.32/0.53        ( ( ( ord_less_int @ I @ J )
% 0.32/0.53          & ( ord_less_eq_int @ K @ L ) )
% 0.32/0.53       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono_thms_linordered_field(3)
% 0.32/0.53  thf(fact_1458_add__mono__thms__linordered__field_I4_J,axiom,
% 0.32/0.53      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 0.32/0.53        ( ( ( ord_le3102999989581377725nteger @ I @ J )
% 0.32/0.53          & ( ord_le6747313008572928689nteger @ K @ L ) )
% 0.32/0.53       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono_thms_linordered_field(4)
% 0.32/0.53  thf(fact_1459_add__mono__thms__linordered__field_I4_J,axiom,
% 0.32/0.53      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.32/0.53        ( ( ( ord_less_eq_rat @ I @ J )
% 0.32/0.53          & ( ord_less_rat @ K @ L ) )
% 0.32/0.53       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono_thms_linordered_field(4)
% 0.32/0.53  thf(fact_1460_add__mono__thms__linordered__field_I4_J,axiom,
% 0.32/0.53      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.53        ( ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.53          & ( ord_less_nat @ K @ L ) )
% 0.32/0.53       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono_thms_linordered_field(4)
% 0.32/0.53  thf(fact_1461_add__mono__thms__linordered__field_I4_J,axiom,
% 0.32/0.53      ! [I: int,J: int,K: int,L: int] :
% 0.32/0.53        ( ( ( ord_less_eq_int @ I @ J )
% 0.32/0.53          & ( ord_less_int @ K @ L ) )
% 0.32/0.53       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono_thms_linordered_field(4)
% 0.32/0.53  thf(fact_1462_add__less__zeroD,axiom,
% 0.32/0.53      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ X2 @ Y ) @ zero_z3403309356797280102nteger )
% 0.32/0.53       => ( ( ord_le6747313008572928689nteger @ X2 @ zero_z3403309356797280102nteger )
% 0.32/0.53          | ( ord_le6747313008572928689nteger @ Y @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_less_zeroD
% 0.32/0.53  thf(fact_1463_add__less__zeroD,axiom,
% 0.32/0.53      ! [X2: rat,Y: rat] :
% 0.32/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ X2 @ Y ) @ zero_zero_rat )
% 0.32/0.53       => ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 0.32/0.53          | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_less_zeroD
% 0.32/0.53  thf(fact_1464_add__less__zeroD,axiom,
% 0.32/0.53      ! [X2: int,Y: int] :
% 0.32/0.53        ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y ) @ zero_zero_int )
% 0.32/0.53       => ( ( ord_less_int @ X2 @ zero_zero_int )
% 0.32/0.53          | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_less_zeroD
% 0.32/0.53  thf(fact_1465_add__neg__neg,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural] :
% 0.32/0.53        ( ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.53       => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 0.32/0.53         => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_neg
% 0.32/0.53  thf(fact_1466_add__neg__neg,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.53       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_neg
% 0.32/0.53  thf(fact_1467_add__neg__neg,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.53       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.32/0.53         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_neg
% 0.32/0.53  thf(fact_1468_add__neg__neg,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.32/0.53       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.32/0.53         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_neg
% 0.32/0.53  thf(fact_1469_add__neg__neg,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.32/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_neg
% 0.32/0.53  thf(fact_1470_add__pos__pos,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural] :
% 0.32/0.53        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.53       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.53         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_pos
% 0.32/0.53  thf(fact_1471_add__pos__pos,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.53       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_pos
% 0.32/0.53  thf(fact_1472_add__pos__pos,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.53       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.32/0.53         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_pos
% 0.32/0.53  thf(fact_1473_add__pos__pos,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.53       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.32/0.53         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_pos
% 0.32/0.53  thf(fact_1474_add__pos__pos,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.53       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.53         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_pos
% 0.32/0.53  thf(fact_1475_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ord_less_nat @ A @ B )
% 0.32/0.53       => ~ ! [C3: nat] :
% 0.32/0.53              ( ( B
% 0.32/0.53                = ( plus_plus_nat @ A @ C3 ) )
% 0.32/0.53             => ( C3 = zero_zero_nat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % canonically_ordered_monoid_add_class.lessE
% 0.32/0.53  thf(fact_1476_pos__add__strict,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.53        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.53       => ( ( ord_le5570908160329646204atural @ B @ C )
% 0.32/0.53         => ( ord_le5570908160329646204atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % pos_add_strict
% 0.32/0.53  thf(fact_1477_pos__add__strict,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % pos_add_strict
% 0.32/0.53  thf(fact_1478_pos__add__strict,axiom,
% 0.32/0.53      ! [A: rat,B: rat,C: rat] :
% 0.32/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.53       => ( ( ord_less_rat @ B @ C )
% 0.32/0.53         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % pos_add_strict
% 0.32/0.53  thf(fact_1479_pos__add__strict,axiom,
% 0.32/0.53      ! [A: nat,B: nat,C: nat] :
% 0.32/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.53       => ( ( ord_less_nat @ B @ C )
% 0.32/0.53         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % pos_add_strict
% 0.32/0.53  thf(fact_1480_pos__add__strict,axiom,
% 0.32/0.53      ! [A: int,B: int,C: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.53       => ( ( ord_less_int @ B @ C )
% 0.32/0.53         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % pos_add_strict
% 0.32/0.53  thf(fact_1481_zero__less__one,axiom,
% 0.32/0.53      ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_one
% 0.32/0.53  thf(fact_1482_zero__less__one,axiom,
% 0.32/0.53      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_one
% 0.32/0.53  thf(fact_1483_zero__less__one,axiom,
% 0.32/0.53      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_one
% 0.32/0.53  thf(fact_1484_zero__less__one,axiom,
% 0.32/0.53      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_one
% 0.32/0.53  thf(fact_1485_zero__less__one,axiom,
% 0.32/0.53      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_one
% 0.32/0.53  thf(fact_1486_not__one__less__zero,axiom,
% 0.32/0.53      ~ ( ord_le5570908160329646204atural @ one_one_Code_natural @ zero_z2226904508553997617atural ) ).
% 0.32/0.53  
% 0.32/0.53  % not_one_less_zero
% 0.32/0.53  thf(fact_1487_not__one__less__zero,axiom,
% 0.32/0.53      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 0.32/0.53  
% 0.32/0.53  % not_one_less_zero
% 0.32/0.53  thf(fact_1488_not__one__less__zero,axiom,
% 0.32/0.53      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % not_one_less_zero
% 0.32/0.53  thf(fact_1489_not__one__less__zero,axiom,
% 0.32/0.53      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.32/0.53  
% 0.32/0.53  % not_one_less_zero
% 0.32/0.53  thf(fact_1490_not__one__less__zero,axiom,
% 0.32/0.53      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % not_one_less_zero
% 0.32/0.53  thf(fact_1491_less__numeral__extra_I1_J,axiom,
% 0.32/0.53      ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 0.32/0.53  
% 0.32/0.53  % less_numeral_extra(1)
% 0.32/0.53  thf(fact_1492_less__numeral__extra_I1_J,axiom,
% 0.32/0.53      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.32/0.53  
% 0.32/0.53  % less_numeral_extra(1)
% 0.32/0.53  thf(fact_1493_less__numeral__extra_I1_J,axiom,
% 0.32/0.53      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.32/0.53  
% 0.32/0.53  % less_numeral_extra(1)
% 0.32/0.53  thf(fact_1494_less__numeral__extra_I1_J,axiom,
% 0.32/0.53      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.32/0.53  
% 0.32/0.53  % less_numeral_extra(1)
% 0.32/0.53  thf(fact_1495_less__numeral__extra_I1_J,axiom,
% 0.32/0.53      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.32/0.53  
% 0.32/0.53  % less_numeral_extra(1)
% 0.32/0.53  thf(fact_1496_less__add__one,axiom,
% 0.32/0.53      ! [A: code_natural] : ( ord_le5570908160329646204atural @ A @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_add_one
% 0.32/0.53  thf(fact_1497_less__add__one,axiom,
% 0.32/0.53      ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_add_one
% 0.32/0.53  thf(fact_1498_less__add__one,axiom,
% 0.32/0.53      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_add_one
% 0.32/0.53  thf(fact_1499_less__add__one,axiom,
% 0.32/0.53      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_add_one
% 0.32/0.53  thf(fact_1500_less__add__one,axiom,
% 0.32/0.53      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_add_one
% 0.32/0.53  thf(fact_1501_add__mono1,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural] :
% 0.32/0.53        ( ( ord_le5570908160329646204atural @ A @ B )
% 0.32/0.53       => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ B @ one_one_Code_natural ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono1
% 0.32/0.53  thf(fact_1502_add__mono1,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.53       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono1
% 0.32/0.53  thf(fact_1503_add__mono1,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_rat @ A @ B )
% 0.32/0.53       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono1
% 0.32/0.53  thf(fact_1504_add__mono1,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ord_less_nat @ A @ B )
% 0.32/0.53       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono1
% 0.32/0.53  thf(fact_1505_add__mono1,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_int @ A @ B )
% 0.32/0.53       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_mono1
% 0.32/0.53  thf(fact_1506_floor__le__ceiling,axiom,
% 0.32/0.53      ! [X2: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_le_ceiling
% 0.32/0.53  thf(fact_1507_of__nat__less__0__iff,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_less_0_iff
% 0.32/0.53  thf(fact_1508_of__nat__less__0__iff,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_less_0_iff
% 0.32/0.53  thf(fact_1509_of__nat__less__0__iff,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ~ ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_less_0_iff
% 0.32/0.53  thf(fact_1510_of__nat__less__0__iff,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_less_0_iff
% 0.32/0.53  thf(fact_1511_of__nat__less__0__iff,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ~ ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ M ) @ zero_z2226904508553997617atural ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_less_0_iff
% 0.32/0.53  thf(fact_1512_ex__least__nat__le,axiom,
% 0.32/0.53      ! [P: nat > $o,N: nat] :
% 0.32/0.53        ( ( P @ N )
% 0.32/0.53       => ( ~ ( P @ zero_zero_nat )
% 0.32/0.53         => ? [K3: nat] :
% 0.32/0.53              ( ( ord_less_eq_nat @ K3 @ N )
% 0.32/0.53              & ! [I4: nat] :
% 0.32/0.53                  ( ( ord_less_nat @ I4 @ K3 )
% 0.32/0.53                 => ~ ( P @ I4 ) )
% 0.32/0.53              & ( P @ K3 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % ex_least_nat_le
% 0.32/0.53  thf(fact_1513_less__imp__add__positive,axiom,
% 0.32/0.53      ! [I: nat,J: nat] :
% 0.32/0.53        ( ( ord_less_nat @ I @ J )
% 0.32/0.53       => ? [K3: nat] :
% 0.32/0.53            ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 0.32/0.53            & ( ( plus_plus_nat @ I @ K3 )
% 0.32/0.53              = J ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_imp_add_positive
% 0.32/0.53  thf(fact_1514_mono__nat__linear__lb,axiom,
% 0.32/0.53      ! [F: nat > nat,M: nat,K: nat] :
% 0.32/0.53        ( ! [M4: nat,N2: nat] :
% 0.32/0.53            ( ( ord_less_nat @ M4 @ N2 )
% 0.32/0.53           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 0.32/0.53       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % mono_nat_linear_lb
% 0.32/0.53  thf(fact_1515_zless__add1__eq,axiom,
% 0.32/0.53      ! [W2: int,Z2: int] :
% 0.32/0.53        ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 0.32/0.53        = ( ( ord_less_int @ W2 @ Z2 )
% 0.32/0.53          | ( W2 = Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zless_add1_eq
% 0.32/0.53  thf(fact_1516_int__gr__induct,axiom,
% 0.32/0.53      ! [K: int,I: int,P: int > $o] :
% 0.32/0.53        ( ( ord_less_int @ K @ I )
% 0.32/0.53       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 0.32/0.53         => ( ! [I3: int] :
% 0.32/0.53                ( ( ord_less_int @ K @ I3 )
% 0.32/0.53               => ( ( P @ I3 )
% 0.32/0.53                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 0.32/0.53           => ( P @ I ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_gr_induct
% 0.32/0.53  thf(fact_1517_power__int__0__left__If,axiom,
% 0.32/0.53      ! [M: int] :
% 0.32/0.53        ( ( ( M = zero_zero_int )
% 0.32/0.53         => ( ( power_int_rat @ zero_zero_rat @ M )
% 0.32/0.53            = one_one_rat ) )
% 0.32/0.53        & ( ( M != zero_zero_int )
% 0.32/0.53         => ( ( power_int_rat @ zero_zero_rat @ M )
% 0.32/0.53            = zero_zero_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % power_int_0_left_If
% 0.32/0.53  thf(fact_1518_power__int__increasing,axiom,
% 0.32/0.53      ! [N: int,N4: int,A: rat] :
% 0.32/0.53        ( ( ord_less_eq_int @ N @ N4 )
% 0.32/0.53       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.32/0.53         => ( ord_less_eq_rat @ ( power_int_rat @ A @ N ) @ ( power_int_rat @ A @ N4 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % power_int_increasing
% 0.32/0.53  thf(fact_1519_le__floor__iff,axiom,
% 0.32/0.53      ! [Z2: int,X2: rat] :
% 0.32/0.53        ( ( ord_less_eq_int @ Z2 @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.32/0.53        = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_floor_iff
% 0.32/0.53  thf(fact_1520_le__floor__add,axiom,
% 0.32/0.53      ! [X2: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_floor_add
% 0.32/0.53  thf(fact_1521_int__add__floor,axiom,
% 0.32/0.53      ! [Z2: int,X2: rat] :
% 0.32/0.53        ( ( plus_plus_int @ Z2 @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.32/0.53        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_add_floor
% 0.32/0.53  thf(fact_1522_floor__add__int,axiom,
% 0.32/0.53      ! [X2: rat,Z2: int] :
% 0.32/0.53        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z2 )
% 0.32/0.53        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_add_int
% 0.32/0.53  thf(fact_1523_nat__le__iff,axiom,
% 0.32/0.53      ! [X2: int,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ ( nat2 @ X2 ) @ N )
% 0.32/0.53        = ( ord_less_eq_int @ X2 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_le_iff
% 0.32/0.53  thf(fact_1524_nat__0__le,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.53       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 0.32/0.53          = Z2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_0_le
% 0.32/0.53  thf(fact_1525_int__eq__iff,axiom,
% 0.32/0.53      ! [M: nat,Z2: int] :
% 0.32/0.53        ( ( ( semiri1314217659103216013at_int @ M )
% 0.32/0.53          = Z2 )
% 0.32/0.53        = ( ( M
% 0.32/0.53            = ( nat2 @ Z2 ) )
% 0.32/0.53          & ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_eq_iff
% 0.32/0.53  thf(fact_1526_of__nat__ceiling,axiom,
% 0.32/0.53      ! [R: rat] : ( ord_less_eq_rat @ R @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_ceiling
% 0.32/0.53  thf(fact_1527_nat__int__add,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 0.32/0.53        = ( plus_plus_nat @ A @ B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_int_add
% 0.32/0.53  thf(fact_1528_add__neg__nonpos,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural] :
% 0.32/0.53        ( ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.53       => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 0.32/0.53         => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_nonpos
% 0.32/0.53  thf(fact_1529_add__neg__nonpos,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.53       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_nonpos
% 0.32/0.53  thf(fact_1530_add__neg__nonpos,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.53       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.32/0.53         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_nonpos
% 0.32/0.53  thf(fact_1531_add__neg__nonpos,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.32/0.53       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.32/0.53         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_nonpos
% 0.32/0.53  thf(fact_1532_add__neg__nonpos,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.53       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.32/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_nonpos
% 0.32/0.53  thf(fact_1533_add__nonneg__pos,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural] :
% 0.32/0.53        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.53       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.53         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonneg_pos
% 0.32/0.53  thf(fact_1534_add__nonneg__pos,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.53       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonneg_pos
% 0.32/0.53  thf(fact_1535_add__nonneg__pos,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.53       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.32/0.53         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonneg_pos
% 0.32/0.53  thf(fact_1536_add__nonneg__pos,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.53       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.32/0.53         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonneg_pos
% 0.32/0.53  thf(fact_1537_add__nonneg__pos,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.53       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.53         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonneg_pos
% 0.32/0.53  thf(fact_1538_add__nonpos__neg,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural] :
% 0.32/0.53        ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.53       => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 0.32/0.53         => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonpos_neg
% 0.32/0.53  thf(fact_1539_add__nonpos__neg,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.53       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonpos_neg
% 0.32/0.53  thf(fact_1540_add__nonpos__neg,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.53       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.32/0.53         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonpos_neg
% 0.32/0.53  thf(fact_1541_add__nonpos__neg,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.32/0.53       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.32/0.53         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonpos_neg
% 0.32/0.53  thf(fact_1542_add__nonpos__neg,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.32/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_nonpos_neg
% 0.32/0.53  thf(fact_1543_add__pos__nonneg,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural] :
% 0.32/0.53        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.53       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.53         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_nonneg
% 0.32/0.53  thf(fact_1544_add__pos__nonneg,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.53       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_nonneg
% 0.32/0.53  thf(fact_1545_add__pos__nonneg,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.53         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_nonneg
% 0.32/0.53  thf(fact_1546_add__pos__nonneg,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.53         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_nonneg
% 0.32/0.53  thf(fact_1547_add__pos__nonneg,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.53         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_pos_nonneg
% 0.32/0.53  thf(fact_1548_add__strict__increasing,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.53        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.53       => ( ( ord_le1926595141338095240atural @ B @ C )
% 0.32/0.53         => ( ord_le5570908160329646204atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing
% 0.32/0.53  thf(fact_1549_add__strict__increasing,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.53       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing
% 0.32/0.53  thf(fact_1550_add__strict__increasing,axiom,
% 0.32/0.53      ! [A: rat,B: rat,C: rat] :
% 0.32/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.53         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing
% 0.32/0.53  thf(fact_1551_add__strict__increasing,axiom,
% 0.32/0.53      ! [A: nat,B: nat,C: nat] :
% 0.32/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.53         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing
% 0.32/0.53  thf(fact_1552_add__strict__increasing,axiom,
% 0.32/0.53      ! [A: int,B: int,C: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.53         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing
% 0.32/0.53  thf(fact_1553_add__strict__increasing2,axiom,
% 0.32/0.53      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.53        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.53       => ( ( ord_le5570908160329646204atural @ B @ C )
% 0.32/0.53         => ( ord_le5570908160329646204atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing2
% 0.32/0.53  thf(fact_1554_add__strict__increasing2,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing2
% 0.32/0.53  thf(fact_1555_add__strict__increasing2,axiom,
% 0.32/0.53      ! [A: rat,B: rat,C: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.53       => ( ( ord_less_rat @ B @ C )
% 0.32/0.53         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing2
% 0.32/0.53  thf(fact_1556_add__strict__increasing2,axiom,
% 0.32/0.53      ! [A: nat,B: nat,C: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.53       => ( ( ord_less_nat @ B @ C )
% 0.32/0.53         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing2
% 0.32/0.53  thf(fact_1557_add__strict__increasing2,axiom,
% 0.32/0.53      ! [A: int,B: int,C: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.53       => ( ( ord_less_int @ B @ C )
% 0.32/0.53         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_strict_increasing2
% 0.32/0.53  thf(fact_1558_zero__less__two,axiom,
% 0.32/0.53      ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_two
% 0.32/0.53  thf(fact_1559_zero__less__two,axiom,
% 0.32/0.53      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_two
% 0.32/0.53  thf(fact_1560_zero__less__two,axiom,
% 0.32/0.53      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_two
% 0.32/0.53  thf(fact_1561_zero__less__two,axiom,
% 0.32/0.53      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_two
% 0.32/0.53  thf(fact_1562_zero__less__two,axiom,
% 0.32/0.53      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_two
% 0.32/0.53  thf(fact_1563_int__one__le__iff__zero__less,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ one_one_int @ Z2 )
% 0.32/0.53        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_one_le_iff_zero_less
% 0.32/0.53  thf(fact_1564_odd__less__0__iff,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 ) @ zero_zero_int )
% 0.32/0.53        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % odd_less_0_iff
% 0.32/0.53  thf(fact_1565_add1__zle__eq,axiom,
% 0.32/0.53      ! [W2: int,Z2: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 )
% 0.32/0.53        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add1_zle_eq
% 0.32/0.53  thf(fact_1566_zless__imp__add1__zle,axiom,
% 0.32/0.53      ! [W2: int,Z2: int] :
% 0.32/0.53        ( ( ord_less_int @ W2 @ Z2 )
% 0.32/0.53       => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zless_imp_add1_zle
% 0.32/0.53  thf(fact_1567_nat__plus__as__int,axiom,
% 0.32/0.53      ( plus_plus_nat
% 0.32/0.53      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_plus_as_int
% 0.32/0.53  thf(fact_1568_power__int__mono,axiom,
% 0.32/0.53      ! [X2: rat,Y: rat,N: int] :
% 0.32/0.53        ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.32/0.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.53           => ( ord_less_eq_rat @ ( power_int_rat @ X2 @ N ) @ ( power_int_rat @ Y @ N ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % power_int_mono
% 0.32/0.53  thf(fact_1569_one__le__power__int,axiom,
% 0.32/0.53      ! [X2: rat,N: int] :
% 0.32/0.53        ( ( ord_less_eq_rat @ one_one_rat @ X2 )
% 0.32/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.32/0.53         => ( ord_less_eq_rat @ one_one_rat @ ( power_int_rat @ X2 @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % one_le_power_int
% 0.32/0.53  thf(fact_1570_one__add__floor,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 0.32/0.53        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % one_add_floor
% 0.32/0.53  thf(fact_1571_nat__eq__iff2,axiom,
% 0.32/0.53      ! [M: nat,W2: int] :
% 0.32/0.53        ( ( M
% 0.32/0.53          = ( nat2 @ W2 ) )
% 0.32/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.32/0.53           => ( W2
% 0.32/0.53              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.32/0.53          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.32/0.53           => ( M = zero_zero_nat ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_eq_iff2
% 0.32/0.53  thf(fact_1572_nat__eq__iff,axiom,
% 0.32/0.53      ! [W2: int,M: nat] :
% 0.32/0.53        ( ( ( nat2 @ W2 )
% 0.32/0.53          = M )
% 0.32/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.32/0.53           => ( W2
% 0.32/0.53              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.32/0.53          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.32/0.53           => ( M = zero_zero_nat ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_eq_iff
% 0.32/0.53  thf(fact_1573_le__nat__iff,axiom,
% 0.32/0.53      ! [K: int,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 0.32/0.53          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_nat_iff
% 0.32/0.53  thf(fact_1574_nat__add__distrib,axiom,
% 0.32/0.53      ! [Z2: int,Z6: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 0.32/0.53         => ( ( nat2 @ ( plus_plus_int @ Z2 @ Z6 ) )
% 0.32/0.53            = ( plus_plus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_add_distrib
% 0.32/0.53  thf(fact_1575_ceiling__altdef,axiom,
% 0.32/0.53      ( archim2889992004027027881ng_rat
% 0.32/0.53      = ( ^ [X: rat] :
% 0.32/0.53            ( if_int
% 0.32/0.53            @ ( X
% 0.32/0.53              = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 0.32/0.53            @ ( archim3151403230148437115or_rat @ X )
% 0.32/0.53            @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % ceiling_altdef
% 0.32/0.53  thf(fact_1576_floor__exists,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53      ? [Z4: int] :
% 0.32/0.53        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X2 )
% 0.32/0.53        & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_exists
% 0.32/0.53  thf(fact_1577_floor__exists1,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53      ? [X3: int] :
% 0.32/0.53        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X2 )
% 0.32/0.53        & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 0.32/0.53        & ! [Y5: int] :
% 0.32/0.53            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X2 )
% 0.32/0.53              & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 0.32/0.53           => ( Y5 = X3 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_exists1
% 0.32/0.53  thf(fact_1578_discrete,axiom,
% 0.32/0.53      ( ord_le6747313008572928689nteger
% 0.32/0.53      = ( ^ [A2: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % discrete
% 0.32/0.53  thf(fact_1579_discrete,axiom,
% 0.32/0.53      ( ord_less_nat
% 0.32/0.53      = ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % discrete
% 0.32/0.53  thf(fact_1580_discrete,axiom,
% 0.32/0.53      ( ord_less_int
% 0.32/0.53      = ( ^ [A2: int] : ( ord_less_eq_int @ ( plus_plus_int @ A2 @ one_one_int ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % discrete
% 0.32/0.53  thf(fact_1581_field__le__epsilon,axiom,
% 0.32/0.53      ! [X2: rat,Y: rat] :
% 0.32/0.53        ( ! [E3: rat] :
% 0.32/0.53            ( ( ord_less_rat @ zero_zero_rat @ E3 )
% 0.32/0.53           => ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ Y @ E3 ) ) )
% 0.32/0.53       => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 0.32/0.53  
% 0.32/0.53  % field_le_epsilon
% 0.32/0.53  thf(fact_1582_floor__add,axiom,
% 0.32/0.53      ! [X2: rat,Y: rat] :
% 0.32/0.53        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.32/0.53         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 0.32/0.53            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 0.32/0.53        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.32/0.53         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 0.32/0.53            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_add
% 0.32/0.53  thf(fact_1583_complete__interval,axiom,
% 0.32/0.53      ! [A: nat,B: nat,P: nat > $o] :
% 0.32/0.53        ( ( ord_less_nat @ A @ B )
% 0.32/0.53       => ( ( P @ A )
% 0.32/0.53         => ( ~ ( P @ B )
% 0.32/0.53           => ? [C3: nat] :
% 0.32/0.53                ( ( ord_less_eq_nat @ A @ C3 )
% 0.32/0.53                & ( ord_less_eq_nat @ C3 @ B )
% 0.32/0.53                & ! [X4: nat] :
% 0.32/0.53                    ( ( ( ord_less_eq_nat @ A @ X4 )
% 0.32/0.53                      & ( ord_less_nat @ X4 @ C3 ) )
% 0.32/0.53                   => ( P @ X4 ) )
% 0.32/0.53                & ! [D2: nat] :
% 0.32/0.53                    ( ! [X3: nat] :
% 0.32/0.53                        ( ( ( ord_less_eq_nat @ A @ X3 )
% 0.32/0.53                          & ( ord_less_nat @ X3 @ D2 ) )
% 0.32/0.53                       => ( P @ X3 ) )
% 0.32/0.53                   => ( ord_less_eq_nat @ D2 @ C3 ) ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % complete_interval
% 0.32/0.53  thf(fact_1584_complete__interval,axiom,
% 0.32/0.53      ! [A: int,B: int,P: int > $o] :
% 0.32/0.53        ( ( ord_less_int @ A @ B )
% 0.32/0.53       => ( ( P @ A )
% 0.32/0.53         => ( ~ ( P @ B )
% 0.32/0.53           => ? [C3: int] :
% 0.32/0.53                ( ( ord_less_eq_int @ A @ C3 )
% 0.32/0.53                & ( ord_less_eq_int @ C3 @ B )
% 0.32/0.53                & ! [X4: int] :
% 0.32/0.53                    ( ( ( ord_less_eq_int @ A @ X4 )
% 0.32/0.53                      & ( ord_less_int @ X4 @ C3 ) )
% 0.32/0.53                   => ( P @ X4 ) )
% 0.32/0.53                & ! [D2: int] :
% 0.32/0.53                    ( ! [X3: int] :
% 0.32/0.53                        ( ( ( ord_less_eq_int @ A @ X3 )
% 0.32/0.53                          & ( ord_less_int @ X3 @ D2 ) )
% 0.32/0.53                       => ( P @ X3 ) )
% 0.32/0.53                   => ( ord_less_eq_int @ D2 @ C3 ) ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % complete_interval
% 0.32/0.53  thf(fact_1585_zero__le__ceiling,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.32/0.53        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_le_ceiling
% 0.32/0.53  thf(fact_1586_ceiling__less__zero,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 0.32/0.53        = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % ceiling_less_zero
% 0.32/0.53  thf(fact_1587_time__array__of__list,axiom,
% 0.32/0.53      ! [Xs: list_nat,H: heap_e7401611519738050253t_unit] :
% 0.32/0.53        ( ( time_time_array_nat @ ( array_of_list_nat @ Xs ) @ H )
% 0.32/0.53        = ( plus_plus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % time_array_of_list
% 0.32/0.53  thf(fact_1588_time__array__of__list,axiom,
% 0.32/0.53      ! [Xs: list_int,H: heap_e7401611519738050253t_unit] :
% 0.32/0.53        ( ( time_time_array_int @ ( array_of_list_int @ Xs ) @ H )
% 0.32/0.53        = ( plus_plus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % time_array_of_list
% 0.32/0.53  thf(fact_1589_time__array__of__list,axiom,
% 0.32/0.53      ! [Xs: list_o,H: heap_e7401611519738050253t_unit] :
% 0.32/0.53        ( ( time_time_array_o @ ( array_of_list_o @ Xs ) @ H )
% 0.32/0.53        = ( plus_plus_nat @ ( size_size_list_o @ Xs ) @ one_one_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % time_array_of_list
% 0.32/0.53  thf(fact_1590_Suc__nat__eq__nat__zadd1,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.53       => ( ( suc @ ( nat2 @ Z2 ) )
% 0.32/0.53          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_nat_eq_nat_zadd1
% 0.32/0.53  thf(fact_1591_gen__length__def,axiom,
% 0.32/0.53      ( gen_length_nat
% 0.32/0.53      = ( ^ [N3: nat,Xs3: list_nat] : ( plus_plus_nat @ N3 @ ( size_size_list_nat @ Xs3 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % gen_length_def
% 0.32/0.53  thf(fact_1592_gen__length__def,axiom,
% 0.32/0.53      ( gen_length_int
% 0.32/0.53      = ( ^ [N3: nat,Xs3: list_int] : ( plus_plus_nat @ N3 @ ( size_size_list_int @ Xs3 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % gen_length_def
% 0.32/0.53  thf(fact_1593_gen__length__def,axiom,
% 0.32/0.53      ( gen_length_o
% 0.32/0.53      = ( ^ [N3: nat,Xs3: list_o] : ( plus_plus_nat @ N3 @ ( size_size_list_o @ Xs3 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % gen_length_def
% 0.32/0.53  thf(fact_1594_verit__minus__simplify_I4_J,axiom,
% 0.32/0.53      ! [B: int] :
% 0.32/0.53        ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 0.32/0.53        = B ) ).
% 0.32/0.53  
% 0.32/0.53  % verit_minus_simplify(4)
% 0.32/0.53  thf(fact_1595_verit__minus__simplify_I4_J,axiom,
% 0.32/0.53      ! [B: code_integer] :
% 0.32/0.53        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.53        = B ) ).
% 0.32/0.53  
% 0.32/0.53  % verit_minus_simplify(4)
% 0.32/0.53  thf(fact_1596_verit__minus__simplify_I4_J,axiom,
% 0.32/0.53      ! [B: rat] :
% 0.32/0.53        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 0.32/0.53        = B ) ).
% 0.32/0.53  
% 0.32/0.53  % verit_minus_simplify(4)
% 0.32/0.53  thf(fact_1597_neg__equal__iff__equal,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ( uminus_uminus_int @ A )
% 0.32/0.53          = ( uminus_uminus_int @ B ) )
% 0.32/0.53        = ( A = B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_equal_iff_equal
% 0.32/0.53  thf(fact_1598_neg__equal__iff__equal,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.53          = ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.53        = ( A = B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_equal_iff_equal
% 0.32/0.53  thf(fact_1599_neg__equal__iff__equal,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.53          = ( uminus_uminus_rat @ B ) )
% 0.32/0.53        = ( A = B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_equal_iff_equal
% 0.32/0.53  thf(fact_1600_add_Oinverse__inverse,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.32/0.53        = A ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_inverse
% 0.32/0.53  thf(fact_1601_add_Oinverse__inverse,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = A ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_inverse
% 0.32/0.53  thf(fact_1602_add_Oinverse__inverse,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = A ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_inverse
% 0.32/0.53  thf(fact_1603_old_Onat_Oinject,axiom,
% 0.32/0.53      ! [Nat: nat,Nat2: nat] :
% 0.32/0.53        ( ( ( suc @ Nat )
% 0.32/0.53          = ( suc @ Nat2 ) )
% 0.32/0.53        = ( Nat = Nat2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % old.nat.inject
% 0.32/0.53  thf(fact_1604_nat_Oinject,axiom,
% 0.32/0.53      ! [X22: nat,Y22: nat] :
% 0.32/0.53        ( ( ( suc @ X22 )
% 0.32/0.53          = ( suc @ Y22 ) )
% 0.32/0.53        = ( X22 = Y22 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat.inject
% 0.32/0.53  thf(fact_1605_neg__le__iff__le,axiom,
% 0.32/0.53      ! [B: code_integer,A: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_le_iff_le
% 0.32/0.53  thf(fact_1606_neg__le__iff__le,axiom,
% 0.32/0.53      ! [B: rat,A: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_le_iff_le
% 0.32/0.53  thf(fact_1607_neg__le__iff__le,axiom,
% 0.32/0.53      ! [B: int,A: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.32/0.53        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_le_iff_le
% 0.32/0.53  thf(fact_1608_add_Oinverse__neutral,axiom,
% 0.32/0.53      ( ( uminus_uminus_int @ zero_zero_int )
% 0.32/0.53      = zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_neutral
% 0.32/0.53  thf(fact_1609_add_Oinverse__neutral,axiom,
% 0.32/0.53      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.32/0.53      = zero_z3403309356797280102nteger ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_neutral
% 0.32/0.53  thf(fact_1610_add_Oinverse__neutral,axiom,
% 0.32/0.53      ( ( uminus_uminus_rat @ zero_zero_rat )
% 0.32/0.53      = zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_neutral
% 0.32/0.53  thf(fact_1611_neg__0__equal__iff__equal,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( zero_zero_int
% 0.32/0.53          = ( uminus_uminus_int @ A ) )
% 0.32/0.53        = ( zero_zero_int = A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_0_equal_iff_equal
% 0.32/0.53  thf(fact_1612_neg__0__equal__iff__equal,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( zero_z3403309356797280102nteger
% 0.32/0.53          = ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = ( zero_z3403309356797280102nteger = A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_0_equal_iff_equal
% 0.32/0.53  thf(fact_1613_neg__0__equal__iff__equal,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( zero_zero_rat
% 0.32/0.53          = ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = ( zero_zero_rat = A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_0_equal_iff_equal
% 0.32/0.53  thf(fact_1614_neg__equal__0__iff__equal,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ( uminus_uminus_int @ A )
% 0.32/0.53          = zero_zero_int )
% 0.32/0.53        = ( A = zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_equal_0_iff_equal
% 0.32/0.53  thf(fact_1615_neg__equal__0__iff__equal,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.53          = zero_z3403309356797280102nteger )
% 0.32/0.53        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_equal_0_iff_equal
% 0.32/0.53  thf(fact_1616_neg__equal__0__iff__equal,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.53          = zero_zero_rat )
% 0.32/0.53        = ( A = zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_equal_0_iff_equal
% 0.32/0.53  thf(fact_1617_equal__neg__zero,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( A
% 0.32/0.53          = ( uminus_uminus_int @ A ) )
% 0.32/0.53        = ( A = zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % equal_neg_zero
% 0.32/0.53  thf(fact_1618_equal__neg__zero,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( A
% 0.32/0.53          = ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.53  
% 0.32/0.53  % equal_neg_zero
% 0.32/0.53  thf(fact_1619_equal__neg__zero,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( A
% 0.32/0.53          = ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = ( A = zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % equal_neg_zero
% 0.32/0.53  thf(fact_1620_neg__equal__zero,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ( uminus_uminus_int @ A )
% 0.32/0.53          = A )
% 0.32/0.53        = ( A = zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_equal_zero
% 0.32/0.53  thf(fact_1621_neg__equal__zero,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.53          = A )
% 0.32/0.53        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_equal_zero
% 0.32/0.53  thf(fact_1622_neg__equal__zero,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.53          = A )
% 0.32/0.53        = ( A = zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_equal_zero
% 0.32/0.53  thf(fact_1623_neg__less__iff__less,axiom,
% 0.32/0.53      ! [B: int,A: int] :
% 0.32/0.53        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.32/0.53        = ( ord_less_int @ A @ B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_iff_less
% 0.32/0.53  thf(fact_1624_neg__less__iff__less,axiom,
% 0.32/0.53      ! [B: code_integer,A: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_iff_less
% 0.32/0.53  thf(fact_1625_neg__less__iff__less,axiom,
% 0.32/0.53      ! [B: rat,A: rat] :
% 0.32/0.53        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = ( ord_less_rat @ A @ B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_iff_less
% 0.32/0.53  thf(fact_1626_minus__add__distrib,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.32/0.53        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_add_distrib
% 0.32/0.53  thf(fact_1627_minus__add__distrib,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.53        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_add_distrib
% 0.32/0.53  thf(fact_1628_minus__add__distrib,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.53        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_add_distrib
% 0.32/0.53  thf(fact_1629_minus__add__cancel,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.32/0.53        = B ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_add_cancel
% 0.32/0.53  thf(fact_1630_minus__add__cancel,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.53        = B ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_add_cancel
% 0.32/0.53  thf(fact_1631_minus__add__cancel,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.53        = B ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_add_cancel
% 0.32/0.53  thf(fact_1632_add__minus__cancel,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.32/0.53        = B ) ).
% 0.32/0.53  
% 0.32/0.53  % add_minus_cancel
% 0.32/0.53  thf(fact_1633_add__minus__cancel,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 0.32/0.53        = B ) ).
% 0.32/0.53  
% 0.32/0.53  % add_minus_cancel
% 0.32/0.53  thf(fact_1634_add__minus__cancel,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.32/0.53        = B ) ).
% 0.32/0.53  
% 0.32/0.53  % add_minus_cancel
% 0.32/0.53  thf(fact_1635_lessI,axiom,
% 0.32/0.53      ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lessI
% 0.32/0.53  thf(fact_1636_Suc__mono,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ N )
% 0.32/0.53       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_mono
% 0.32/0.53  thf(fact_1637_Suc__less__eq,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.32/0.53        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_less_eq
% 0.32/0.53  thf(fact_1638_Suc__le__mono,axiom,
% 0.32/0.53      ! [N: nat,M: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.32/0.53        = ( ord_less_eq_nat @ N @ M ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_le_mono
% 0.32/0.53  thf(fact_1639_add__Suc__right,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.32/0.53        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_Suc_right
% 0.32/0.53  thf(fact_1640_negative__eq__positive,axiom,
% 0.32/0.53      ! [N: nat,M: nat] :
% 0.32/0.53        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.53          = ( semiri1314217659103216013at_int @ M ) )
% 0.32/0.53        = ( ( N = zero_zero_nat )
% 0.32/0.53          & ( M = zero_zero_nat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % negative_eq_positive
% 0.32/0.53  thf(fact_1641_of__int__minus,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z2 ) )
% 0.32/0.53        = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_minus
% 0.32/0.53  thf(fact_1642_of__int__minus,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z2 ) )
% 0.32/0.53        = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_minus
% 0.32/0.53  thf(fact_1643_of__int__minus,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z2 ) )
% 0.32/0.53        = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_minus
% 0.32/0.53  thf(fact_1644_negative__zle,axiom,
% 0.32/0.53      ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.32/0.53  
% 0.32/0.53  % negative_zle
% 0.32/0.53  thf(fact_1645_neg__less__eq__nonneg,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.32/0.53        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_eq_nonneg
% 0.32/0.53  thf(fact_1646_neg__less__eq__nonneg,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.32/0.53        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_eq_nonneg
% 0.32/0.53  thf(fact_1647_neg__less__eq__nonneg,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.32/0.53        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_eq_nonneg
% 0.32/0.53  thf(fact_1648_less__eq__neg__nonpos,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_eq_neg_nonpos
% 0.32/0.53  thf(fact_1649_less__eq__neg__nonpos,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_eq_neg_nonpos
% 0.32/0.53  thf(fact_1650_less__eq__neg__nonpos,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.32/0.53        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_eq_neg_nonpos
% 0.32/0.53  thf(fact_1651_neg__le__0__iff__le,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.32/0.53        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_le_0_iff_le
% 0.32/0.53  thf(fact_1652_neg__le__0__iff__le,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.32/0.53        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_le_0_iff_le
% 0.32/0.53  thf(fact_1653_neg__le__0__iff__le,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.32/0.53        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_le_0_iff_le
% 0.32/0.53  thf(fact_1654_neg__0__le__iff__le,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_0_le_iff_le
% 0.32/0.53  thf(fact_1655_neg__0__le__iff__le,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_0_le_iff_le
% 0.32/0.53  thf(fact_1656_neg__0__le__iff__le,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.32/0.53        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_0_le_iff_le
% 0.32/0.53  thf(fact_1657_neg__less__0__iff__less,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.32/0.53        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_0_iff_less
% 0.32/0.53  thf(fact_1658_neg__less__0__iff__less,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.32/0.53        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_0_iff_less
% 0.32/0.53  thf(fact_1659_neg__less__0__iff__less,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.32/0.53        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_0_iff_less
% 0.32/0.53  thf(fact_1660_neg__0__less__iff__less,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.32/0.53        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_0_less_iff_less
% 0.32/0.53  thf(fact_1661_neg__0__less__iff__less,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_0_less_iff_less
% 0.32/0.53  thf(fact_1662_neg__0__less__iff__less,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_0_less_iff_less
% 0.32/0.53  thf(fact_1663_neg__less__pos,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.32/0.53        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_pos
% 0.32/0.53  thf(fact_1664_neg__less__pos,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.32/0.53        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_pos
% 0.32/0.53  thf(fact_1665_neg__less__pos,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.32/0.53        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_less_pos
% 0.32/0.53  thf(fact_1666_less__neg__neg,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.32/0.53        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_neg_neg
% 0.32/0.53  thf(fact_1667_less__neg__neg,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_neg_neg
% 0.32/0.53  thf(fact_1668_less__neg__neg,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_neg_neg
% 0.32/0.53  thf(fact_1669_ab__left__minus,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.32/0.53        = zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % ab_left_minus
% 0.32/0.53  thf(fact_1670_ab__left__minus,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.32/0.53        = zero_z3403309356797280102nteger ) ).
% 0.32/0.53  
% 0.32/0.53  % ab_left_minus
% 0.32/0.53  thf(fact_1671_ab__left__minus,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.32/0.53        = zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % ab_left_minus
% 0.32/0.53  thf(fact_1672_add_Oright__inverse,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.32/0.53        = zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % add.right_inverse
% 0.32/0.53  thf(fact_1673_add_Oright__inverse,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.53        = zero_z3403309356797280102nteger ) ).
% 0.32/0.53  
% 0.32/0.53  % add.right_inverse
% 0.32/0.53  thf(fact_1674_add_Oright__inverse,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.32/0.53        = zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % add.right_inverse
% 0.32/0.53  thf(fact_1675_zero__less__Suc,axiom,
% 0.32/0.53      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_less_Suc
% 0.32/0.53  thf(fact_1676_less__Suc0,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.32/0.53        = ( N = zero_zero_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_Suc0
% 0.32/0.53  thf(fact_1677_negative__zless,axiom,
% 0.32/0.53      ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.32/0.53  
% 0.32/0.53  % negative_zless
% 0.32/0.53  thf(fact_1678_nat__zminus__int,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.53        = zero_zero_nat ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_zminus_int
% 0.32/0.53  thf(fact_1679_floor__uminus__of__int,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z2 ) ) )
% 0.32/0.53        = ( uminus_uminus_int @ Z2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_uminus_of_int
% 0.32/0.53  thf(fact_1680_frac__of__int,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.53        = zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % frac_of_int
% 0.32/0.53  thf(fact_1681_dbl__inc__simps_I4_J,axiom,
% 0.32/0.53      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.53      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % dbl_inc_simps(4)
% 0.32/0.53  thf(fact_1682_dbl__inc__simps_I4_J,axiom,
% 0.32/0.53      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.53      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.53  
% 0.32/0.53  % dbl_inc_simps(4)
% 0.32/0.53  thf(fact_1683_dbl__inc__simps_I4_J,axiom,
% 0.32/0.53      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.53      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % dbl_inc_simps(4)
% 0.32/0.53  thf(fact_1684_add__neg__numeral__special_I8_J,axiom,
% 0.32/0.53      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.32/0.53      = zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_numeral_special(8)
% 0.32/0.53  thf(fact_1685_add__neg__numeral__special_I8_J,axiom,
% 0.32/0.53      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.32/0.53      = zero_z3403309356797280102nteger ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_numeral_special(8)
% 0.32/0.53  thf(fact_1686_add__neg__numeral__special_I8_J,axiom,
% 0.32/0.53      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.32/0.53      = zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_numeral_special(8)
% 0.32/0.53  thf(fact_1687_add__neg__numeral__special_I7_J,axiom,
% 0.32/0.53      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.53      = zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_numeral_special(7)
% 0.32/0.53  thf(fact_1688_add__neg__numeral__special_I7_J,axiom,
% 0.32/0.53      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.53      = zero_z3403309356797280102nteger ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_numeral_special(7)
% 0.32/0.53  thf(fact_1689_add__neg__numeral__special_I7_J,axiom,
% 0.32/0.53      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.53      = zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % add_neg_numeral_special(7)
% 0.32/0.53  thf(fact_1690_of__nat__Suc,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 0.32/0.53        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_Suc
% 0.32/0.53  thf(fact_1691_of__nat__Suc,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 0.32/0.53        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_Suc
% 0.32/0.53  thf(fact_1692_of__nat__Suc,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 0.32/0.53        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_Suc
% 0.32/0.53  thf(fact_1693_of__nat__Suc,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 0.32/0.53        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_Suc
% 0.32/0.53  thf(fact_1694_of__nat__Suc,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ( ( semiri3763490453095760265atural @ ( suc @ M ) )
% 0.32/0.53        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( semiri3763490453095760265atural @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_Suc
% 0.32/0.53  thf(fact_1695_nat__1,axiom,
% 0.32/0.53      ( ( nat2 @ one_one_int )
% 0.32/0.53      = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_1
% 0.32/0.53  thf(fact_1696_one__less__nat__eq,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
% 0.32/0.53        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % one_less_nat_eq
% 0.32/0.53  thf(fact_1697_Nat_OlessE,axiom,
% 0.32/0.53      ! [I: nat,K: nat] :
% 0.32/0.53        ( ( ord_less_nat @ I @ K )
% 0.32/0.53       => ( ( K
% 0.32/0.53           != ( suc @ I ) )
% 0.32/0.53         => ~ ! [J2: nat] :
% 0.32/0.53                ( ( ord_less_nat @ I @ J2 )
% 0.32/0.53               => ( K
% 0.32/0.53                 != ( suc @ J2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Nat.lessE
% 0.32/0.53  thf(fact_1698_Suc__lessD,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.32/0.53       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_lessD
% 0.32/0.53  thf(fact_1699_Suc__lessE,axiom,
% 0.32/0.53      ! [I: nat,K: nat] :
% 0.32/0.53        ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.32/0.53       => ~ ! [J2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ I @ J2 )
% 0.32/0.53             => ( K
% 0.32/0.53               != ( suc @ J2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_lessE
% 0.32/0.53  thf(fact_1700_Suc__lessI,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ N )
% 0.32/0.53       => ( ( ( suc @ M )
% 0.32/0.53           != N )
% 0.32/0.53         => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_lessI
% 0.32/0.53  thf(fact_1701_less__SucE,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.32/0.53       => ( ~ ( ord_less_nat @ M @ N )
% 0.32/0.53         => ( M = N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_SucE
% 0.32/0.53  thf(fact_1702_less__SucI,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ N )
% 0.32/0.53       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_SucI
% 0.32/0.53  thf(fact_1703_Ex__less__Suc,axiom,
% 0.32/0.53      ! [N: nat,P: nat > $o] :
% 0.32/0.53        ( ( ? [I2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.32/0.53              & ( P @ I2 ) ) )
% 0.32/0.53        = ( ( P @ N )
% 0.32/0.53          | ? [I2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ I2 @ N )
% 0.32/0.53              & ( P @ I2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Ex_less_Suc
% 0.32/0.53  thf(fact_1704_less__Suc__eq,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.32/0.53        = ( ( ord_less_nat @ M @ N )
% 0.32/0.53          | ( M = N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_Suc_eq
% 0.32/0.53  thf(fact_1705_nat__neq__iff,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( M != N )
% 0.32/0.53        = ( ( ord_less_nat @ M @ N )
% 0.32/0.53          | ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_neq_iff
% 0.32/0.53  thf(fact_1706_not__less__eq,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.32/0.53        = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % not_less_eq
% 0.32/0.53  thf(fact_1707_All__less__Suc,axiom,
% 0.32/0.53      ! [N: nat,P: nat > $o] :
% 0.32/0.53        ( ( ! [I2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.32/0.53             => ( P @ I2 ) ) )
% 0.32/0.53        = ( ( P @ N )
% 0.32/0.53          & ! [I2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ I2 @ N )
% 0.32/0.53             => ( P @ I2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % All_less_Suc
% 0.32/0.53  thf(fact_1708_Suc__less__eq2,axiom,
% 0.32/0.53      ! [N: nat,M: nat] :
% 0.32/0.53        ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.53        = ( ? [M7: nat] :
% 0.32/0.53              ( ( M
% 0.32/0.53                = ( suc @ M7 ) )
% 0.32/0.53              & ( ord_less_nat @ N @ M7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_less_eq2
% 0.32/0.53  thf(fact_1709_less__antisym,axiom,
% 0.32/0.53      ! [N: nat,M: nat] :
% 0.32/0.53        ( ~ ( ord_less_nat @ N @ M )
% 0.32/0.53       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.32/0.53         => ( M = N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_antisym
% 0.32/0.53  thf(fact_1710_Suc__less__SucD,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.32/0.53       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_less_SucD
% 0.32/0.53  thf(fact_1711_less__not__refl,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ~ ( ord_less_nat @ N @ N ) ).
% 0.32/0.53  
% 0.32/0.53  % less_not_refl
% 0.32/0.53  thf(fact_1712_less__not__refl2,axiom,
% 0.32/0.53      ! [N: nat,M: nat] :
% 0.32/0.53        ( ( ord_less_nat @ N @ M )
% 0.32/0.53       => ( M != N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_not_refl2
% 0.32/0.53  thf(fact_1713_less__not__refl3,axiom,
% 0.32/0.53      ! [S: nat,T: nat] :
% 0.32/0.53        ( ( ord_less_nat @ S @ T )
% 0.32/0.53       => ( S != T ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_not_refl3
% 0.32/0.53  thf(fact_1714_less__trans__Suc,axiom,
% 0.32/0.53      ! [I: nat,J: nat,K: nat] :
% 0.32/0.53        ( ( ord_less_nat @ I @ J )
% 0.32/0.53       => ( ( ord_less_nat @ J @ K )
% 0.32/0.53         => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_trans_Suc
% 0.32/0.53  thf(fact_1715_less__Suc__induct,axiom,
% 0.32/0.53      ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.32/0.53        ( ( ord_less_nat @ I @ J )
% 0.32/0.53       => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 0.32/0.53         => ( ! [I3: nat,J2: nat,K3: nat] :
% 0.32/0.53                ( ( ord_less_nat @ I3 @ J2 )
% 0.32/0.53               => ( ( ord_less_nat @ J2 @ K3 )
% 0.32/0.53                 => ( ( P @ I3 @ J2 )
% 0.32/0.53                   => ( ( P @ J2 @ K3 )
% 0.32/0.53                     => ( P @ I3 @ K3 ) ) ) ) )
% 0.32/0.53           => ( P @ I @ J ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_Suc_induct
% 0.32/0.53  thf(fact_1716_less__irrefl__nat,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ~ ( ord_less_nat @ N @ N ) ).
% 0.32/0.53  
% 0.32/0.53  % less_irrefl_nat
% 0.32/0.53  thf(fact_1717_nat__less__induct,axiom,
% 0.32/0.53      ! [P: nat > $o,N: nat] :
% 0.32/0.53        ( ! [N2: nat] :
% 0.32/0.53            ( ! [M6: nat] :
% 0.32/0.53                ( ( ord_less_nat @ M6 @ N2 )
% 0.32/0.53               => ( P @ M6 ) )
% 0.32/0.53           => ( P @ N2 ) )
% 0.32/0.53       => ( P @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_less_induct
% 0.32/0.53  thf(fact_1718_infinite__descent,axiom,
% 0.32/0.53      ! [P: nat > $o,N: nat] :
% 0.32/0.53        ( ! [N2: nat] :
% 0.32/0.53            ( ~ ( P @ N2 )
% 0.32/0.53           => ? [M6: nat] :
% 0.32/0.53                ( ( ord_less_nat @ M6 @ N2 )
% 0.32/0.53                & ~ ( P @ M6 ) ) )
% 0.32/0.53       => ( P @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % infinite_descent
% 0.32/0.53  thf(fact_1719_linorder__neqE__nat,axiom,
% 0.32/0.53      ! [X2: nat,Y: nat] :
% 0.32/0.53        ( ( X2 != Y )
% 0.32/0.53       => ( ~ ( ord_less_nat @ X2 @ Y )
% 0.32/0.53         => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % linorder_neqE_nat
% 0.32/0.53  thf(fact_1720_strict__inc__induct,axiom,
% 0.32/0.53      ! [I: nat,J: nat,P: nat > $o] :
% 0.32/0.53        ( ( ord_less_nat @ I @ J )
% 0.32/0.53       => ( ! [I3: nat] :
% 0.32/0.53              ( ( J
% 0.32/0.53                = ( suc @ I3 ) )
% 0.32/0.53             => ( P @ I3 ) )
% 0.32/0.53         => ( ! [I3: nat] :
% 0.32/0.53                ( ( ord_less_nat @ I3 @ J )
% 0.32/0.53               => ( ( P @ ( suc @ I3 ) )
% 0.32/0.53                 => ( P @ I3 ) ) )
% 0.32/0.53           => ( P @ I ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % strict_inc_induct
% 0.32/0.53  thf(fact_1721_not__less__less__Suc__eq,axiom,
% 0.32/0.53      ! [N: nat,M: nat] :
% 0.32/0.53        ( ~ ( ord_less_nat @ N @ M )
% 0.32/0.53       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.32/0.53          = ( N = M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % not_less_less_Suc_eq
% 0.32/0.53  thf(fact_1722_verit__negate__coefficient_I3_J,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( A = B )
% 0.32/0.53       => ( ( uminus_uminus_int @ A )
% 0.32/0.53          = ( uminus_uminus_int @ B ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % verit_negate_coefficient(3)
% 0.32/0.53  thf(fact_1723_verit__negate__coefficient_I3_J,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( A = B )
% 0.32/0.53       => ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.53          = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % verit_negate_coefficient(3)
% 0.32/0.53  thf(fact_1724_verit__negate__coefficient_I3_J,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( A = B )
% 0.32/0.53       => ( ( uminus_uminus_rat @ A )
% 0.32/0.53          = ( uminus_uminus_rat @ B ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % verit_negate_coefficient(3)
% 0.32/0.53  thf(fact_1725_n__not__Suc__n,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( N
% 0.32/0.53       != ( suc @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % n_not_Suc_n
% 0.32/0.53  thf(fact_1726_Suc__inject,axiom,
% 0.32/0.53      ! [X2: nat,Y: nat] :
% 0.32/0.53        ( ( ( suc @ X2 )
% 0.32/0.53          = ( suc @ Y ) )
% 0.32/0.53       => ( X2 = Y ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_inject
% 0.32/0.53  thf(fact_1727_minus__equation__iff,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ( uminus_uminus_int @ A )
% 0.32/0.53          = B )
% 0.32/0.53        = ( ( uminus_uminus_int @ B )
% 0.32/0.53          = A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_equation_iff
% 0.32/0.53  thf(fact_1728_minus__equation__iff,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.53          = B )
% 0.32/0.53        = ( ( uminus1351360451143612070nteger @ B )
% 0.32/0.53          = A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_equation_iff
% 0.32/0.53  thf(fact_1729_minus__equation__iff,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.53          = B )
% 0.32/0.53        = ( ( uminus_uminus_rat @ B )
% 0.32/0.53          = A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_equation_iff
% 0.32/0.53  thf(fact_1730_equation__minus__iff,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( A
% 0.32/0.53          = ( uminus_uminus_int @ B ) )
% 0.32/0.53        = ( B
% 0.32/0.53          = ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % equation_minus_iff
% 0.32/0.53  thf(fact_1731_equation__minus__iff,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( A
% 0.32/0.53          = ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.53        = ( B
% 0.32/0.53          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % equation_minus_iff
% 0.32/0.53  thf(fact_1732_equation__minus__iff,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( A
% 0.32/0.53          = ( uminus_uminus_rat @ B ) )
% 0.32/0.53        = ( B
% 0.32/0.53          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % equation_minus_iff
% 0.32/0.53  thf(fact_1733_int__of__nat__induct,axiom,
% 0.32/0.53      ! [P: int > $o,Z2: int] :
% 0.32/0.53        ( ! [N2: nat] : ( P @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.32/0.53       => ( ! [N2: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
% 0.32/0.53         => ( P @ Z2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_of_nat_induct
% 0.32/0.53  thf(fact_1734_int__cases,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ! [N2: nat] :
% 0.32/0.53            ( Z2
% 0.32/0.53           != ( semiri1314217659103216013at_int @ N2 ) )
% 0.32/0.53       => ~ ! [N2: nat] :
% 0.32/0.53              ( Z2
% 0.32/0.53             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_cases
% 0.32/0.53  thf(fact_1735_ceiling__def,axiom,
% 0.32/0.53      ( archim2889992004027027881ng_rat
% 0.32/0.53      = ( ^ [X: rat] : ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % ceiling_def
% 0.32/0.53  thf(fact_1736_floor__minus,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X2 ) )
% 0.32/0.53        = ( uminus_uminus_int @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % floor_minus
% 0.32/0.53  thf(fact_1737_ceiling__minus,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ X2 ) )
% 0.32/0.53        = ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ X2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % ceiling_minus
% 0.32/0.53  thf(fact_1738_le__imp__neg__le,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.53       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_imp_neg_le
% 0.32/0.53  thf(fact_1739_le__imp__neg__le,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.53       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_imp_neg_le
% 0.32/0.53  thf(fact_1740_le__imp__neg__le,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.53       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_imp_neg_le
% 0.32/0.53  thf(fact_1741_minus__le__iff,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.53        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_le_iff
% 0.32/0.53  thf(fact_1742_minus__le__iff,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.53        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_le_iff
% 0.32/0.53  thf(fact_1743_minus__le__iff,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.53        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_le_iff
% 0.32/0.53  thf(fact_1744_le__minus__iff,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.53        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_iff
% 0.32/0.53  thf(fact_1745_le__minus__iff,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.32/0.53        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_iff
% 0.32/0.53  thf(fact_1746_le__minus__iff,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.53        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_iff
% 0.32/0.53  thf(fact_1747_verit__negate__coefficient_I2_J,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_int @ A @ B )
% 0.32/0.53       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % verit_negate_coefficient(2)
% 0.32/0.53  thf(fact_1748_verit__negate__coefficient_I2_J,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.53       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % verit_negate_coefficient(2)
% 0.32/0.53  thf(fact_1749_verit__negate__coefficient_I2_J,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_rat @ A @ B )
% 0.32/0.53       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % verit_negate_coefficient(2)
% 0.32/0.53  thf(fact_1750_minus__less__iff,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.53        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_less_iff
% 0.32/0.53  thf(fact_1751_minus__less__iff,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.53        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_less_iff
% 0.32/0.53  thf(fact_1752_minus__less__iff,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.53        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % minus_less_iff
% 0.32/0.53  thf(fact_1753_less__minus__iff,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.53        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_iff
% 0.32/0.53  thf(fact_1754_less__minus__iff,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.53        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_iff
% 0.32/0.53  thf(fact_1755_less__minus__iff,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.32/0.53        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_iff
% 0.32/0.53  thf(fact_1756_add_Oinverse__distrib__swap,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.32/0.53        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_distrib_swap
% 0.32/0.53  thf(fact_1757_add_Oinverse__distrib__swap,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.53        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_distrib_swap
% 0.32/0.53  thf(fact_1758_add_Oinverse__distrib__swap,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.53        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_distrib_swap
% 0.32/0.53  thf(fact_1759_group__cancel_Oneg1,axiom,
% 0.32/0.53      ! [A4: int,K: int,A: int] :
% 0.32/0.53        ( ( A4
% 0.32/0.53          = ( plus_plus_int @ K @ A ) )
% 0.32/0.53       => ( ( uminus_uminus_int @ A4 )
% 0.32/0.53          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % group_cancel.neg1
% 0.32/0.53  thf(fact_1760_group__cancel_Oneg1,axiom,
% 0.32/0.53      ! [A4: code_integer,K: code_integer,A: code_integer] :
% 0.32/0.53        ( ( A4
% 0.32/0.53          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.32/0.53       => ( ( uminus1351360451143612070nteger @ A4 )
% 0.32/0.53          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % group_cancel.neg1
% 0.32/0.53  thf(fact_1761_group__cancel_Oneg1,axiom,
% 0.32/0.53      ! [A4: rat,K: rat,A: rat] :
% 0.32/0.53        ( ( A4
% 0.32/0.53          = ( plus_plus_rat @ K @ A ) )
% 0.32/0.53       => ( ( uminus_uminus_rat @ A4 )
% 0.32/0.53          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % group_cancel.neg1
% 0.32/0.53  thf(fact_1762_is__num__normalize_I8_J,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.32/0.53        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % is_num_normalize(8)
% 0.32/0.53  thf(fact_1763_is__num__normalize_I8_J,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.53        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % is_num_normalize(8)
% 0.32/0.53  thf(fact_1764_is__num__normalize_I8_J,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.53        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % is_num_normalize(8)
% 0.32/0.53  thf(fact_1765_one__neq__neg__one,axiom,
% 0.32/0.53      ( one_one_int
% 0.32/0.53     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % one_neq_neg_one
% 0.32/0.53  thf(fact_1766_one__neq__neg__one,axiom,
% 0.32/0.53      ( one_one_Code_integer
% 0.32/0.53     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.53  
% 0.32/0.53  % one_neq_neg_one
% 0.32/0.53  thf(fact_1767_one__neq__neg__one,axiom,
% 0.32/0.53      ( one_one_rat
% 0.32/0.53     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % one_neq_neg_one
% 0.32/0.53  thf(fact_1768_lift__Suc__mono__less__iff,axiom,
% 0.32/0.53      ! [F: nat > code_integer,N: nat,M: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_le6747313008572928689nteger @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_le6747313008572928689nteger @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.53          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less_iff
% 0.32/0.53  thf(fact_1769_lift__Suc__mono__less__iff,axiom,
% 0.32/0.53      ! [F: nat > rat,N: nat,M: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.53          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less_iff
% 0.32/0.53  thf(fact_1770_lift__Suc__mono__less__iff,axiom,
% 0.32/0.53      ! [F: nat > num,N: nat,M: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.53          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less_iff
% 0.32/0.53  thf(fact_1771_lift__Suc__mono__less__iff,axiom,
% 0.32/0.53      ! [F: nat > nat,N: nat,M: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.53          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less_iff
% 0.32/0.53  thf(fact_1772_lift__Suc__mono__less__iff,axiom,
% 0.32/0.53      ! [F: nat > int,N: nat,M: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.53          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less_iff
% 0.32/0.53  thf(fact_1773_lift__Suc__mono__less,axiom,
% 0.32/0.53      ! [F: nat > code_integer,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_le6747313008572928689nteger @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_nat @ N @ N7 )
% 0.32/0.53         => ( ord_le6747313008572928689nteger @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less
% 0.32/0.53  thf(fact_1774_lift__Suc__mono__less,axiom,
% 0.32/0.53      ! [F: nat > rat,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_rat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less
% 0.32/0.53  thf(fact_1775_lift__Suc__mono__less,axiom,
% 0.32/0.53      ! [F: nat > num,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_num @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less
% 0.32/0.53  thf(fact_1776_lift__Suc__mono__less,axiom,
% 0.32/0.53      ! [F: nat > nat,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less
% 0.32/0.53  thf(fact_1777_lift__Suc__mono__less,axiom,
% 0.32/0.53      ! [F: nat > int,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_less
% 0.32/0.53  thf(fact_1778_not0__implies__Suc,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( N != zero_zero_nat )
% 0.32/0.53       => ? [M4: nat] :
% 0.32/0.53            ( N
% 0.32/0.53            = ( suc @ M4 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % not0_implies_Suc
% 0.32/0.53  thf(fact_1779_Zero__not__Suc,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ( zero_zero_nat
% 0.32/0.53       != ( suc @ M ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Zero_not_Suc
% 0.32/0.53  thf(fact_1780_Zero__neq__Suc,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ( zero_zero_nat
% 0.32/0.53       != ( suc @ M ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Zero_neq_Suc
% 0.32/0.53  thf(fact_1781_Suc__neq__Zero,axiom,
% 0.32/0.53      ! [M: nat] :
% 0.32/0.53        ( ( suc @ M )
% 0.32/0.53       != zero_zero_nat ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_neq_Zero
% 0.32/0.53  thf(fact_1782_zero__induct,axiom,
% 0.32/0.53      ! [P: nat > $o,K: nat] :
% 0.32/0.53        ( ( P @ K )
% 0.32/0.53       => ( ! [N2: nat] :
% 0.32/0.53              ( ( P @ ( suc @ N2 ) )
% 0.32/0.53             => ( P @ N2 ) )
% 0.32/0.53         => ( P @ zero_zero_nat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_induct
% 0.32/0.53  thf(fact_1783_diff__induct,axiom,
% 0.32/0.53      ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.32/0.53        ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.32/0.53       => ( ! [Y2: nat] : ( P @ zero_zero_nat @ ( suc @ Y2 ) )
% 0.32/0.53         => ( ! [X3: nat,Y2: nat] :
% 0.32/0.53                ( ( P @ X3 @ Y2 )
% 0.32/0.53               => ( P @ ( suc @ X3 ) @ ( suc @ Y2 ) ) )
% 0.32/0.53           => ( P @ M @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % diff_induct
% 0.32/0.53  thf(fact_1784_nat__induct,axiom,
% 0.32/0.53      ! [P: nat > $o,N: nat] :
% 0.32/0.53        ( ( P @ zero_zero_nat )
% 0.32/0.53       => ( ! [N2: nat] :
% 0.32/0.53              ( ( P @ N2 )
% 0.32/0.53             => ( P @ ( suc @ N2 ) ) )
% 0.32/0.53         => ( P @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_induct
% 0.32/0.53  thf(fact_1785_old_Onat_Oexhaust,axiom,
% 0.32/0.53      ! [Y: nat] :
% 0.32/0.53        ( ( Y != zero_zero_nat )
% 0.32/0.53       => ~ ! [Nat3: nat] :
% 0.32/0.53              ( Y
% 0.32/0.53             != ( suc @ Nat3 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % old.nat.exhaust
% 0.32/0.53  thf(fact_1786_nat_OdiscI,axiom,
% 0.32/0.53      ! [Nat: nat,X22: nat] :
% 0.32/0.53        ( ( Nat
% 0.32/0.53          = ( suc @ X22 ) )
% 0.32/0.53       => ( Nat != zero_zero_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat.discI
% 0.32/0.53  thf(fact_1787_old_Onat_Odistinct_I1_J,axiom,
% 0.32/0.53      ! [Nat2: nat] :
% 0.32/0.53        ( zero_zero_nat
% 0.32/0.53       != ( suc @ Nat2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % old.nat.distinct(1)
% 0.32/0.53  thf(fact_1788_old_Onat_Odistinct_I2_J,axiom,
% 0.32/0.53      ! [Nat2: nat] :
% 0.32/0.53        ( ( suc @ Nat2 )
% 0.32/0.53       != zero_zero_nat ) ).
% 0.32/0.53  
% 0.32/0.53  % old.nat.distinct(2)
% 0.32/0.53  thf(fact_1789_nat_Odistinct_I1_J,axiom,
% 0.32/0.53      ! [X22: nat] :
% 0.32/0.53        ( zero_zero_nat
% 0.32/0.53       != ( suc @ X22 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat.distinct(1)
% 0.32/0.53  thf(fact_1790_exists__least__lemma,axiom,
% 0.32/0.53      ! [P: nat > $o] :
% 0.32/0.53        ( ~ ( P @ zero_zero_nat )
% 0.32/0.53       => ( ? [X_1: nat] : ( P @ X_1 )
% 0.32/0.53         => ? [N2: nat] :
% 0.32/0.53              ( ~ ( P @ N2 )
% 0.32/0.53              & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % exists_least_lemma
% 0.32/0.53  thf(fact_1791_less__Suc__eq__0__disj,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.32/0.53        = ( ( M = zero_zero_nat )
% 0.32/0.53          | ? [J3: nat] :
% 0.32/0.53              ( ( M
% 0.32/0.53                = ( suc @ J3 ) )
% 0.32/0.53              & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_Suc_eq_0_disj
% 0.32/0.53  thf(fact_1792_gr0__implies__Suc,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.53       => ? [M4: nat] :
% 0.32/0.53            ( N
% 0.32/0.53            = ( suc @ M4 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % gr0_implies_Suc
% 0.32/0.53  thf(fact_1793_All__less__Suc2,axiom,
% 0.32/0.53      ! [N: nat,P: nat > $o] :
% 0.32/0.53        ( ( ! [I2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.32/0.53             => ( P @ I2 ) ) )
% 0.32/0.53        = ( ( P @ zero_zero_nat )
% 0.32/0.53          & ! [I2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ I2 @ N )
% 0.32/0.53             => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % All_less_Suc2
% 0.32/0.53  thf(fact_1794_gr0__conv__Suc,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.53        = ( ? [M2: nat] :
% 0.32/0.53              ( N
% 0.32/0.53              = ( suc @ M2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % gr0_conv_Suc
% 0.32/0.53  thf(fact_1795_Ex__less__Suc2,axiom,
% 0.32/0.53      ! [N: nat,P: nat > $o] :
% 0.32/0.53        ( ( ? [I2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.32/0.53              & ( P @ I2 ) ) )
% 0.32/0.53        = ( ( P @ zero_zero_nat )
% 0.32/0.53          | ? [I2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ I2 @ N )
% 0.32/0.53              & ( P @ ( suc @ I2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Ex_less_Suc2
% 0.32/0.53  thf(fact_1796_uminus__int__code_I1_J,axiom,
% 0.32/0.53      ( ( uminus_uminus_int @ zero_zero_int )
% 0.32/0.53      = zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % uminus_int_code(1)
% 0.32/0.53  thf(fact_1797_transitive__stepwise__le,axiom,
% 0.32/0.53      ! [M: nat,N: nat,R3: nat > nat > $o] :
% 0.32/0.53        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.53       => ( ! [X3: nat] : ( R3 @ X3 @ X3 )
% 0.32/0.53         => ( ! [X3: nat,Y2: nat,Z4: nat] :
% 0.32/0.53                ( ( R3 @ X3 @ Y2 )
% 0.32/0.53               => ( ( R3 @ Y2 @ Z4 )
% 0.32/0.53                 => ( R3 @ X3 @ Z4 ) ) )
% 0.32/0.53           => ( ! [N2: nat] : ( R3 @ N2 @ ( suc @ N2 ) )
% 0.32/0.53             => ( R3 @ M @ N ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % transitive_stepwise_le
% 0.32/0.53  thf(fact_1798_nat__induct__at__least,axiom,
% 0.32/0.53      ! [M: nat,N: nat,P: nat > $o] :
% 0.32/0.53        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.53       => ( ( P @ M )
% 0.32/0.53         => ( ! [N2: nat] :
% 0.32/0.53                ( ( ord_less_eq_nat @ M @ N2 )
% 0.32/0.53               => ( ( P @ N2 )
% 0.32/0.53                 => ( P @ ( suc @ N2 ) ) ) )
% 0.32/0.53           => ( P @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_induct_at_least
% 0.32/0.53  thf(fact_1799_full__nat__induct,axiom,
% 0.32/0.53      ! [P: nat > $o,N: nat] :
% 0.32/0.53        ( ! [N2: nat] :
% 0.32/0.53            ( ! [M6: nat] :
% 0.32/0.53                ( ( ord_less_eq_nat @ ( suc @ M6 ) @ N2 )
% 0.32/0.53               => ( P @ M6 ) )
% 0.32/0.53           => ( P @ N2 ) )
% 0.32/0.53       => ( P @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % full_nat_induct
% 0.32/0.53  thf(fact_1800_not__less__eq__eq,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 0.32/0.53        = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.32/0.53  
% 0.32/0.53  % not_less_eq_eq
% 0.32/0.53  thf(fact_1801_Suc__n__not__le__n,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_n_not_le_n
% 0.32/0.53  thf(fact_1802_le__Suc__eq,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.53        = ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.53          | ( M
% 0.32/0.53            = ( suc @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_Suc_eq
% 0.32/0.53  thf(fact_1803_Suc__le__D,axiom,
% 0.32/0.53      ! [N: nat,M5: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ ( suc @ N ) @ M5 )
% 0.32/0.53       => ? [M4: nat] :
% 0.32/0.53            ( M5
% 0.32/0.53            = ( suc @ M4 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_le_D
% 0.32/0.53  thf(fact_1804_le__SucI,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.53       => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_SucI
% 0.32/0.53  thf(fact_1805_le__SucE,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.53       => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.32/0.53         => ( M
% 0.32/0.53            = ( suc @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_SucE
% 0.32/0.53  thf(fact_1806_Suc__leD,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.32/0.53       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_leD
% 0.32/0.53  thf(fact_1807_Suc__leI,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ N )
% 0.32/0.53       => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_leI
% 0.32/0.53  thf(fact_1808_Suc__le__eq,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.32/0.53        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_le_eq
% 0.32/0.53  thf(fact_1809_dec__induct,axiom,
% 0.32/0.53      ! [I: nat,J: nat,P: nat > $o] :
% 0.32/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.53       => ( ( P @ I )
% 0.32/0.53         => ( ! [N2: nat] :
% 0.32/0.53                ( ( ord_less_eq_nat @ I @ N2 )
% 0.32/0.53               => ( ( ord_less_nat @ N2 @ J )
% 0.32/0.53                 => ( ( P @ N2 )
% 0.32/0.53                   => ( P @ ( suc @ N2 ) ) ) ) )
% 0.32/0.53           => ( P @ J ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % dec_induct
% 0.32/0.53  thf(fact_1810_inc__induct,axiom,
% 0.32/0.53      ! [I: nat,J: nat,P: nat > $o] :
% 0.32/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.53       => ( ( P @ J )
% 0.32/0.53         => ( ! [N2: nat] :
% 0.32/0.53                ( ( ord_less_eq_nat @ I @ N2 )
% 0.32/0.53               => ( ( ord_less_nat @ N2 @ J )
% 0.32/0.53                 => ( ( P @ ( suc @ N2 ) )
% 0.32/0.53                   => ( P @ N2 ) ) ) )
% 0.32/0.53           => ( P @ I ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % inc_induct
% 0.32/0.53  thf(fact_1811_Suc__le__lessD,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.32/0.53       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_le_lessD
% 0.32/0.53  thf(fact_1812_le__less__Suc__eq,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.53       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.32/0.53          = ( N = M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_less_Suc_eq
% 0.32/0.53  thf(fact_1813_less__Suc__eq__le,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.32/0.53        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_Suc_eq_le
% 0.32/0.53  thf(fact_1814_less__eq__Suc__le,axiom,
% 0.32/0.53      ( ord_less_nat
% 0.32/0.53      = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_eq_Suc_le
% 0.32/0.53  thf(fact_1815_le__imp__less__Suc,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.53       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_imp_less_Suc
% 0.32/0.53  thf(fact_1816_nat__in__between__eq_I1_J,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ( ord_less_nat @ A @ B )
% 0.32/0.53          & ( ord_less_eq_nat @ B @ ( suc @ A ) ) )
% 0.32/0.53        = ( B
% 0.32/0.53          = ( suc @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_in_between_eq(1)
% 0.32/0.53  thf(fact_1817_nat__in__between__eq_I2_J,axiom,
% 0.32/0.53      ! [A: nat,B: nat] :
% 0.32/0.53        ( ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.53          & ( ord_less_nat @ B @ ( suc @ A ) ) )
% 0.32/0.53        = ( B = A ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_in_between_eq(2)
% 0.32/0.53  thf(fact_1818_add__Suc__shift,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.32/0.53        = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_Suc_shift
% 0.32/0.53  thf(fact_1819_add__Suc,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.32/0.53        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_Suc
% 0.32/0.53  thf(fact_1820_nat__arith_Osuc1,axiom,
% 0.32/0.53      ! [A4: nat,K: nat,A: nat] :
% 0.32/0.53        ( ( A4
% 0.32/0.53          = ( plus_plus_nat @ K @ A ) )
% 0.32/0.53       => ( ( suc @ A4 )
% 0.32/0.53          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_arith.suc1
% 0.32/0.53  thf(fact_1821_less__imp__Suc__add,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ N )
% 0.32/0.53       => ? [K3: nat] :
% 0.32/0.53            ( N
% 0.32/0.53            = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_imp_Suc_add
% 0.32/0.53  thf(fact_1822_less__iff__Suc__add,axiom,
% 0.32/0.53      ( ord_less_nat
% 0.32/0.53      = ( ^ [M2: nat,N3: nat] :
% 0.32/0.53          ? [K2: nat] :
% 0.32/0.53            ( N3
% 0.32/0.53            = ( suc @ ( plus_plus_nat @ M2 @ K2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_iff_Suc_add
% 0.32/0.53  thf(fact_1823_less__add__Suc2,axiom,
% 0.32/0.53      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_add_Suc2
% 0.32/0.53  thf(fact_1824_less__add__Suc1,axiom,
% 0.32/0.53      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_add_Suc1
% 0.32/0.53  thf(fact_1825_less__natE,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ord_less_nat @ M @ N )
% 0.32/0.53       => ~ ! [Q4: nat] :
% 0.32/0.53              ( N
% 0.32/0.53             != ( suc @ ( plus_plus_nat @ M @ Q4 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_natE
% 0.32/0.53  thf(fact_1826_int__cases2,axiom,
% 0.32/0.53      ! [Z2: int] :
% 0.32/0.53        ( ! [N2: nat] :
% 0.32/0.53            ( Z2
% 0.32/0.53           != ( semiri1314217659103216013at_int @ N2 ) )
% 0.32/0.53       => ~ ! [N2: nat] :
% 0.32/0.53              ( Z2
% 0.32/0.53             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_cases2
% 0.32/0.53  thf(fact_1827_not__zle__0__negative,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % not_zle_0_negative
% 0.32/0.53  thf(fact_1828_negD,axiom,
% 0.32/0.53      ! [X2: int] :
% 0.32/0.53        ( ( ord_less_int @ X2 @ zero_zero_int )
% 0.32/0.53       => ? [N2: nat] :
% 0.32/0.53            ( X2
% 0.32/0.53            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % negD
% 0.32/0.53  thf(fact_1829_negative__zless__0,axiom,
% 0.32/0.53      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % negative_zless_0
% 0.32/0.53  thf(fact_1830_neg__eq__iff__add__eq__0,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ( uminus_uminus_int @ A )
% 0.32/0.53          = B )
% 0.32/0.53        = ( ( plus_plus_int @ A @ B )
% 0.32/0.53          = zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_eq_iff_add_eq_0
% 0.32/0.53  thf(fact_1831_neg__eq__iff__add__eq__0,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.53          = B )
% 0.32/0.53        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.53          = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_eq_iff_add_eq_0
% 0.32/0.53  thf(fact_1832_neg__eq__iff__add__eq__0,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.53          = B )
% 0.32/0.53        = ( ( plus_plus_rat @ A @ B )
% 0.32/0.53          = zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_eq_iff_add_eq_0
% 0.32/0.53  thf(fact_1833_eq__neg__iff__add__eq__0,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( A
% 0.32/0.53          = ( uminus_uminus_int @ B ) )
% 0.32/0.53        = ( ( plus_plus_int @ A @ B )
% 0.32/0.53          = zero_zero_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % eq_neg_iff_add_eq_0
% 0.32/0.53  thf(fact_1834_eq__neg__iff__add__eq__0,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( A
% 0.32/0.53          = ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.53        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.53          = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.53  
% 0.32/0.53  % eq_neg_iff_add_eq_0
% 0.32/0.53  thf(fact_1835_eq__neg__iff__add__eq__0,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( A
% 0.32/0.53          = ( uminus_uminus_rat @ B ) )
% 0.32/0.53        = ( ( plus_plus_rat @ A @ B )
% 0.32/0.53          = zero_zero_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % eq_neg_iff_add_eq_0
% 0.32/0.53  thf(fact_1836_add_Oinverse__unique,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ( plus_plus_int @ A @ B )
% 0.32/0.53          = zero_zero_int )
% 0.32/0.53       => ( ( uminus_uminus_int @ A )
% 0.32/0.53          = B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_unique
% 0.32/0.53  thf(fact_1837_add_Oinverse__unique,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.53          = zero_z3403309356797280102nteger )
% 0.32/0.53       => ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.53          = B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_unique
% 0.32/0.53  thf(fact_1838_add_Oinverse__unique,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ( plus_plus_rat @ A @ B )
% 0.32/0.53          = zero_zero_rat )
% 0.32/0.53       => ( ( uminus_uminus_rat @ A )
% 0.32/0.53          = B ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add.inverse_unique
% 0.32/0.53  thf(fact_1839_ab__group__add__class_Oab__left__minus,axiom,
% 0.32/0.53      ! [A: int] :
% 0.32/0.53        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.32/0.53        = zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % ab_group_add_class.ab_left_minus
% 0.32/0.53  thf(fact_1840_ab__group__add__class_Oab__left__minus,axiom,
% 0.32/0.53      ! [A: code_integer] :
% 0.32/0.53        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.32/0.53        = zero_z3403309356797280102nteger ) ).
% 0.32/0.53  
% 0.32/0.53  % ab_group_add_class.ab_left_minus
% 0.32/0.53  thf(fact_1841_ab__group__add__class_Oab__left__minus,axiom,
% 0.32/0.53      ! [A: rat] :
% 0.32/0.53        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.32/0.53        = zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % ab_group_add_class.ab_left_minus
% 0.32/0.53  thf(fact_1842_add__eq__0__iff,axiom,
% 0.32/0.53      ! [A: int,B: int] :
% 0.32/0.53        ( ( ( plus_plus_int @ A @ B )
% 0.32/0.53          = zero_zero_int )
% 0.32/0.53        = ( B
% 0.32/0.53          = ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_eq_0_iff
% 0.32/0.53  thf(fact_1843_add__eq__0__iff,axiom,
% 0.32/0.53      ! [A: code_integer,B: code_integer] :
% 0.32/0.53        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.53          = zero_z3403309356797280102nteger )
% 0.32/0.53        = ( B
% 0.32/0.53          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_eq_0_iff
% 0.32/0.53  thf(fact_1844_add__eq__0__iff,axiom,
% 0.32/0.53      ! [A: rat,B: rat] :
% 0.32/0.53        ( ( ( plus_plus_rat @ A @ B )
% 0.32/0.53          = zero_zero_rat )
% 0.32/0.53        = ( B
% 0.32/0.53          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_eq_0_iff
% 0.32/0.53  thf(fact_1845_le__minus__one__simps_I4_J,axiom,
% 0.32/0.53      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(4)
% 0.32/0.53  thf(fact_1846_le__minus__one__simps_I4_J,axiom,
% 0.32/0.53      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(4)
% 0.32/0.53  thf(fact_1847_le__minus__one__simps_I4_J,axiom,
% 0.32/0.53      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(4)
% 0.32/0.53  thf(fact_1848_le__minus__one__simps_I2_J,axiom,
% 0.32/0.53      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(2)
% 0.32/0.53  thf(fact_1849_le__minus__one__simps_I2_J,axiom,
% 0.32/0.53      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(2)
% 0.32/0.53  thf(fact_1850_le__minus__one__simps_I2_J,axiom,
% 0.32/0.53      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(2)
% 0.32/0.53  thf(fact_1851_zero__neq__neg__one,axiom,
% 0.32/0.53      ( zero_zero_int
% 0.32/0.53     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_neq_neg_one
% 0.32/0.53  thf(fact_1852_zero__neq__neg__one,axiom,
% 0.32/0.53      ( zero_z3403309356797280102nteger
% 0.32/0.53     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_neq_neg_one
% 0.32/0.53  thf(fact_1853_zero__neq__neg__one,axiom,
% 0.32/0.53      ( zero_zero_rat
% 0.32/0.53     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zero_neq_neg_one
% 0.32/0.53  thf(fact_1854_less__minus__one__simps_I2_J,axiom,
% 0.32/0.53      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(2)
% 0.32/0.53  thf(fact_1855_less__minus__one__simps_I2_J,axiom,
% 0.32/0.53      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(2)
% 0.32/0.53  thf(fact_1856_less__minus__one__simps_I2_J,axiom,
% 0.32/0.53      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(2)
% 0.32/0.53  thf(fact_1857_less__minus__one__simps_I4_J,axiom,
% 0.32/0.53      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(4)
% 0.32/0.53  thf(fact_1858_less__minus__one__simps_I4_J,axiom,
% 0.32/0.53      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(4)
% 0.32/0.53  thf(fact_1859_less__minus__one__simps_I4_J,axiom,
% 0.32/0.53      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(4)
% 0.32/0.53  thf(fact_1860_lift__Suc__antimono__le,axiom,
% 0.32/0.53      ! [F: nat > set_nat,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_set_nat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_antimono_le
% 0.32/0.53  thf(fact_1861_lift__Suc__antimono__le,axiom,
% 0.32/0.53      ! [F: nat > rat,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_rat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_antimono_le
% 0.32/0.53  thf(fact_1862_lift__Suc__antimono__le,axiom,
% 0.32/0.53      ! [F: nat > num,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_num @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_antimono_le
% 0.32/0.53  thf(fact_1863_lift__Suc__antimono__le,axiom,
% 0.32/0.53      ! [F: nat > nat,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_nat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_antimono_le
% 0.32/0.53  thf(fact_1864_lift__Suc__antimono__le,axiom,
% 0.32/0.53      ! [F: nat > int,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_int @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_antimono_le
% 0.32/0.53  thf(fact_1865_lift__Suc__mono__le,axiom,
% 0.32/0.53      ! [F: nat > set_nat,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_le
% 0.32/0.53  thf(fact_1866_lift__Suc__mono__le,axiom,
% 0.32/0.53      ! [F: nat > rat,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_le
% 0.32/0.53  thf(fact_1867_lift__Suc__mono__le,axiom,
% 0.32/0.53      ! [F: nat > num,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_le
% 0.32/0.53  thf(fact_1868_lift__Suc__mono__le,axiom,
% 0.32/0.53      ! [F: nat > nat,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_le
% 0.32/0.53  thf(fact_1869_lift__Suc__mono__le,axiom,
% 0.32/0.53      ! [F: nat > int,N: nat,N7: nat] :
% 0.32/0.53        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.53       => ( ( ord_less_eq_nat @ N @ N7 )
% 0.32/0.53         => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % lift_Suc_mono_le
% 0.32/0.53  thf(fact_1870_of__nat__neq__0,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.32/0.53       != zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_neq_0
% 0.32/0.53  thf(fact_1871_of__nat__neq__0,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 0.32/0.53       != zero_zero_nat ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_neq_0
% 0.32/0.53  thf(fact_1872_of__nat__neq__0,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( semiri4939895301339042750nteger @ ( suc @ N ) )
% 0.32/0.53       != zero_z3403309356797280102nteger ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_neq_0
% 0.32/0.53  thf(fact_1873_of__nat__neq__0,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 0.32/0.53       != zero_zero_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_neq_0
% 0.32/0.53  thf(fact_1874_of__nat__neq__0,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( semiri3763490453095760265atural @ ( suc @ N ) )
% 0.32/0.53       != zero_z2226904508553997617atural ) ).
% 0.32/0.53  
% 0.32/0.53  % of_nat_neq_0
% 0.32/0.53  thf(fact_1875_nat__compl__induct_H,axiom,
% 0.32/0.53      ! [P: nat > $o,N: nat] :
% 0.32/0.53        ( ( P @ zero_zero_nat )
% 0.32/0.53       => ( ! [N2: nat] :
% 0.32/0.53              ( ! [Nn: nat] :
% 0.32/0.53                  ( ( ord_less_eq_nat @ Nn @ N2 )
% 0.32/0.53                 => ( P @ Nn ) )
% 0.32/0.53             => ( P @ ( suc @ N2 ) ) )
% 0.32/0.53         => ( P @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_compl_induct'
% 0.32/0.53  thf(fact_1876_nat__compl__induct,axiom,
% 0.32/0.53      ! [P: nat > $o,N: nat] :
% 0.32/0.53        ( ( P @ zero_zero_nat )
% 0.32/0.53       => ( ! [N2: nat] :
% 0.32/0.53              ( ! [Nn: nat] :
% 0.32/0.53                  ( ( ord_less_eq_nat @ Nn @ N2 )
% 0.32/0.53                 => ( P @ Nn ) )
% 0.32/0.53             => ( P @ ( suc @ N2 ) ) )
% 0.32/0.53         => ( P @ N ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_compl_induct
% 0.32/0.53  thf(fact_1877_ex__least__nat__less,axiom,
% 0.32/0.53      ! [P: nat > $o,N: nat] :
% 0.32/0.53        ( ( P @ N )
% 0.32/0.53       => ( ~ ( P @ zero_zero_nat )
% 0.32/0.53         => ? [K3: nat] :
% 0.32/0.53              ( ( ord_less_nat @ K3 @ N )
% 0.32/0.53              & ! [I4: nat] :
% 0.32/0.53                  ( ( ord_less_eq_nat @ I4 @ K3 )
% 0.32/0.53                 => ~ ( P @ I4 ) )
% 0.32/0.53              & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % ex_least_nat_less
% 0.32/0.53  thf(fact_1878_one__is__add,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ( suc @ zero_zero_nat )
% 0.32/0.53          = ( plus_plus_nat @ M @ N ) )
% 0.32/0.53        = ( ( ( M
% 0.32/0.53              = ( suc @ zero_zero_nat ) )
% 0.32/0.53            & ( N = zero_zero_nat ) )
% 0.32/0.53          | ( ( M = zero_zero_nat )
% 0.32/0.53            & ( N
% 0.32/0.53              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % one_is_add
% 0.32/0.53  thf(fact_1879_add__is__1,axiom,
% 0.32/0.53      ! [M: nat,N: nat] :
% 0.32/0.53        ( ( ( plus_plus_nat @ M @ N )
% 0.32/0.53          = ( suc @ zero_zero_nat ) )
% 0.32/0.53        = ( ( ( M
% 0.32/0.53              = ( suc @ zero_zero_nat ) )
% 0.32/0.53            & ( N = zero_zero_nat ) )
% 0.32/0.53          | ( ( M = zero_zero_nat )
% 0.32/0.53            & ( N
% 0.32/0.53              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % add_is_1
% 0.32/0.53  thf(fact_1880_One__nat__def,axiom,
% 0.32/0.53      ( one_one_nat
% 0.32/0.53      = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % One_nat_def
% 0.32/0.53  thf(fact_1881_nat__induct__non__zero,axiom,
% 0.32/0.53      ! [N: nat,P: nat > $o] :
% 0.32/0.53        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.53       => ( ( P @ one_one_nat )
% 0.32/0.53         => ( ! [N2: nat] :
% 0.32/0.53                ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.32/0.53               => ( ( P @ N2 )
% 0.32/0.53                 => ( P @ ( suc @ N2 ) ) ) )
% 0.32/0.53           => ( P @ N ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_induct_non_zero
% 0.32/0.53  thf(fact_1882_int__cases4,axiom,
% 0.32/0.53      ! [M: int] :
% 0.32/0.53        ( ! [N2: nat] :
% 0.32/0.53            ( M
% 0.32/0.53           != ( semiri1314217659103216013at_int @ N2 ) )
% 0.32/0.53       => ~ ! [N2: nat] :
% 0.32/0.53              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.32/0.53             => ( M
% 0.32/0.53               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_cases4
% 0.32/0.53  thf(fact_1883_Suc__eq__plus1__left,axiom,
% 0.32/0.53      ( suc
% 0.32/0.53      = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_eq_plus1_left
% 0.32/0.53  thf(fact_1884_plus__1__eq__Suc,axiom,
% 0.32/0.53      ( ( plus_plus_nat @ one_one_nat )
% 0.32/0.53      = suc ) ).
% 0.32/0.53  
% 0.32/0.53  % plus_1_eq_Suc
% 0.32/0.53  thf(fact_1885_Suc__eq__plus1,axiom,
% 0.32/0.53      ( suc
% 0.32/0.53      = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_eq_plus1
% 0.32/0.53  thf(fact_1886_not__int__zless__negative,axiom,
% 0.32/0.53      ! [N: nat,M: nat] :
% 0.32/0.53        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % not_int_zless_negative
% 0.32/0.53  thf(fact_1887_of__int__of__nat,axiom,
% 0.32/0.53      ( ring_1_of_int_int
% 0.32/0.53      = ( ^ [K2: int] : ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_of_nat
% 0.32/0.53  thf(fact_1888_of__int__of__nat,axiom,
% 0.32/0.53      ( ring_18347121197199848620nteger
% 0.32/0.53      = ( ^ [K2: int] : ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_of_nat
% 0.32/0.53  thf(fact_1889_of__int__of__nat,axiom,
% 0.32/0.53      ( ring_1_of_int_rat
% 0.32/0.53      = ( ^ [K2: int] : ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K2 ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % of_int_of_nat
% 0.32/0.53  thf(fact_1890_frac__ge__0,axiom,
% 0.32/0.53      ! [X2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % frac_ge_0
% 0.32/0.53  thf(fact_1891_frac__lt__1,axiom,
% 0.32/0.53      ! [X2: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X2 ) @ one_one_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % frac_lt_1
% 0.32/0.53  thf(fact_1892_frac__1__eq,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 0.32/0.53        = ( archimedean_frac_rat @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % frac_1_eq
% 0.32/0.53  thf(fact_1893_le__minus__one__simps_I1_J,axiom,
% 0.32/0.53      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(1)
% 0.32/0.53  thf(fact_1894_le__minus__one__simps_I1_J,axiom,
% 0.32/0.53      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(1)
% 0.32/0.53  thf(fact_1895_le__minus__one__simps_I1_J,axiom,
% 0.32/0.53      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(1)
% 0.32/0.53  thf(fact_1896_le__minus__one__simps_I3_J,axiom,
% 0.32/0.53      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(3)
% 0.32/0.53  thf(fact_1897_le__minus__one__simps_I3_J,axiom,
% 0.32/0.53      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(3)
% 0.32/0.53  thf(fact_1898_le__minus__one__simps_I3_J,axiom,
% 0.32/0.53      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % le_minus_one_simps(3)
% 0.32/0.53  thf(fact_1899_less__minus__one__simps_I1_J,axiom,
% 0.32/0.53      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(1)
% 0.32/0.53  thf(fact_1900_less__minus__one__simps_I1_J,axiom,
% 0.32/0.53      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(1)
% 0.32/0.53  thf(fact_1901_less__minus__one__simps_I1_J,axiom,
% 0.32/0.53      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(1)
% 0.32/0.53  thf(fact_1902_less__minus__one__simps_I3_J,axiom,
% 0.32/0.53      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(3)
% 0.32/0.53  thf(fact_1903_less__minus__one__simps_I3_J,axiom,
% 0.32/0.53      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(3)
% 0.32/0.53  thf(fact_1904_less__minus__one__simps_I3_J,axiom,
% 0.32/0.53      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % less_minus_one_simps(3)
% 0.32/0.53  thf(fact_1905_int__cases3,axiom,
% 0.32/0.53      ! [K: int] :
% 0.32/0.53        ( ( K != zero_zero_int )
% 0.32/0.53       => ( ! [N2: nat] :
% 0.32/0.53              ( ( K
% 0.32/0.53                = ( semiri1314217659103216013at_int @ N2 ) )
% 0.32/0.53             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.32/0.53         => ~ ! [N2: nat] :
% 0.32/0.53                ( ( K
% 0.32/0.53                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.32/0.53               => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_cases3
% 0.32/0.53  thf(fact_1906_int__zle__neg,axiom,
% 0.32/0.53      ! [N: nat,M: nat] :
% 0.32/0.53        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.32/0.53        = ( ( N = zero_zero_nat )
% 0.32/0.53          & ( M = zero_zero_nat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_zle_neg
% 0.32/0.53  thf(fact_1907_nonpos__int__cases,axiom,
% 0.32/0.53      ! [K: int] :
% 0.32/0.53        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.32/0.53       => ~ ! [N2: nat] :
% 0.32/0.53              ( K
% 0.32/0.53             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nonpos_int_cases
% 0.32/0.53  thf(fact_1908_negative__zle__0,axiom,
% 0.32/0.53      ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 0.32/0.53  
% 0.32/0.53  % negative_zle_0
% 0.32/0.53  thf(fact_1909_zless__iff__Suc__zadd,axiom,
% 0.32/0.53      ( ord_less_int
% 0.32/0.53      = ( ^ [W: int,Z3: int] :
% 0.32/0.53          ? [N3: nat] :
% 0.32/0.53            ( Z3
% 0.32/0.53            = ( plus_plus_int @ W @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % zless_iff_Suc_zadd
% 0.32/0.53  thf(fact_1910_int__Suc,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.32/0.53        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_Suc
% 0.32/0.53  thf(fact_1911_int__ops_I4_J,axiom,
% 0.32/0.53      ! [A: nat] :
% 0.32/0.53        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.32/0.53        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % int_ops(4)
% 0.32/0.53  thf(fact_1912_neg__int__cases,axiom,
% 0.32/0.53      ! [K: int] :
% 0.32/0.53        ( ( ord_less_int @ K @ zero_zero_int )
% 0.32/0.53       => ~ ! [N2: nat] :
% 0.32/0.53              ( ( K
% 0.32/0.53                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.32/0.53             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % neg_int_cases
% 0.32/0.53  thf(fact_1913_Suc__as__int,axiom,
% 0.32/0.53      ( suc
% 0.32/0.53      = ( ^ [A2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A2 ) @ one_one_int ) ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % Suc_as_int
% 0.32/0.53  thf(fact_1914_frac__eq,axiom,
% 0.32/0.53      ! [X2: rat] :
% 0.32/0.53        ( ( ( archimedean_frac_rat @ X2 )
% 0.32/0.53          = X2 )
% 0.32/0.53        = ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.53          & ( ord_less_rat @ X2 @ one_one_rat ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % frac_eq
% 0.32/0.53  thf(fact_1915_length__code,axiom,
% 0.32/0.53      ( size_size_list_nat
% 0.32/0.53      = ( gen_length_nat @ zero_zero_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % length_code
% 0.32/0.53  thf(fact_1916_length__code,axiom,
% 0.32/0.53      ( size_size_list_int
% 0.32/0.53      = ( gen_length_int @ zero_zero_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % length_code
% 0.32/0.53  thf(fact_1917_length__code,axiom,
% 0.32/0.53      ( size_size_list_o
% 0.32/0.53      = ( gen_length_o @ zero_zero_nat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % length_code
% 0.32/0.53  thf(fact_1918_compl__le__compl__iff,axiom,
% 0.32/0.53      ! [X2: set_nat,Y: set_nat] :
% 0.32/0.53        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 0.32/0.53        = ( ord_less_eq_set_nat @ Y @ X2 ) ) ).
% 0.32/0.53  
% 0.32/0.53  % compl_le_compl_iff
% 0.32/0.53  thf(fact_1919_power__int__minus__one__minus,axiom,
% 0.32/0.53      ! [N: int] :
% 0.32/0.53        ( ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_int @ N ) )
% 0.32/0.53        = ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) ) ).
% 0.32/0.53  
% 0.32/0.53  % power_int_minus_one_minus
% 0.32/0.53  thf(fact_1920_dbl__dec__simps_I2_J,axiom,
% 0.32/0.53      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.32/0.53      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.53  
% 0.32/0.53  % dbl_dec_simps(2)
% 0.32/0.53  thf(fact_1921_dbl__dec__simps_I2_J,axiom,
% 0.32/0.53      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 0.32/0.53      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.53  
% 0.32/0.53  % dbl_dec_simps(2)
% 0.32/0.53  thf(fact_1922_dbl__dec__simps_I2_J,axiom,
% 0.32/0.53      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.32/0.53      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.53  
% 0.32/0.53  % dbl_dec_simps(2)
% 0.32/0.53  thf(fact_1923_nat__descend__induct,axiom,
% 0.32/0.53      ! [N: nat,P: nat > $o,M: nat] :
% 0.32/0.53        ( ! [K3: nat] :
% 0.32/0.53            ( ( ord_less_nat @ N @ K3 )
% 0.32/0.53           => ( P @ K3 ) )
% 0.32/0.53       => ( ! [K3: nat] :
% 0.32/0.53              ( ( ord_less_eq_nat @ K3 @ N )
% 0.32/0.53             => ( ! [I4: nat] :
% 0.32/0.53                    ( ( ord_less_nat @ K3 @ I4 )
% 0.32/0.53                   => ( P @ I4 ) )
% 0.32/0.53               => ( P @ K3 ) ) )
% 0.32/0.53         => ( P @ M ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % nat_descend_induct
% 0.32/0.53  thf(fact_1924_list__decode_Ocases,axiom,
% 0.32/0.53      ! [X2: nat] :
% 0.32/0.53        ( ( X2 != zero_zero_nat )
% 0.32/0.53       => ~ ! [N2: nat] :
% 0.32/0.53              ( X2
% 0.32/0.53             != ( suc @ N2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % list_decode.cases
% 0.32/0.53  thf(fact_1925_compl__le__swap2,axiom,
% 0.32/0.53      ! [Y: set_nat,X2: set_nat] :
% 0.32/0.53        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X2 )
% 0.32/0.53       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ Y ) ) ).
% 0.32/0.53  
% 0.32/0.53  % compl_le_swap2
% 0.32/0.53  thf(fact_1926_compl__le__swap1,axiom,
% 0.32/0.53      ! [Y: set_nat,X2: set_nat] :
% 0.32/0.53        ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X2 ) )
% 0.32/0.53       => ( ord_less_eq_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % compl_le_swap1
% 0.32/0.53  thf(fact_1927_compl__mono,axiom,
% 0.32/0.53      ! [X2: set_nat,Y: set_nat] :
% 0.32/0.53        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 0.32/0.53       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X2 ) ) ) ).
% 0.32/0.53  
% 0.32/0.53  % compl_mono
% 0.32/0.53  thf(fact_1928_dbl__dec__simps_I3_J,axiom,
% 0.32/0.53      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 0.32/0.53      = one_one_int ) ).
% 0.32/0.53  
% 0.32/0.53  % dbl_dec_simps(3)
% 0.32/0.53  thf(fact_1929_dbl__dec__simps_I3_J,axiom,
% 0.32/0.53      ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 0.32/0.53      = one_one_Code_integer ) ).
% 0.32/0.53  
% 0.32/0.53  % dbl_dec_simps(3)
% 0.32/0.53  thf(fact_1930_dbl__dec__simps_I3_J,axiom,
% 0.32/0.53      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 0.32/0.53      = one_one_rat ) ).
% 0.32/0.53  
% 0.32/0.53  % dbl_dec_simps(3)
% 0.32/0.53  thf(fact_1931_triangle__Suc,axiom,
% 0.32/0.53      ! [N: nat] :
% 0.32/0.53        ( ( nat_triangle @ ( suc @ N ) )
% 0.32/0.53        = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % triangle_Suc
% 0.32/0.54  thf(fact_1932_bot__nat__0_Oordering__top__axioms,axiom,
% 0.32/0.54      ( ordering_top_nat
% 0.32/0.54      @ ^ [X: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X )
% 0.32/0.54      @ ^ [X: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X )
% 0.32/0.54      @ zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % bot_nat_0.ordering_top_axioms
% 0.32/0.54  thf(fact_1933_power__int__add__1_H,axiom,
% 0.32/0.54      ! [X2: rat,M: int] :
% 0.32/0.54        ( ( ( X2 != zero_zero_rat )
% 0.32/0.54          | ( M
% 0.32/0.54           != ( uminus_uminus_int @ one_one_int ) ) )
% 0.32/0.54       => ( ( power_int_rat @ X2 @ ( plus_plus_int @ M @ one_one_int ) )
% 0.32/0.54          = ( times_times_rat @ X2 @ ( power_int_rat @ X2 @ M ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % power_int_add_1'
% 0.32/0.54  thf(fact_1934_power__int__add__1,axiom,
% 0.32/0.54      ! [X2: rat,M: int] :
% 0.32/0.54        ( ( ( X2 != zero_zero_rat )
% 0.32/0.54          | ( M
% 0.32/0.54           != ( uminus_uminus_int @ one_one_int ) ) )
% 0.32/0.54       => ( ( power_int_rat @ X2 @ ( plus_plus_int @ M @ one_one_int ) )
% 0.32/0.54          = ( times_times_rat @ ( power_int_rat @ X2 @ M ) @ X2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % power_int_add_1
% 0.32/0.54  thf(fact_1935_length__ge__1__conv,axiom,
% 0.32/0.54      ! [L: list_char] :
% 0.32/0.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_char @ L ) )
% 0.32/0.54        = ( L != nil_char ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_ge_1_conv
% 0.32/0.54  thf(fact_1936_length__ge__1__conv,axiom,
% 0.32/0.54      ! [L: list_nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_nat @ L ) )
% 0.32/0.54        = ( L != nil_nat ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_ge_1_conv
% 0.32/0.54  thf(fact_1937_length__ge__1__conv,axiom,
% 0.32/0.54      ! [L: list_int] :
% 0.32/0.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_int @ L ) )
% 0.32/0.54        = ( L != nil_int ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_ge_1_conv
% 0.32/0.54  thf(fact_1938_length__ge__1__conv,axiom,
% 0.32/0.54      ! [L: list_o] :
% 0.32/0.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_o @ L ) )
% 0.32/0.54        = ( L != nil_o ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_ge_1_conv
% 0.32/0.54  thf(fact_1939_foldr__length,axiom,
% 0.32/0.54      ! [L: list_nat] :
% 0.32/0.54        ( ( foldr_nat_nat
% 0.32/0.54          @ ^ [X: nat] : suc
% 0.32/0.54          @ L
% 0.32/0.54          @ zero_zero_nat )
% 0.32/0.54        = ( size_size_list_nat @ L ) ) ).
% 0.32/0.54  
% 0.32/0.54  % foldr_length
% 0.32/0.54  thf(fact_1940_foldr__length,axiom,
% 0.32/0.54      ! [L: list_int] :
% 0.32/0.54        ( ( foldr_int_nat
% 0.32/0.54          @ ^ [X: int] : suc
% 0.32/0.54          @ L
% 0.32/0.54          @ zero_zero_nat )
% 0.32/0.54        = ( size_size_list_int @ L ) ) ).
% 0.32/0.54  
% 0.32/0.54  % foldr_length
% 0.32/0.54  thf(fact_1941_foldr__length,axiom,
% 0.32/0.54      ! [L: list_o] :
% 0.32/0.54        ( ( foldr_o_nat
% 0.32/0.54          @ ^ [X: $o] : suc
% 0.32/0.54          @ L
% 0.32/0.54          @ zero_zero_nat )
% 0.32/0.54        = ( size_size_list_o @ L ) ) ).
% 0.32/0.54  
% 0.32/0.54  % foldr_length
% 0.32/0.54  thf(fact_1942_le__ceiling__iff,axiom,
% 0.32/0.54      ! [Z2: int,X2: rat] :
% 0.32/0.54        ( ( ord_less_eq_int @ Z2 @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.32/0.54        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) @ X2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_ceiling_iff
% 0.32/0.54  thf(fact_1943_diff__self__eq__0,axiom,
% 0.32/0.54      ! [M: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ M @ M )
% 0.32/0.54        = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_self_eq_0
% 0.32/0.54  thf(fact_1944_diff__0__eq__0,axiom,
% 0.32/0.54      ! [N: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.32/0.54        = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_0_eq_0
% 0.32/0.54  thf(fact_1945_mult__cancel2,axiom,
% 0.32/0.54      ! [M: nat,K: nat,N: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ M @ K )
% 0.32/0.54          = ( times_times_nat @ N @ K ) )
% 0.32/0.54        = ( ( M = N )
% 0.32/0.54          | ( K = zero_zero_nat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel2
% 0.32/0.54  thf(fact_1946_mult__cancel1,axiom,
% 0.32/0.54      ! [K: nat,M: nat,N: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ K @ M )
% 0.32/0.54          = ( times_times_nat @ K @ N ) )
% 0.32/0.54        = ( ( M = N )
% 0.32/0.54          | ( K = zero_zero_nat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel1
% 0.32/0.54  thf(fact_1947_mult__0__right,axiom,
% 0.32/0.54      ! [M: nat] :
% 0.32/0.54        ( ( times_times_nat @ M @ zero_zero_nat )
% 0.32/0.54        = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_0_right
% 0.32/0.54  thf(fact_1948_mult__is__0,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ M @ N )
% 0.32/0.54          = zero_zero_nat )
% 0.32/0.54        = ( ( M = zero_zero_nat )
% 0.32/0.54          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_is_0
% 0.32/0.54  thf(fact_1949_Suc__diff__diff,axiom,
% 0.32/0.54      ! [M: nat,N: nat,K: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.32/0.54        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Suc_diff_diff
% 0.32/0.54  thf(fact_1950_diff__Suc__Suc,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.32/0.54        = ( minus_minus_nat @ M @ N ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_Suc_Suc
% 0.32/0.54  thf(fact_1951_diff__diff__cancel,axiom,
% 0.32/0.54      ! [I: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ I @ N )
% 0.32/0.54       => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.32/0.54          = I ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_diff_cancel
% 0.32/0.54  thf(fact_1952_diff__diff__left,axiom,
% 0.32/0.54      ! [I: nat,J: nat,K: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.32/0.54        = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_diff_left
% 0.32/0.54  thf(fact_1953_nat__1__eq__mult__iff,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( one_one_nat
% 0.32/0.54          = ( times_times_nat @ M @ N ) )
% 0.32/0.54        = ( ( M = one_one_nat )
% 0.32/0.54          & ( N = one_one_nat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_1_eq_mult_iff
% 0.32/0.54  thf(fact_1954_nat__mult__eq__1__iff,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ M @ N )
% 0.32/0.54          = one_one_nat )
% 0.32/0.54        = ( ( M = one_one_nat )
% 0.32/0.54          & ( N = one_one_nat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_mult_eq_1_iff
% 0.32/0.54  thf(fact_1955_mult__zero__left,axiom,
% 0.32/0.54      ! [A: code_natural] :
% 0.32/0.54        ( ( times_2397367101498566445atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.54        = zero_z2226904508553997617atural ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_left
% 0.32/0.54  thf(fact_1956_mult__zero__left,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.54        = zero_z3403309356797280102nteger ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_left
% 0.32/0.54  thf(fact_1957_mult__zero__left,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( times_times_rat @ zero_zero_rat @ A )
% 0.32/0.54        = zero_zero_rat ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_left
% 0.32/0.54  thf(fact_1958_mult__zero__left,axiom,
% 0.32/0.54      ! [A: nat] :
% 0.32/0.54        ( ( times_times_nat @ zero_zero_nat @ A )
% 0.32/0.54        = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_left
% 0.32/0.54  thf(fact_1959_mult__zero__left,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( times_times_int @ zero_zero_int @ A )
% 0.32/0.54        = zero_zero_int ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_left
% 0.32/0.54  thf(fact_1960_mult__zero__right,axiom,
% 0.32/0.54      ! [A: code_natural] :
% 0.32/0.54        ( ( times_2397367101498566445atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.54        = zero_z2226904508553997617atural ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_right
% 0.32/0.54  thf(fact_1961_mult__zero__right,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.54        = zero_z3403309356797280102nteger ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_right
% 0.32/0.54  thf(fact_1962_mult__zero__right,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( times_times_rat @ A @ zero_zero_rat )
% 0.32/0.54        = zero_zero_rat ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_right
% 0.32/0.54  thf(fact_1963_mult__zero__right,axiom,
% 0.32/0.54      ! [A: nat] :
% 0.32/0.54        ( ( times_times_nat @ A @ zero_zero_nat )
% 0.32/0.54        = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_right
% 0.32/0.54  thf(fact_1964_mult__zero__right,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( times_times_int @ A @ zero_zero_int )
% 0.32/0.54        = zero_zero_int ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_zero_right
% 0.32/0.54  thf(fact_1965_mult__eq__0__iff,axiom,
% 0.32/0.54      ! [A: code_natural,B: code_natural] :
% 0.32/0.54        ( ( ( times_2397367101498566445atural @ A @ B )
% 0.32/0.54          = zero_z2226904508553997617atural )
% 0.32/0.54        = ( ( A = zero_z2226904508553997617atural )
% 0.32/0.54          | ( B = zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_eq_0_iff
% 0.32/0.54  thf(fact_1966_mult__eq__0__iff,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.32/0.54          = zero_z3403309356797280102nteger )
% 0.32/0.54        = ( ( A = zero_z3403309356797280102nteger )
% 0.32/0.54          | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_eq_0_iff
% 0.32/0.54  thf(fact_1967_mult__eq__0__iff,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ( times_times_rat @ A @ B )
% 0.32/0.54          = zero_zero_rat )
% 0.32/0.54        = ( ( A = zero_zero_rat )
% 0.32/0.54          | ( B = zero_zero_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_eq_0_iff
% 0.32/0.54  thf(fact_1968_mult__eq__0__iff,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ A @ B )
% 0.32/0.54          = zero_zero_nat )
% 0.32/0.54        = ( ( A = zero_zero_nat )
% 0.32/0.54          | ( B = zero_zero_nat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_eq_0_iff
% 0.32/0.54  thf(fact_1969_mult__eq__0__iff,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( ( times_times_int @ A @ B )
% 0.32/0.54          = zero_zero_int )
% 0.32/0.54        = ( ( A = zero_zero_int )
% 0.32/0.54          | ( B = zero_zero_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_eq_0_iff
% 0.32/0.54  thf(fact_1970_mult__cancel__left,axiom,
% 0.32/0.54      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.32/0.54        ( ( ( times_2397367101498566445atural @ C @ A )
% 0.32/0.54          = ( times_2397367101498566445atural @ C @ B ) )
% 0.32/0.54        = ( ( C = zero_z2226904508553997617atural )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left
% 0.32/0.54  thf(fact_1971_mult__cancel__left,axiom,
% 0.32/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ( times_3573771949741848930nteger @ C @ A )
% 0.32/0.54          = ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.54        = ( ( C = zero_z3403309356797280102nteger )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left
% 0.32/0.54  thf(fact_1972_mult__cancel__left,axiom,
% 0.32/0.54      ! [C: rat,A: rat,B: rat] :
% 0.32/0.54        ( ( ( times_times_rat @ C @ A )
% 0.32/0.54          = ( times_times_rat @ C @ B ) )
% 0.32/0.54        = ( ( C = zero_zero_rat )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left
% 0.32/0.54  thf(fact_1973_mult__cancel__left,axiom,
% 0.32/0.54      ! [C: nat,A: nat,B: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ C @ A )
% 0.32/0.54          = ( times_times_nat @ C @ B ) )
% 0.32/0.54        = ( ( C = zero_zero_nat )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left
% 0.32/0.54  thf(fact_1974_mult__cancel__left,axiom,
% 0.32/0.54      ! [C: int,A: int,B: int] :
% 0.32/0.54        ( ( ( times_times_int @ C @ A )
% 0.32/0.54          = ( times_times_int @ C @ B ) )
% 0.32/0.54        = ( ( C = zero_zero_int )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left
% 0.32/0.54  thf(fact_1975_mult__cancel__right,axiom,
% 0.32/0.54      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.32/0.54        ( ( ( times_2397367101498566445atural @ A @ C )
% 0.32/0.54          = ( times_2397367101498566445atural @ B @ C ) )
% 0.32/0.54        = ( ( C = zero_z2226904508553997617atural )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right
% 0.32/0.54  thf(fact_1976_mult__cancel__right,axiom,
% 0.32/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ( times_3573771949741848930nteger @ A @ C )
% 0.32/0.54          = ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.54        = ( ( C = zero_z3403309356797280102nteger )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right
% 0.32/0.54  thf(fact_1977_mult__cancel__right,axiom,
% 0.32/0.54      ! [A: rat,C: rat,B: rat] :
% 0.32/0.54        ( ( ( times_times_rat @ A @ C )
% 0.32/0.54          = ( times_times_rat @ B @ C ) )
% 0.32/0.54        = ( ( C = zero_zero_rat )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right
% 0.32/0.54  thf(fact_1978_mult__cancel__right,axiom,
% 0.32/0.54      ! [A: nat,C: nat,B: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ A @ C )
% 0.32/0.54          = ( times_times_nat @ B @ C ) )
% 0.32/0.54        = ( ( C = zero_zero_nat )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right
% 0.32/0.54  thf(fact_1979_mult__cancel__right,axiom,
% 0.32/0.54      ! [A: int,C: int,B: int] :
% 0.32/0.54        ( ( ( times_times_int @ A @ C )
% 0.32/0.54          = ( times_times_int @ B @ C ) )
% 0.32/0.54        = ( ( C = zero_zero_int )
% 0.32/0.54          | ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right
% 0.32/0.54  thf(fact_1980_diff__self,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ A @ A )
% 0.32/0.54        = zero_z3403309356797280102nteger ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_self
% 0.32/0.54  thf(fact_1981_diff__self,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ A @ A )
% 0.32/0.54        = zero_zero_rat ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_self
% 0.32/0.54  thf(fact_1982_diff__self,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( minus_minus_int @ A @ A )
% 0.32/0.54        = zero_zero_int ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_self
% 0.32/0.54  thf(fact_1983_diff__0__right,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_0_right
% 0.32/0.54  thf(fact_1984_diff__0__right,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_0_right
% 0.32/0.54  thf(fact_1985_diff__0__right,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_0_right
% 0.32/0.54  thf(fact_1986_zero__diff,axiom,
% 0.32/0.54      ! [A: code_natural] :
% 0.32/0.54        ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.54        = zero_z2226904508553997617atural ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_diff
% 0.32/0.54  thf(fact_1987_zero__diff,axiom,
% 0.32/0.54      ! [A: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.32/0.54        = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_diff
% 0.32/0.54  thf(fact_1988_diff__zero,axiom,
% 0.32/0.54      ! [A: code_natural] :
% 0.32/0.54        ( ( minus_7197305767214868737atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_zero
% 0.32/0.54  thf(fact_1989_diff__zero,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_zero
% 0.32/0.54  thf(fact_1990_diff__zero,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_zero
% 0.32/0.54  thf(fact_1991_diff__zero,axiom,
% 0.32/0.54      ! [A: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_zero
% 0.32/0.54  thf(fact_1992_diff__zero,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_zero
% 0.32/0.54  thf(fact_1993_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.32/0.54      ! [A: code_natural] :
% 0.32/0.54        ( ( minus_7197305767214868737atural @ A @ A )
% 0.32/0.54        = zero_z2226904508553997617atural ) ).
% 0.32/0.54  
% 0.32/0.54  % cancel_comm_monoid_add_class.diff_cancel
% 0.32/0.54  thf(fact_1994_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ A @ A )
% 0.32/0.54        = zero_z3403309356797280102nteger ) ).
% 0.32/0.54  
% 0.32/0.54  % cancel_comm_monoid_add_class.diff_cancel
% 0.32/0.54  thf(fact_1995_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ A @ A )
% 0.32/0.54        = zero_zero_rat ) ).
% 0.32/0.54  
% 0.32/0.54  % cancel_comm_monoid_add_class.diff_cancel
% 0.32/0.54  thf(fact_1996_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.32/0.54      ! [A: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ A @ A )
% 0.32/0.54        = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % cancel_comm_monoid_add_class.diff_cancel
% 0.32/0.54  thf(fact_1997_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( minus_minus_int @ A @ A )
% 0.32/0.54        = zero_zero_int ) ).
% 0.32/0.54  
% 0.32/0.54  % cancel_comm_monoid_add_class.diff_cancel
% 0.32/0.54  thf(fact_1998_mult__1,axiom,
% 0.32/0.54      ! [A: code_natural] :
% 0.32/0.54        ( ( times_2397367101498566445atural @ one_one_Code_natural @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_1
% 0.32/0.54  thf(fact_1999_mult__1,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_1
% 0.32/0.54  thf(fact_2000_mult__1,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( times_times_rat @ one_one_rat @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_1
% 0.32/0.54  thf(fact_2001_mult__1,axiom,
% 0.32/0.54      ! [A: nat] :
% 0.32/0.54        ( ( times_times_nat @ one_one_nat @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_1
% 0.32/0.54  thf(fact_2002_mult__1,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( times_times_int @ one_one_int @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_1
% 0.32/0.54  thf(fact_2003_mult_Oright__neutral,axiom,
% 0.32/0.54      ! [A: code_natural] :
% 0.32/0.54        ( ( times_2397367101498566445atural @ A @ one_one_Code_natural )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.right_neutral
% 0.32/0.54  thf(fact_2004_mult_Oright__neutral,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.right_neutral
% 0.32/0.54  thf(fact_2005_mult_Oright__neutral,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( times_times_rat @ A @ one_one_rat )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.right_neutral
% 0.32/0.54  thf(fact_2006_mult_Oright__neutral,axiom,
% 0.32/0.54      ! [A: nat] :
% 0.32/0.54        ( ( times_times_nat @ A @ one_one_nat )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.right_neutral
% 0.32/0.54  thf(fact_2007_mult_Oright__neutral,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( times_times_int @ A @ one_one_int )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.right_neutral
% 0.32/0.54  thf(fact_2008_add__diff__cancel__right_H,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_right'
% 0.32/0.54  thf(fact_2009_add__diff__cancel__right_H,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_right'
% 0.32/0.54  thf(fact_2010_add__diff__cancel__right_H,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_right'
% 0.32/0.54  thf(fact_2011_add__diff__cancel__right_H,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_right'
% 0.32/0.54  thf(fact_2012_add__diff__cancel__right,axiom,
% 0.32/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_right
% 0.32/0.54  thf(fact_2013_add__diff__cancel__right,axiom,
% 0.32/0.54      ! [A: rat,C: rat,B: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.54        = ( minus_minus_rat @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_right
% 0.32/0.54  thf(fact_2014_add__diff__cancel__right,axiom,
% 0.32/0.54      ! [A: nat,C: nat,B: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.54        = ( minus_minus_nat @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_right
% 0.32/0.54  thf(fact_2015_add__diff__cancel__right,axiom,
% 0.32/0.54      ! [A: int,C: int,B: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.32/0.54        = ( minus_minus_int @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_right
% 0.32/0.54  thf(fact_2016_add__diff__cancel__left_H,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ A )
% 0.32/0.54        = B ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_left'
% 0.32/0.54  thf(fact_2017_add__diff__cancel__left_H,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.32/0.54        = B ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_left'
% 0.32/0.54  thf(fact_2018_add__diff__cancel__left_H,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.32/0.54        = B ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_left'
% 0.32/0.54  thf(fact_2019_add__diff__cancel__left_H,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.32/0.54        = B ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_left'
% 0.32/0.54  thf(fact_2020_add__diff__cancel__left,axiom,
% 0.32/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_left
% 0.32/0.54  thf(fact_2021_add__diff__cancel__left,axiom,
% 0.32/0.54      ! [C: rat,A: rat,B: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.32/0.54        = ( minus_minus_rat @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_left
% 0.32/0.54  thf(fact_2022_add__diff__cancel__left,axiom,
% 0.32/0.54      ! [C: nat,A: nat,B: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.32/0.54        = ( minus_minus_nat @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_left
% 0.32/0.54  thf(fact_2023_add__diff__cancel__left,axiom,
% 0.32/0.54      ! [C: int,A: int,B: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.32/0.54        = ( minus_minus_int @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel_left
% 0.32/0.54  thf(fact_2024_diff__add__cancel,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_cancel
% 0.32/0.54  thf(fact_2025_diff__add__cancel,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_cancel
% 0.32/0.54  thf(fact_2026_diff__add__cancel,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_cancel
% 0.32/0.54  thf(fact_2027_add__diff__cancel,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel
% 0.32/0.54  thf(fact_2028_add__diff__cancel,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel
% 0.32/0.54  thf(fact_2029_add__diff__cancel,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_cancel
% 0.32/0.54  thf(fact_2030_minus__diff__eq,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.32/0.54        = ( minus_minus_int @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % minus_diff_eq
% 0.32/0.54  thf(fact_2031_minus__diff__eq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % minus_diff_eq
% 0.32/0.54  thf(fact_2032_minus__diff__eq,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.54        = ( minus_minus_rat @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % minus_diff_eq
% 0.32/0.54  thf(fact_2033_one__eq__mult__iff,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ( suc @ zero_zero_nat )
% 0.32/0.54          = ( times_times_nat @ M @ N ) )
% 0.32/0.54        = ( ( M
% 0.32/0.54            = ( suc @ zero_zero_nat ) )
% 0.32/0.54          & ( N
% 0.32/0.54            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % one_eq_mult_iff
% 0.32/0.54  thf(fact_2034_mult__eq__1__iff,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ M @ N )
% 0.32/0.54          = ( suc @ zero_zero_nat ) )
% 0.32/0.54        = ( ( M
% 0.32/0.54            = ( suc @ zero_zero_nat ) )
% 0.32/0.54          & ( N
% 0.32/0.54            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_eq_1_iff
% 0.32/0.54  thf(fact_2035_zero__less__diff,axiom,
% 0.32/0.54      ! [N: nat,M: nat] :
% 0.32/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.32/0.54        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_less_diff
% 0.32/0.54  thf(fact_2036_nat__0__less__mult__iff,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.32/0.54        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.54          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_0_less_mult_iff
% 0.32/0.54  thf(fact_2037_mult__less__cancel2,axiom,
% 0.32/0.54      ! [M: nat,K: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.32/0.54        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.54          & ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_less_cancel2
% 0.32/0.54  thf(fact_2038_of__nat__mult,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 0.32/0.54        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_mult
% 0.32/0.54  thf(fact_2039_of__nat__mult,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 0.32/0.54        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_mult
% 0.32/0.54  thf(fact_2040_of__nat__mult,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N ) )
% 0.32/0.54        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_mult
% 0.32/0.54  thf(fact_2041_of__nat__mult,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 0.32/0.54        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_mult
% 0.32/0.54  thf(fact_2042_of__nat__mult,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( semiri3763490453095760265atural @ ( times_times_nat @ M @ N ) )
% 0.32/0.54        = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_mult
% 0.32/0.54  thf(fact_2043_diff__is__0__eq,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ( minus_minus_nat @ M @ N )
% 0.32/0.54          = zero_zero_nat )
% 0.32/0.54        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_is_0_eq
% 0.32/0.54  thf(fact_2044_diff__is__0__eq_H,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.54       => ( ( minus_minus_nat @ M @ N )
% 0.32/0.54          = zero_zero_nat ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_is_0_eq'
% 0.32/0.54  thf(fact_2045_mult__Suc__right,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( times_times_nat @ M @ ( suc @ N ) )
% 0.32/0.54        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_Suc_right
% 0.32/0.54  thf(fact_2046_Nat_Oadd__diff__assoc,axiom,
% 0.32/0.54      ! [K: nat,J: nat,I: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.54       => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.32/0.54          = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Nat.add_diff_assoc
% 0.32/0.54  thf(fact_2047_Nat_Oadd__diff__assoc2,axiom,
% 0.32/0.54      ! [K: nat,J: nat,I: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.54       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.32/0.54          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Nat.add_diff_assoc2
% 0.32/0.54  thf(fact_2048_Nat_Odiff__diff__right,axiom,
% 0.32/0.54      ! [K: nat,J: nat,I: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.54       => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.32/0.54          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Nat.diff_diff_right
% 0.32/0.54  thf(fact_2049_of__int__mult,axiom,
% 0.32/0.54      ! [W2: int,Z2: int] :
% 0.32/0.54        ( ( ring_18347121197199848620nteger @ ( times_times_int @ W2 @ Z2 ) )
% 0.32/0.54        = ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_int_mult
% 0.32/0.54  thf(fact_2050_of__int__mult,axiom,
% 0.32/0.54      ! [W2: int,Z2: int] :
% 0.32/0.54        ( ( ring_1_of_int_rat @ ( times_times_int @ W2 @ Z2 ) )
% 0.32/0.54        = ( times_times_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_int_mult
% 0.32/0.54  thf(fact_2051_of__int__mult,axiom,
% 0.32/0.54      ! [W2: int,Z2: int] :
% 0.32/0.54        ( ( ring_1_of_int_int @ ( times_times_int @ W2 @ Z2 ) )
% 0.32/0.54        = ( times_times_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_int_mult
% 0.32/0.54  thf(fact_2052_diff__Suc__1,axiom,
% 0.32/0.54      ! [N: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.32/0.54        = N ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_Suc_1
% 0.32/0.54  thf(fact_2053_of__int__diff,axiom,
% 0.32/0.54      ! [W2: int,Z2: int] :
% 0.32/0.54        ( ( ring_18347121197199848620nteger @ ( minus_minus_int @ W2 @ Z2 ) )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_int_diff
% 0.32/0.54  thf(fact_2054_of__int__diff,axiom,
% 0.32/0.54      ! [W2: int,Z2: int] :
% 0.32/0.54        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W2 @ Z2 ) )
% 0.32/0.54        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_int_diff
% 0.32/0.54  thf(fact_2055_of__int__diff,axiom,
% 0.32/0.54      ! [W2: int,Z2: int] :
% 0.32/0.54        ( ( ring_1_of_int_int @ ( minus_minus_int @ W2 @ Z2 ) )
% 0.32/0.54        = ( minus_minus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_int_diff
% 0.32/0.54  thf(fact_2056_triangle__0,axiom,
% 0.32/0.54      ( ( nat_triangle @ zero_zero_nat )
% 0.32/0.54      = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % triangle_0
% 0.32/0.54  thf(fact_2057_diff__ge__0__iff__ge,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.54        = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_ge_0_iff_ge
% 0.32/0.54  thf(fact_2058_diff__ge__0__iff__ge,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.54        = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_ge_0_iff_ge
% 0.32/0.54  thf(fact_2059_diff__ge__0__iff__ge,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.32/0.54        = ( ord_less_eq_int @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_ge_0_iff_ge
% 0.32/0.54  thf(fact_2060_zero__comp__diff__simps_I1_J,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.54        = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_comp_diff_simps(1)
% 0.32/0.54  thf(fact_2061_zero__comp__diff__simps_I1_J,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.54        = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_comp_diff_simps(1)
% 0.32/0.54  thf(fact_2062_zero__comp__diff__simps_I1_J,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.32/0.54        = ( ord_less_eq_int @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_comp_diff_simps(1)
% 0.32/0.54  thf(fact_2063_diff__gt__0__iff__gt,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.54        = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_gt_0_iff_gt
% 0.32/0.54  thf(fact_2064_diff__gt__0__iff__gt,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.54        = ( ord_less_rat @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_gt_0_iff_gt
% 0.32/0.54  thf(fact_2065_diff__gt__0__iff__gt,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.32/0.54        = ( ord_less_int @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_gt_0_iff_gt
% 0.32/0.54  thf(fact_2066_zero__comp__diff__simps_I2_J,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.54        = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_comp_diff_simps(2)
% 0.32/0.54  thf(fact_2067_zero__comp__diff__simps_I2_J,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.54        = ( ord_less_rat @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_comp_diff_simps(2)
% 0.32/0.54  thf(fact_2068_zero__comp__diff__simps_I2_J,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.32/0.54        = ( ord_less_int @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_comp_diff_simps(2)
% 0.32/0.54  thf(fact_2069_le__add__diff__inverse,axiom,
% 0.32/0.54      ! [B: code_integer,A: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.54       => ( ( plus_p5714425477246183910nteger @ B @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_diff_inverse
% 0.32/0.54  thf(fact_2070_le__add__diff__inverse,axiom,
% 0.32/0.54      ! [B: rat,A: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.54       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_diff_inverse
% 0.32/0.54  thf(fact_2071_le__add__diff__inverse,axiom,
% 0.32/0.54      ! [B: nat,A: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.54       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_diff_inverse
% 0.32/0.54  thf(fact_2072_le__add__diff__inverse,axiom,
% 0.32/0.54      ! [B: int,A: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.54       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_diff_inverse
% 0.32/0.54  thf(fact_2073_le__add__diff__inverse2,axiom,
% 0.32/0.54      ! [B: code_integer,A: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.54       => ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_diff_inverse2
% 0.32/0.54  thf(fact_2074_le__add__diff__inverse2,axiom,
% 0.32/0.54      ! [B: rat,A: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.54       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_diff_inverse2
% 0.32/0.54  thf(fact_2075_le__add__diff__inverse2,axiom,
% 0.32/0.54      ! [B: nat,A: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.54       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_diff_inverse2
% 0.32/0.54  thf(fact_2076_le__add__diff__inverse2,axiom,
% 0.32/0.54      ! [B: int,A: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.54       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_diff_inverse2
% 0.32/0.54  thf(fact_2077_mult__cancel__right2,axiom,
% 0.32/0.54      ! [A: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ( times_3573771949741848930nteger @ A @ C )
% 0.32/0.54          = C )
% 0.32/0.54        = ( ( C = zero_z3403309356797280102nteger )
% 0.32/0.54          | ( A = one_one_Code_integer ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right2
% 0.32/0.54  thf(fact_2078_mult__cancel__right2,axiom,
% 0.32/0.54      ! [A: rat,C: rat] :
% 0.32/0.54        ( ( ( times_times_rat @ A @ C )
% 0.32/0.54          = C )
% 0.32/0.54        = ( ( C = zero_zero_rat )
% 0.32/0.54          | ( A = one_one_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right2
% 0.32/0.54  thf(fact_2079_mult__cancel__right2,axiom,
% 0.32/0.54      ! [A: int,C: int] :
% 0.32/0.54        ( ( ( times_times_int @ A @ C )
% 0.32/0.54          = C )
% 0.32/0.54        = ( ( C = zero_zero_int )
% 0.32/0.54          | ( A = one_one_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right2
% 0.32/0.54  thf(fact_2080_mult__cancel__right1,axiom,
% 0.32/0.54      ! [C: code_integer,B: code_integer] :
% 0.32/0.54        ( ( C
% 0.32/0.54          = ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.54        = ( ( C = zero_z3403309356797280102nteger )
% 0.32/0.54          | ( B = one_one_Code_integer ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right1
% 0.32/0.54  thf(fact_2081_mult__cancel__right1,axiom,
% 0.32/0.54      ! [C: rat,B: rat] :
% 0.32/0.54        ( ( C
% 0.32/0.54          = ( times_times_rat @ B @ C ) )
% 0.32/0.54        = ( ( C = zero_zero_rat )
% 0.32/0.54          | ( B = one_one_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right1
% 0.32/0.54  thf(fact_2082_mult__cancel__right1,axiom,
% 0.32/0.54      ! [C: int,B: int] :
% 0.32/0.54        ( ( C
% 0.32/0.54          = ( times_times_int @ B @ C ) )
% 0.32/0.54        = ( ( C = zero_zero_int )
% 0.32/0.54          | ( B = one_one_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_right1
% 0.32/0.54  thf(fact_2083_mult__cancel__left2,axiom,
% 0.32/0.54      ! [C: code_integer,A: code_integer] :
% 0.32/0.54        ( ( ( times_3573771949741848930nteger @ C @ A )
% 0.32/0.54          = C )
% 0.32/0.54        = ( ( C = zero_z3403309356797280102nteger )
% 0.32/0.54          | ( A = one_one_Code_integer ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left2
% 0.32/0.54  thf(fact_2084_mult__cancel__left2,axiom,
% 0.32/0.54      ! [C: rat,A: rat] :
% 0.32/0.54        ( ( ( times_times_rat @ C @ A )
% 0.32/0.54          = C )
% 0.32/0.54        = ( ( C = zero_zero_rat )
% 0.32/0.54          | ( A = one_one_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left2
% 0.32/0.54  thf(fact_2085_mult__cancel__left2,axiom,
% 0.32/0.54      ! [C: int,A: int] :
% 0.32/0.54        ( ( ( times_times_int @ C @ A )
% 0.32/0.54          = C )
% 0.32/0.54        = ( ( C = zero_zero_int )
% 0.32/0.54          | ( A = one_one_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left2
% 0.32/0.54  thf(fact_2086_mult__cancel__left1,axiom,
% 0.32/0.54      ! [C: code_integer,B: code_integer] :
% 0.32/0.54        ( ( C
% 0.32/0.54          = ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.54        = ( ( C = zero_z3403309356797280102nteger )
% 0.32/0.54          | ( B = one_one_Code_integer ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left1
% 0.32/0.54  thf(fact_2087_mult__cancel__left1,axiom,
% 0.32/0.54      ! [C: rat,B: rat] :
% 0.32/0.54        ( ( C
% 0.32/0.54          = ( times_times_rat @ C @ B ) )
% 0.32/0.54        = ( ( C = zero_zero_rat )
% 0.32/0.54          | ( B = one_one_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left1
% 0.32/0.54  thf(fact_2088_mult__cancel__left1,axiom,
% 0.32/0.54      ! [C: int,B: int] :
% 0.32/0.54        ( ( C
% 0.32/0.54          = ( times_times_int @ C @ B ) )
% 0.32/0.54        = ( ( C = zero_zero_int )
% 0.32/0.54          | ( B = one_one_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_cancel_left1
% 0.32/0.54  thf(fact_2089_diff__add__zero,axiom,
% 0.32/0.54      ! [A: code_natural,B: code_natural] :
% 0.32/0.54        ( ( minus_7197305767214868737atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 0.32/0.54        = zero_z2226904508553997617atural ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_zero
% 0.32/0.54  thf(fact_2090_diff__add__zero,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.32/0.54        = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_zero
% 0.32/0.54  thf(fact_2091_diff__numeral__special_I9_J,axiom,
% 0.32/0.54      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 0.32/0.54      = zero_z3403309356797280102nteger ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_numeral_special(9)
% 0.32/0.54  thf(fact_2092_diff__numeral__special_I9_J,axiom,
% 0.32/0.54      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.32/0.54      = zero_zero_rat ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_numeral_special(9)
% 0.32/0.54  thf(fact_2093_diff__numeral__special_I9_J,axiom,
% 0.32/0.54      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.32/0.54      = zero_zero_int ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_numeral_special(9)
% 0.32/0.54  thf(fact_2094_diff__0,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( minus_minus_int @ zero_zero_int @ A )
% 0.32/0.54        = ( uminus_uminus_int @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_0
% 0.32/0.54  thf(fact_2095_diff__0,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.54        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_0
% 0.32/0.54  thf(fact_2096_diff__0,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.32/0.54        = ( uminus_uminus_rat @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_0
% 0.32/0.54  thf(fact_2097_verit__minus__simplify_I3_J,axiom,
% 0.32/0.54      ! [B: int] :
% 0.32/0.54        ( ( minus_minus_int @ zero_zero_int @ B )
% 0.32/0.54        = ( uminus_uminus_int @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % verit_minus_simplify(3)
% 0.32/0.54  thf(fact_2098_verit__minus__simplify_I3_J,axiom,
% 0.32/0.54      ! [B: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.54        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % verit_minus_simplify(3)
% 0.32/0.54  thf(fact_2099_verit__minus__simplify_I3_J,axiom,
% 0.32/0.54      ! [B: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 0.32/0.54        = ( uminus_uminus_rat @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % verit_minus_simplify(3)
% 0.32/0.54  thf(fact_2100_mult__minus1__right,axiom,
% 0.32/0.54      ! [Z2: int] :
% 0.32/0.54        ( ( times_times_int @ Z2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.54        = ( uminus_uminus_int @ Z2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_minus1_right
% 0.32/0.54  thf(fact_2101_mult__minus1__right,axiom,
% 0.32/0.54      ! [Z2: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ Z2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.54        = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_minus1_right
% 0.32/0.54  thf(fact_2102_mult__minus1__right,axiom,
% 0.32/0.54      ! [Z2: rat] :
% 0.32/0.54        ( ( times_times_rat @ Z2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.54        = ( uminus_uminus_rat @ Z2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_minus1_right
% 0.32/0.54  thf(fact_2103_mult__minus1,axiom,
% 0.32/0.54      ! [Z2: int] :
% 0.32/0.54        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z2 )
% 0.32/0.54        = ( uminus_uminus_int @ Z2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_minus1
% 0.32/0.54  thf(fact_2104_mult__minus1,axiom,
% 0.32/0.54      ! [Z2: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z2 )
% 0.32/0.54        = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_minus1
% 0.32/0.54  thf(fact_2105_mult__minus1,axiom,
% 0.32/0.54      ! [Z2: rat] :
% 0.32/0.54        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z2 )
% 0.32/0.54        = ( uminus_uminus_rat @ Z2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_minus1
% 0.32/0.54  thf(fact_2106_uminus__add__conv__diff,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.54        = ( minus_minus_int @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % uminus_add_conv_diff
% 0.32/0.54  thf(fact_2107_uminus__add__conv__diff,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % uminus_add_conv_diff
% 0.32/0.54  thf(fact_2108_uminus__add__conv__diff,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.54        = ( minus_minus_rat @ B @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % uminus_add_conv_diff
% 0.32/0.54  thf(fact_2109_diff__minus__eq__add,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.54        = ( plus_plus_int @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_minus_eq_add
% 0.32/0.54  thf(fact_2110_diff__minus__eq__add,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.54        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_minus_eq_add
% 0.32/0.54  thf(fact_2111_diff__minus__eq__add,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.32/0.54        = ( plus_plus_rat @ A @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_minus_eq_add
% 0.32/0.54  thf(fact_2112_Suc__pred,axiom,
% 0.32/0.54      ! [N: nat] :
% 0.32/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.54       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.32/0.54          = N ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Suc_pred
% 0.32/0.54  thf(fact_2113_length__0__conv,axiom,
% 0.32/0.54      ! [Xs: list_char] :
% 0.32/0.54        ( ( ( size_size_list_char @ Xs )
% 0.32/0.54          = zero_zero_nat )
% 0.32/0.54        = ( Xs = nil_char ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_0_conv
% 0.32/0.54  thf(fact_2114_length__0__conv,axiom,
% 0.32/0.54      ! [Xs: list_nat] :
% 0.32/0.54        ( ( ( size_size_list_nat @ Xs )
% 0.32/0.54          = zero_zero_nat )
% 0.32/0.54        = ( Xs = nil_nat ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_0_conv
% 0.32/0.54  thf(fact_2115_length__0__conv,axiom,
% 0.32/0.54      ! [Xs: list_int] :
% 0.32/0.54        ( ( ( size_size_list_int @ Xs )
% 0.32/0.54          = zero_zero_nat )
% 0.32/0.54        = ( Xs = nil_int ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_0_conv
% 0.32/0.54  thf(fact_2116_length__0__conv,axiom,
% 0.32/0.54      ! [Xs: list_o] :
% 0.32/0.54        ( ( ( size_size_list_o @ Xs )
% 0.32/0.54          = zero_zero_nat )
% 0.32/0.54        = ( Xs = nil_o ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_0_conv
% 0.32/0.54  thf(fact_2117_one__le__mult__iff,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 0.32/0.54        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.32/0.54          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % one_le_mult_iff
% 0.32/0.54  thf(fact_2118_mult__le__cancel2,axiom,
% 0.32/0.54      ! [M: nat,K: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.32/0.54        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.54         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_le_cancel2
% 0.32/0.54  thf(fact_2119_diff__Suc__diff__eq1,axiom,
% 0.32/0.54      ! [K: nat,J: nat,I: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.54       => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 0.32/0.54          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_Suc_diff_eq1
% 0.32/0.54  thf(fact_2120_diff__Suc__diff__eq2,axiom,
% 0.32/0.54      ! [K: nat,J: nat,I: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.54       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 0.32/0.54          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_Suc_diff_eq2
% 0.32/0.54  thf(fact_2121_Suc__diff,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.54       => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.32/0.54         => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 0.32/0.54            = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Suc_diff
% 0.32/0.54  thf(fact_2122_zle__diff1__eq,axiom,
% 0.32/0.54      ! [W2: int,Z2: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z2 @ one_one_int ) )
% 0.32/0.54        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zle_diff1_eq
% 0.32/0.54  thf(fact_2123_floor__diff__of__int,axiom,
% 0.32/0.54      ! [X2: rat,Z2: int] :
% 0.32/0.54        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) )
% 0.32/0.54        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % floor_diff_of_int
% 0.32/0.54  thf(fact_2124_ceiling__diff__of__int,axiom,
% 0.32/0.54      ! [X2: rat,Z2: int] :
% 0.32/0.54        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) )
% 0.32/0.54        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z2 ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ceiling_diff_of_int
% 0.32/0.54  thf(fact_2125_diff__numeral__special_I12_J,axiom,
% 0.32/0.54      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.54      = zero_zero_int ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_numeral_special(12)
% 0.32/0.54  thf(fact_2126_diff__numeral__special_I12_J,axiom,
% 0.32/0.54      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.54      = zero_z3403309356797280102nteger ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_numeral_special(12)
% 0.32/0.54  thf(fact_2127_diff__numeral__special_I12_J,axiom,
% 0.32/0.54      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.54      = zero_zero_rat ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_numeral_special(12)
% 0.32/0.54  thf(fact_2128_length__greater__0__conv,axiom,
% 0.32/0.54      ! [Xs: list_char] :
% 0.32/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_char @ Xs ) )
% 0.32/0.54        = ( Xs != nil_char ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_greater_0_conv
% 0.32/0.54  thf(fact_2129_length__greater__0__conv,axiom,
% 0.32/0.54      ! [Xs: list_nat] :
% 0.32/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) )
% 0.32/0.54        = ( Xs != nil_nat ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_greater_0_conv
% 0.32/0.54  thf(fact_2130_length__greater__0__conv,axiom,
% 0.32/0.54      ! [Xs: list_int] :
% 0.32/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) )
% 0.32/0.54        = ( Xs != nil_int ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_greater_0_conv
% 0.32/0.54  thf(fact_2131_length__greater__0__conv,axiom,
% 0.32/0.54      ! [Xs: list_o] :
% 0.32/0.54        ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) )
% 0.32/0.54        = ( Xs != nil_o ) ) ).
% 0.32/0.54  
% 0.32/0.54  % length_greater_0_conv
% 0.32/0.54  thf(fact_2132_Suc__diff__1,axiom,
% 0.32/0.54      ! [N: nat] :
% 0.32/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.54       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.32/0.54          = N ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Suc_diff_1
% 0.32/0.54  thf(fact_2133_power__int__minus__one__mult__self,axiom,
% 0.32/0.54      ! [M: int] :
% 0.32/0.54        ( ( times_times_rat @ ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) )
% 0.32/0.54        = one_one_rat ) ).
% 0.32/0.54  
% 0.32/0.54  % power_int_minus_one_mult_self
% 0.32/0.54  thf(fact_2134_power__int__minus__one__mult__self_H,axiom,
% 0.32/0.54      ! [M: int,B: rat] :
% 0.32/0.54        ( ( times_times_rat @ ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( times_times_rat @ ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ B ) )
% 0.32/0.54        = B ) ).
% 0.32/0.54  
% 0.32/0.54  % power_int_minus_one_mult_self'
% 0.32/0.54  thf(fact_2135_floor__diff__one,axiom,
% 0.32/0.54      ! [X2: rat] :
% 0.32/0.54        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 0.32/0.54        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ).
% 0.32/0.54  
% 0.32/0.54  % floor_diff_one
% 0.32/0.54  thf(fact_2136_ceiling__diff__one,axiom,
% 0.32/0.54      ! [X2: rat] :
% 0.32/0.54        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 0.32/0.54        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ceiling_diff_one
% 0.32/0.54  thf(fact_2137_int__ops_I7_J,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 0.32/0.54        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % int_ops(7)
% 0.32/0.54  thf(fact_2138_ordering__top_Oextremum__uniqueI,axiom,
% 0.32/0.54      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.32/0.54        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.32/0.54       => ( ( Less_eq @ Top @ A )
% 0.32/0.54         => ( A = Top ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordering_top.extremum_uniqueI
% 0.32/0.54  thf(fact_2139_ordering__top_Onot__eq__extremum,axiom,
% 0.32/0.54      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.32/0.54        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.32/0.54       => ( ( A != Top )
% 0.32/0.54          = ( Less @ A @ Top ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordering_top.not_eq_extremum
% 0.32/0.54  thf(fact_2140_ordering__top_Oextremum__unique,axiom,
% 0.32/0.54      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.32/0.54        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.32/0.54       => ( ( Less_eq @ Top @ A )
% 0.32/0.54          = ( A = Top ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordering_top.extremum_unique
% 0.32/0.54  thf(fact_2141_ordering__top_Oextremum__strict,axiom,
% 0.32/0.54      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.32/0.54        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.32/0.54       => ~ ( Less @ Top @ A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordering_top.extremum_strict
% 0.32/0.54  thf(fact_2142_ordering__top_Oextremum,axiom,
% 0.32/0.54      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.32/0.54        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.32/0.54       => ( Less_eq @ A @ Top ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordering_top.extremum
% 0.32/0.54  thf(fact_2143_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.32/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % cancel_ab_semigroup_add_class.diff_right_commute
% 0.32/0.54  thf(fact_2144_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.32/0.54      ! [A: rat,C: rat,B: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 0.32/0.54        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % cancel_ab_semigroup_add_class.diff_right_commute
% 0.32/0.54  thf(fact_2145_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.32/0.54      ! [A: nat,C: nat,B: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.32/0.54        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % cancel_ab_semigroup_add_class.diff_right_commute
% 0.32/0.54  thf(fact_2146_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.32/0.54      ! [A: int,C: int,B: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 0.32/0.54        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % cancel_ab_semigroup_add_class.diff_right_commute
% 0.32/0.54  thf(fact_2147_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.32/0.54      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ B @ ( times_3573771949741848930nteger @ A @ C ) )
% 0.32/0.54        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_semigroup_mult_class.mult.left_commute
% 0.32/0.54  thf(fact_2148_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.32/0.54      ! [B: rat,A: rat,C: rat] :
% 0.32/0.54        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 0.32/0.54        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_semigroup_mult_class.mult.left_commute
% 0.32/0.54  thf(fact_2149_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.32/0.54      ! [B: nat,A: nat,C: nat] :
% 0.32/0.54        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.32/0.54        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_semigroup_mult_class.mult.left_commute
% 0.32/0.54  thf(fact_2150_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.32/0.54      ! [B: int,A: int,C: int] :
% 0.32/0.54        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 0.32/0.54        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_semigroup_mult_class.mult.left_commute
% 0.32/0.54  thf(fact_2151_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.32/0.54      ( times_3573771949741848930nteger
% 0.32/0.54      = ( ^ [A2: code_integer,B2: code_integer] : ( times_3573771949741848930nteger @ B2 @ A2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_semigroup_mult_class.mult.commute
% 0.32/0.54  thf(fact_2152_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.32/0.54      ( times_times_rat
% 0.32/0.54      = ( ^ [A2: rat,B2: rat] : ( times_times_rat @ B2 @ A2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_semigroup_mult_class.mult.commute
% 0.32/0.54  thf(fact_2153_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.32/0.54      ( times_times_nat
% 0.32/0.54      = ( ^ [A2: nat,B2: nat] : ( times_times_nat @ B2 @ A2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_semigroup_mult_class.mult.commute
% 0.32/0.54  thf(fact_2154_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.32/0.54      ( times_times_int
% 0.32/0.54      = ( ^ [A2: int,B2: int] : ( times_times_int @ B2 @ A2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_semigroup_mult_class.mult.commute
% 0.32/0.54  thf(fact_2155_mult_Oassoc,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.32/0.54        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.assoc
% 0.32/0.54  thf(fact_2156_mult_Oassoc,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.32/0.54        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.assoc
% 0.32/0.54  thf(fact_2157_mult_Oassoc,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.32/0.54        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.assoc
% 0.32/0.54  thf(fact_2158_mult_Oassoc,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.32/0.54        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.assoc
% 0.32/0.54  thf(fact_2159_diff__eq__diff__eq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ( minus_8373710615458151222nteger @ A @ B )
% 0.32/0.54          = ( minus_8373710615458151222nteger @ C @ D ) )
% 0.32/0.54       => ( ( A = B )
% 0.32/0.54          = ( C = D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_diff_eq
% 0.32/0.54  thf(fact_2160_diff__eq__diff__eq,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.54        ( ( ( minus_minus_rat @ A @ B )
% 0.32/0.54          = ( minus_minus_rat @ C @ D ) )
% 0.32/0.54       => ( ( A = B )
% 0.32/0.54          = ( C = D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_diff_eq
% 0.32/0.54  thf(fact_2161_diff__eq__diff__eq,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.54        ( ( ( minus_minus_int @ A @ B )
% 0.32/0.54          = ( minus_minus_int @ C @ D ) )
% 0.32/0.54       => ( ( A = B )
% 0.32/0.54          = ( C = D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_diff_eq
% 0.32/0.54  thf(fact_2162_inf__period_I1_J,axiom,
% 0.32/0.54      ! [P: code_integer > $o,D3: code_integer,Q: code_integer > $o] :
% 0.32/0.54        ( ! [X3: code_integer,K3: code_integer] :
% 0.32/0.54            ( ( P @ X3 )
% 0.32/0.54            = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) )
% 0.32/0.54       => ( ! [X3: code_integer,K3: code_integer] :
% 0.32/0.54              ( ( Q @ X3 )
% 0.32/0.54              = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) )
% 0.32/0.54         => ! [X4: code_integer,K4: code_integer] :
% 0.32/0.54              ( ( ( P @ X4 )
% 0.32/0.54                & ( Q @ X4 ) )
% 0.32/0.54              = ( ( P @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) )
% 0.32/0.54                & ( Q @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % inf_period(1)
% 0.32/0.54  thf(fact_2163_inf__period_I1_J,axiom,
% 0.32/0.54      ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 0.32/0.54        ( ! [X3: rat,K3: rat] :
% 0.32/0.54            ( ( P @ X3 )
% 0.32/0.54            = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D3 ) ) ) )
% 0.32/0.54       => ( ! [X3: rat,K3: rat] :
% 0.32/0.54              ( ( Q @ X3 )
% 0.32/0.54              = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D3 ) ) ) )
% 0.32/0.54         => ! [X4: rat,K4: rat] :
% 0.32/0.54              ( ( ( P @ X4 )
% 0.32/0.54                & ( Q @ X4 ) )
% 0.32/0.54              = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D3 ) ) )
% 0.32/0.54                & ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % inf_period(1)
% 0.32/0.54  thf(fact_2164_inf__period_I1_J,axiom,
% 0.32/0.54      ! [P: int > $o,D3: int,Q: int > $o] :
% 0.32/0.54        ( ! [X3: int,K3: int] :
% 0.32/0.54            ( ( P @ X3 )
% 0.32/0.54            = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 0.32/0.54       => ( ! [X3: int,K3: int] :
% 0.32/0.54              ( ( Q @ X3 )
% 0.32/0.54              = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 0.32/0.54         => ! [X4: int,K4: int] :
% 0.32/0.54              ( ( ( P @ X4 )
% 0.32/0.54                & ( Q @ X4 ) )
% 0.32/0.54              = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D3 ) ) )
% 0.32/0.54                & ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % inf_period(1)
% 0.32/0.54  thf(fact_2165_inf__period_I2_J,axiom,
% 0.32/0.54      ! [P: code_integer > $o,D3: code_integer,Q: code_integer > $o] :
% 0.32/0.54        ( ! [X3: code_integer,K3: code_integer] :
% 0.32/0.54            ( ( P @ X3 )
% 0.32/0.54            = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) )
% 0.32/0.54       => ( ! [X3: code_integer,K3: code_integer] :
% 0.32/0.54              ( ( Q @ X3 )
% 0.32/0.54              = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) )
% 0.32/0.54         => ! [X4: code_integer,K4: code_integer] :
% 0.32/0.54              ( ( ( P @ X4 )
% 0.32/0.54                | ( Q @ X4 ) )
% 0.32/0.54              = ( ( P @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) )
% 0.32/0.54                | ( Q @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % inf_period(2)
% 0.32/0.54  thf(fact_2166_inf__period_I2_J,axiom,
% 0.32/0.54      ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 0.32/0.54        ( ! [X3: rat,K3: rat] :
% 0.32/0.54            ( ( P @ X3 )
% 0.32/0.54            = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D3 ) ) ) )
% 0.32/0.54       => ( ! [X3: rat,K3: rat] :
% 0.32/0.54              ( ( Q @ X3 )
% 0.32/0.54              = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D3 ) ) ) )
% 0.32/0.54         => ! [X4: rat,K4: rat] :
% 0.32/0.54              ( ( ( P @ X4 )
% 0.32/0.54                | ( Q @ X4 ) )
% 0.32/0.54              = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D3 ) ) )
% 0.32/0.54                | ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % inf_period(2)
% 0.32/0.54  thf(fact_2167_inf__period_I2_J,axiom,
% 0.32/0.54      ! [P: int > $o,D3: int,Q: int > $o] :
% 0.32/0.54        ( ! [X3: int,K3: int] :
% 0.32/0.54            ( ( P @ X3 )
% 0.32/0.54            = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 0.32/0.54       => ( ! [X3: int,K3: int] :
% 0.32/0.54              ( ( Q @ X3 )
% 0.32/0.54              = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 0.32/0.54         => ! [X4: int,K4: int] :
% 0.32/0.54              ( ( ( P @ X4 )
% 0.32/0.54                | ( Q @ X4 ) )
% 0.32/0.54              = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D3 ) ) )
% 0.32/0.54                | ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % inf_period(2)
% 0.32/0.54  thf(fact_2168_square__diff__square__factored,axiom,
% 0.32/0.54      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 0.32/0.54        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X2 @ Y ) @ ( minus_8373710615458151222nteger @ X2 @ Y ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % square_diff_square_factored
% 0.32/0.54  thf(fact_2169_square__diff__square__factored,axiom,
% 0.32/0.54      ! [X2: rat,Y: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) )
% 0.32/0.54        = ( times_times_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( minus_minus_rat @ X2 @ Y ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % square_diff_square_factored
% 0.32/0.54  thf(fact_2170_square__diff__square__factored,axiom,
% 0.32/0.54      ! [X2: int,Y: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) )
% 0.32/0.54        = ( times_times_int @ ( plus_plus_int @ X2 @ Y ) @ ( minus_minus_int @ X2 @ Y ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % square_diff_square_factored
% 0.32/0.54  thf(fact_2171_eq__add__iff2,axiom,
% 0.32/0.54      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 0.32/0.54          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 0.32/0.54        = ( C
% 0.32/0.54          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_add_iff2
% 0.32/0.54  thf(fact_2172_eq__add__iff2,axiom,
% 0.32/0.54      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.32/0.54        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 0.32/0.54          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.32/0.54        = ( C
% 0.32/0.54          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_add_iff2
% 0.32/0.54  thf(fact_2173_eq__add__iff2,axiom,
% 0.32/0.54      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.32/0.54        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 0.32/0.54          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.32/0.54        = ( C
% 0.32/0.54          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_add_iff2
% 0.32/0.54  thf(fact_2174_eq__add__iff1,axiom,
% 0.32/0.54      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 0.32/0.54          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 0.32/0.54        = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C )
% 0.32/0.54          = D ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_add_iff1
% 0.32/0.54  thf(fact_2175_eq__add__iff1,axiom,
% 0.32/0.54      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.32/0.54        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 0.32/0.54          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.32/0.54        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 0.32/0.54          = D ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_add_iff1
% 0.32/0.54  thf(fact_2176_eq__add__iff1,axiom,
% 0.32/0.54      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.32/0.54        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 0.32/0.54          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.32/0.54        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 0.32/0.54          = D ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_add_iff1
% 0.32/0.54  thf(fact_2177_le__add__iff1,axiom,
% 0.32/0.54      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_iff1
% 0.32/0.54  thf(fact_2178_le__add__iff1,axiom,
% 0.32/0.54      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_iff1
% 0.32/0.54  thf(fact_2179_le__add__iff1,axiom,
% 0.32/0.54      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_iff1
% 0.32/0.54  thf(fact_2180_le__add__iff2,axiom,
% 0.32/0.54      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_iff2
% 0.32/0.54  thf(fact_2181_le__add__iff2,axiom,
% 0.32/0.54      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_iff2
% 0.32/0.54  thf(fact_2182_le__add__iff2,axiom,
% 0.32/0.54      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_iff2
% 0.32/0.54  thf(fact_2183_less__add__iff2,axiom,
% 0.32/0.54      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_add_iff2
% 0.32/0.54  thf(fact_2184_less__add__iff2,axiom,
% 0.32/0.54      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.32/0.54        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_add_iff2
% 0.32/0.54  thf(fact_2185_less__add__iff2,axiom,
% 0.32/0.54      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.32/0.54        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_add_iff2
% 0.32/0.54  thf(fact_2186_less__add__iff1,axiom,
% 0.32/0.54      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_add_iff1
% 0.32/0.54  thf(fact_2187_less__add__iff1,axiom,
% 0.32/0.54      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.32/0.54        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_add_iff1
% 0.32/0.54  thf(fact_2188_less__add__iff1,axiom,
% 0.32/0.54      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.32/0.54        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.32/0.54        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_add_iff1
% 0.32/0.54  thf(fact_2189_square__diff__one__factored,axiom,
% 0.32/0.54      ! [X2: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ one_one_Code_integer )
% 0.32/0.54        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X2 @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X2 @ one_one_Code_integer ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % square_diff_one_factored
% 0.32/0.54  thf(fact_2190_square__diff__one__factored,axiom,
% 0.32/0.54      ! [X2: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ one_one_rat )
% 0.32/0.54        = ( times_times_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % square_diff_one_factored
% 0.32/0.54  thf(fact_2191_square__diff__one__factored,axiom,
% 0.32/0.54      ! [X2: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ one_one_int )
% 0.32/0.54        = ( times_times_int @ ( plus_plus_int @ X2 @ one_one_int ) @ ( minus_minus_int @ X2 @ one_one_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % square_diff_one_factored
% 0.32/0.54  thf(fact_2192_of__nat__diff,axiom,
% 0.32/0.54      ! [N: nat,M: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.54       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.54          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_diff
% 0.32/0.54  thf(fact_2193_of__nat__diff,axiom,
% 0.32/0.54      ! [N: nat,M: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.54       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.54          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_diff
% 0.32/0.54  thf(fact_2194_of__nat__diff,axiom,
% 0.32/0.54      ! [N: nat,M: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.54       => ( ( semiri4939895301339042750nteger @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.54          = ( minus_8373710615458151222nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_diff
% 0.32/0.54  thf(fact_2195_of__nat__diff,axiom,
% 0.32/0.54      ! [N: nat,M: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.54       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.54          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_diff
% 0.32/0.54  thf(fact_2196_of__nat__diff,axiom,
% 0.32/0.54      ! [N: nat,M: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.54       => ( ( semiri3763490453095760265atural @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.54          = ( minus_7197305767214868737atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % of_nat_diff
% 0.32/0.54  thf(fact_2197_minusinfinity,axiom,
% 0.32/0.54      ! [D: int,P1: int > $o,P: int > $o] :
% 0.32/0.54        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.54       => ( ! [X3: int,K3: int] :
% 0.32/0.54              ( ( P1 @ X3 )
% 0.32/0.54              = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D ) ) ) )
% 0.32/0.54         => ( ? [Z5: int] :
% 0.32/0.54              ! [X3: int] :
% 0.32/0.54                ( ( ord_less_int @ X3 @ Z5 )
% 0.32/0.54               => ( ( P @ X3 )
% 0.32/0.54                  = ( P1 @ X3 ) ) )
% 0.32/0.54           => ( ? [X_1: int] : ( P1 @ X_1 )
% 0.32/0.54             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % minusinfinity
% 0.32/0.54  thf(fact_2198_plusinfinity,axiom,
% 0.32/0.54      ! [D: int,P2: int > $o,P: int > $o] :
% 0.32/0.54        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.54       => ( ! [X3: int,K3: int] :
% 0.32/0.54              ( ( P2 @ X3 )
% 0.32/0.54              = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D ) ) ) )
% 0.32/0.54         => ( ? [Z5: int] :
% 0.32/0.54              ! [X3: int] :
% 0.32/0.54                ( ( ord_less_int @ Z5 @ X3 )
% 0.32/0.54               => ( ( P @ X3 )
% 0.32/0.54                  = ( P2 @ X3 ) ) )
% 0.32/0.54           => ( ? [X_1: int] : ( P2 @ X_1 )
% 0.32/0.54             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % plusinfinity
% 0.32/0.54  thf(fact_2199_int__minus,axiom,
% 0.32/0.54      ! [N: nat,M: nat] :
% 0.32/0.54        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 0.32/0.54        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % int_minus
% 0.32/0.54  thf(fact_2200_diff__eq__diff__less__eq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ( minus_8373710615458151222nteger @ A @ B )
% 0.32/0.54          = ( minus_8373710615458151222nteger @ C @ D ) )
% 0.32/0.54       => ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.54          = ( ord_le3102999989581377725nteger @ C @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_diff_less_eq
% 0.32/0.54  thf(fact_2201_diff__eq__diff__less__eq,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.54        ( ( ( minus_minus_rat @ A @ B )
% 0.32/0.54          = ( minus_minus_rat @ C @ D ) )
% 0.32/0.54       => ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.54          = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_diff_less_eq
% 0.32/0.54  thf(fact_2202_diff__eq__diff__less__eq,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.54        ( ( ( minus_minus_int @ A @ B )
% 0.32/0.54          = ( minus_minus_int @ C @ D ) )
% 0.32/0.54       => ( ( ord_less_eq_int @ A @ B )
% 0.32/0.54          = ( ord_less_eq_int @ C @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_diff_less_eq
% 0.32/0.54  thf(fact_2203_diff__right__mono,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.54       => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_right_mono
% 0.32/0.54  thf(fact_2204_diff__right__mono,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.54       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_right_mono
% 0.32/0.54  thf(fact_2205_diff__right__mono,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.54       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_right_mono
% 0.32/0.54  thf(fact_2206_diff__left__mono,axiom,
% 0.32/0.54      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.54       => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_left_mono
% 0.32/0.54  thf(fact_2207_diff__left__mono,axiom,
% 0.32/0.54      ! [B: rat,A: rat,C: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.54       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_left_mono
% 0.32/0.54  thf(fact_2208_diff__left__mono,axiom,
% 0.32/0.54      ! [B: int,A: int,C: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.54       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_left_mono
% 0.32/0.54  thf(fact_2209_diff__mono,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,D: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.54       => ( ( ord_le3102999989581377725nteger @ D @ C )
% 0.32/0.54         => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_mono
% 0.32/0.54  thf(fact_2210_diff__mono,axiom,
% 0.32/0.54      ! [A: rat,B: rat,D: rat,C: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.54       => ( ( ord_less_eq_rat @ D @ C )
% 0.32/0.54         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_mono
% 0.32/0.54  thf(fact_2211_diff__mono,axiom,
% 0.32/0.54      ! [A: int,B: int,D: int,C: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.54       => ( ( ord_less_eq_int @ D @ C )
% 0.32/0.54         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_mono
% 0.32/0.54  thf(fact_2212_eq__iff__diff__eq__0,axiom,
% 0.32/0.54      ( ( ^ [Y3: code_integer,Z: code_integer] : ( Y3 = Z ) )
% 0.32/0.54      = ( ^ [A2: code_integer,B2: code_integer] :
% 0.32/0.54            ( ( minus_8373710615458151222nteger @ A2 @ B2 )
% 0.32/0.54            = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_iff_diff_eq_0
% 0.32/0.54  thf(fact_2213_eq__iff__diff__eq__0,axiom,
% 0.32/0.54      ( ( ^ [Y3: rat,Z: rat] : ( Y3 = Z ) )
% 0.32/0.54      = ( ^ [A2: rat,B2: rat] :
% 0.32/0.54            ( ( minus_minus_rat @ A2 @ B2 )
% 0.32/0.54            = zero_zero_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_iff_diff_eq_0
% 0.32/0.54  thf(fact_2214_eq__iff__diff__eq__0,axiom,
% 0.32/0.54      ( ( ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.32/0.54      = ( ^ [A2: int,B2: int] :
% 0.32/0.54            ( ( minus_minus_int @ A2 @ B2 )
% 0.32/0.54            = zero_zero_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_iff_diff_eq_0
% 0.32/0.54  thf(fact_2215_diff__strict__right__mono,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.54       => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_strict_right_mono
% 0.32/0.54  thf(fact_2216_diff__strict__right__mono,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( ord_less_rat @ A @ B )
% 0.32/0.54       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_strict_right_mono
% 0.32/0.54  thf(fact_2217_diff__strict__right__mono,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( ord_less_int @ A @ B )
% 0.32/0.54       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_strict_right_mono
% 0.32/0.54  thf(fact_2218_diff__strict__left__mono,axiom,
% 0.32/0.54      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.54       => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_strict_left_mono
% 0.32/0.54  thf(fact_2219_diff__strict__left__mono,axiom,
% 0.32/0.54      ! [B: rat,A: rat,C: rat] :
% 0.32/0.54        ( ( ord_less_rat @ B @ A )
% 0.32/0.54       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_strict_left_mono
% 0.32/0.54  thf(fact_2220_diff__strict__left__mono,axiom,
% 0.32/0.54      ! [B: int,A: int,C: int] :
% 0.32/0.54        ( ( ord_less_int @ B @ A )
% 0.32/0.54       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_strict_left_mono
% 0.32/0.54  thf(fact_2221_diff__eq__diff__less,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ( minus_8373710615458151222nteger @ A @ B )
% 0.32/0.54          = ( minus_8373710615458151222nteger @ C @ D ) )
% 0.32/0.54       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.54          = ( ord_le6747313008572928689nteger @ C @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_diff_less
% 0.32/0.54  thf(fact_2222_diff__eq__diff__less,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.54        ( ( ( minus_minus_rat @ A @ B )
% 0.32/0.54          = ( minus_minus_rat @ C @ D ) )
% 0.32/0.54       => ( ( ord_less_rat @ A @ B )
% 0.32/0.54          = ( ord_less_rat @ C @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_diff_less
% 0.32/0.54  thf(fact_2223_diff__eq__diff__less,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.54        ( ( ( minus_minus_int @ A @ B )
% 0.32/0.54          = ( minus_minus_int @ C @ D ) )
% 0.32/0.54       => ( ( ord_less_int @ A @ B )
% 0.32/0.54          = ( ord_less_int @ C @ D ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_diff_less
% 0.32/0.54  thf(fact_2224_diff__strict__mono,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,D: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.54       => ( ( ord_le6747313008572928689nteger @ D @ C )
% 0.32/0.54         => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_strict_mono
% 0.32/0.54  thf(fact_2225_diff__strict__mono,axiom,
% 0.32/0.54      ! [A: rat,B: rat,D: rat,C: rat] :
% 0.32/0.54        ( ( ord_less_rat @ A @ B )
% 0.32/0.54       => ( ( ord_less_rat @ D @ C )
% 0.32/0.54         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_strict_mono
% 0.32/0.54  thf(fact_2226_diff__strict__mono,axiom,
% 0.32/0.54      ! [A: int,B: int,D: int,C: int] :
% 0.32/0.54        ( ( ord_less_int @ A @ B )
% 0.32/0.54       => ( ( ord_less_int @ D @ C )
% 0.32/0.54         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_strict_mono
% 0.32/0.54  thf(fact_2227_diff__diff__eq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_diff_eq
% 0.32/0.54  thf(fact_2228_diff__diff__eq,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.32/0.54        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_diff_eq
% 0.32/0.54  thf(fact_2229_diff__diff__eq,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 0.32/0.54        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_diff_eq
% 0.32/0.54  thf(fact_2230_diff__diff__eq,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.32/0.54        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_diff_eq
% 0.32/0.54  thf(fact_2231_add__implies__diff,axiom,
% 0.32/0.54      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.54        ( ( ( plus_p5714425477246183910nteger @ C @ B )
% 0.32/0.54          = A )
% 0.32/0.54       => ( C
% 0.32/0.54          = ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_implies_diff
% 0.32/0.54  thf(fact_2232_add__implies__diff,axiom,
% 0.32/0.54      ! [C: rat,B: rat,A: rat] :
% 0.32/0.54        ( ( ( plus_plus_rat @ C @ B )
% 0.32/0.54          = A )
% 0.32/0.54       => ( C
% 0.32/0.54          = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_implies_diff
% 0.32/0.54  thf(fact_2233_add__implies__diff,axiom,
% 0.32/0.54      ! [C: nat,B: nat,A: nat] :
% 0.32/0.54        ( ( ( plus_plus_nat @ C @ B )
% 0.32/0.54          = A )
% 0.32/0.54       => ( C
% 0.32/0.54          = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_implies_diff
% 0.32/0.54  thf(fact_2234_add__implies__diff,axiom,
% 0.32/0.54      ! [C: int,B: int,A: int] :
% 0.32/0.54        ( ( ( plus_plus_int @ C @ B )
% 0.32/0.54          = A )
% 0.32/0.54       => ( C
% 0.32/0.54          = ( minus_minus_int @ A @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_implies_diff
% 0.32/0.54  thf(fact_2235_diff__add__eq__diff__diff__swap,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_eq_diff_diff_swap
% 0.32/0.54  thf(fact_2236_diff__add__eq__diff__diff__swap,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.54        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_eq_diff_diff_swap
% 0.32/0.54  thf(fact_2237_diff__add__eq__diff__diff__swap,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.32/0.54        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_eq_diff_diff_swap
% 0.32/0.54  thf(fact_2238_diff__add__eq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_eq
% 0.32/0.54  thf(fact_2239_diff__add__eq,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.32/0.54        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_eq
% 0.32/0.54  thf(fact_2240_diff__add__eq,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.32/0.54        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_eq
% 0.32/0.54  thf(fact_2241_diff__diff__eq2,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_diff_eq2
% 0.32/0.54  thf(fact_2242_diff__diff__eq2,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.32/0.54        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_diff_eq2
% 0.32/0.54  thf(fact_2243_diff__diff__eq2,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.32/0.54        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_diff_eq2
% 0.32/0.54  thf(fact_2244_add__diff__eq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( plus_p5714425477246183910nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_eq
% 0.32/0.54  thf(fact_2245_add__diff__eq,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.32/0.54        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_eq
% 0.32/0.54  thf(fact_2246_add__diff__eq,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.32/0.54        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_diff_eq
% 0.32/0.54  thf(fact_2247_eq__diff__eq,axiom,
% 0.32/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.54        ( ( A
% 0.32/0.54          = ( minus_8373710615458151222nteger @ C @ B ) )
% 0.32/0.54        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.54          = C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_diff_eq
% 0.32/0.54  thf(fact_2248_eq__diff__eq,axiom,
% 0.32/0.54      ! [A: rat,C: rat,B: rat] :
% 0.32/0.54        ( ( A
% 0.32/0.54          = ( minus_minus_rat @ C @ B ) )
% 0.32/0.54        = ( ( plus_plus_rat @ A @ B )
% 0.32/0.54          = C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_diff_eq
% 0.32/0.54  thf(fact_2249_eq__diff__eq,axiom,
% 0.32/0.54      ! [A: int,C: int,B: int] :
% 0.32/0.54        ( ( A
% 0.32/0.54          = ( minus_minus_int @ C @ B ) )
% 0.32/0.54        = ( ( plus_plus_int @ A @ B )
% 0.32/0.54          = C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_diff_eq
% 0.32/0.54  thf(fact_2250_diff__eq__eq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ( minus_8373710615458151222nteger @ A @ B )
% 0.32/0.54          = C )
% 0.32/0.54        = ( A
% 0.32/0.54          = ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_eq
% 0.32/0.54  thf(fact_2251_diff__eq__eq,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( ( minus_minus_rat @ A @ B )
% 0.32/0.54          = C )
% 0.32/0.54        = ( A
% 0.32/0.54          = ( plus_plus_rat @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_eq
% 0.32/0.54  thf(fact_2252_diff__eq__eq,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( ( minus_minus_int @ A @ B )
% 0.32/0.54          = C )
% 0.32/0.54        = ( A
% 0.32/0.54          = ( plus_plus_int @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_eq_eq
% 0.32/0.54  thf(fact_2253_group__cancel_Osub1,axiom,
% 0.32/0.54      ! [A4: code_integer,K: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( A4
% 0.32/0.54          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.32/0.54       => ( ( minus_8373710615458151222nteger @ A4 @ B )
% 0.32/0.54          = ( plus_p5714425477246183910nteger @ K @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % group_cancel.sub1
% 0.32/0.54  thf(fact_2254_group__cancel_Osub1,axiom,
% 0.32/0.54      ! [A4: rat,K: rat,A: rat,B: rat] :
% 0.32/0.54        ( ( A4
% 0.32/0.54          = ( plus_plus_rat @ K @ A ) )
% 0.32/0.54       => ( ( minus_minus_rat @ A4 @ B )
% 0.32/0.54          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % group_cancel.sub1
% 0.32/0.54  thf(fact_2255_group__cancel_Osub1,axiom,
% 0.32/0.54      ! [A4: int,K: int,A: int,B: int] :
% 0.32/0.54        ( ( A4
% 0.32/0.54          = ( plus_plus_int @ K @ A ) )
% 0.32/0.54       => ( ( minus_minus_int @ A4 @ B )
% 0.32/0.54          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % group_cancel.sub1
% 0.32/0.54  thf(fact_2256_minus__diff__commute,axiom,
% 0.32/0.54      ! [B: int,A: int] :
% 0.32/0.54        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.32/0.54        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % minus_diff_commute
% 0.32/0.54  thf(fact_2257_minus__diff__commute,axiom,
% 0.32/0.54      ! [B: code_integer,A: code_integer] :
% 0.32/0.54        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 0.32/0.54        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % minus_diff_commute
% 0.32/0.54  thf(fact_2258_minus__diff__commute,axiom,
% 0.32/0.54      ! [B: rat,A: rat] :
% 0.32/0.54        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.32/0.54        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % minus_diff_commute
% 0.32/0.54  thf(fact_2259_mult__not__zero,axiom,
% 0.32/0.54      ! [A: code_natural,B: code_natural] :
% 0.32/0.54        ( ( ( times_2397367101498566445atural @ A @ B )
% 0.32/0.54         != zero_z2226904508553997617atural )
% 0.32/0.54       => ( ( A != zero_z2226904508553997617atural )
% 0.32/0.54          & ( B != zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_not_zero
% 0.32/0.54  thf(fact_2260_mult__not__zero,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.32/0.54         != zero_z3403309356797280102nteger )
% 0.32/0.54       => ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.54          & ( B != zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_not_zero
% 0.32/0.54  thf(fact_2261_mult__not__zero,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ( times_times_rat @ A @ B )
% 0.32/0.54         != zero_zero_rat )
% 0.32/0.54       => ( ( A != zero_zero_rat )
% 0.32/0.54          & ( B != zero_zero_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_not_zero
% 0.32/0.54  thf(fact_2262_mult__not__zero,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ A @ B )
% 0.32/0.54         != zero_zero_nat )
% 0.32/0.54       => ( ( A != zero_zero_nat )
% 0.32/0.54          & ( B != zero_zero_nat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_not_zero
% 0.32/0.54  thf(fact_2263_mult__not__zero,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( ( times_times_int @ A @ B )
% 0.32/0.54         != zero_zero_int )
% 0.32/0.54       => ( ( A != zero_zero_int )
% 0.32/0.54          & ( B != zero_zero_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_not_zero
% 0.32/0.54  thf(fact_2264_divisors__zero,axiom,
% 0.32/0.54      ! [A: code_natural,B: code_natural] :
% 0.32/0.54        ( ( ( times_2397367101498566445atural @ A @ B )
% 0.32/0.54          = zero_z2226904508553997617atural )
% 0.32/0.54       => ( ( A = zero_z2226904508553997617atural )
% 0.32/0.54          | ( B = zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % divisors_zero
% 0.32/0.54  thf(fact_2265_divisors__zero,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.32/0.54          = zero_z3403309356797280102nteger )
% 0.32/0.54       => ( ( A = zero_z3403309356797280102nteger )
% 0.32/0.54          | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % divisors_zero
% 0.32/0.54  thf(fact_2266_divisors__zero,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ( times_times_rat @ A @ B )
% 0.32/0.54          = zero_zero_rat )
% 0.32/0.54       => ( ( A = zero_zero_rat )
% 0.32/0.54          | ( B = zero_zero_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % divisors_zero
% 0.32/0.54  thf(fact_2267_divisors__zero,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ A @ B )
% 0.32/0.54          = zero_zero_nat )
% 0.32/0.54       => ( ( A = zero_zero_nat )
% 0.32/0.54          | ( B = zero_zero_nat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % divisors_zero
% 0.32/0.54  thf(fact_2268_divisors__zero,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( ( times_times_int @ A @ B )
% 0.32/0.54          = zero_zero_int )
% 0.32/0.54       => ( ( A = zero_zero_int )
% 0.32/0.54          | ( B = zero_zero_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % divisors_zero
% 0.32/0.54  thf(fact_2269_no__zero__divisors,axiom,
% 0.32/0.54      ! [A: code_natural,B: code_natural] :
% 0.32/0.54        ( ( A != zero_z2226904508553997617atural )
% 0.32/0.54       => ( ( B != zero_z2226904508553997617atural )
% 0.32/0.54         => ( ( times_2397367101498566445atural @ A @ B )
% 0.32/0.54           != zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % no_zero_divisors
% 0.32/0.54  thf(fact_2270_no__zero__divisors,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.54       => ( ( B != zero_z3403309356797280102nteger )
% 0.32/0.54         => ( ( times_3573771949741848930nteger @ A @ B )
% 0.32/0.54           != zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % no_zero_divisors
% 0.32/0.54  thf(fact_2271_no__zero__divisors,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( A != zero_zero_rat )
% 0.32/0.54       => ( ( B != zero_zero_rat )
% 0.32/0.54         => ( ( times_times_rat @ A @ B )
% 0.32/0.54           != zero_zero_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % no_zero_divisors
% 0.32/0.54  thf(fact_2272_no__zero__divisors,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( A != zero_zero_nat )
% 0.32/0.54       => ( ( B != zero_zero_nat )
% 0.32/0.54         => ( ( times_times_nat @ A @ B )
% 0.32/0.54           != zero_zero_nat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % no_zero_divisors
% 0.32/0.54  thf(fact_2273_no__zero__divisors,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( A != zero_zero_int )
% 0.32/0.54       => ( ( B != zero_zero_int )
% 0.32/0.54         => ( ( times_times_int @ A @ B )
% 0.32/0.54           != zero_zero_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % no_zero_divisors
% 0.32/0.54  thf(fact_2274_mult__left__cancel,axiom,
% 0.32/0.54      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.32/0.54        ( ( C != zero_z2226904508553997617atural )
% 0.32/0.54       => ( ( ( times_2397367101498566445atural @ C @ A )
% 0.32/0.54            = ( times_2397367101498566445atural @ C @ B ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_left_cancel
% 0.32/0.54  thf(fact_2275_mult__left__cancel,axiom,
% 0.32/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( C != zero_z3403309356797280102nteger )
% 0.32/0.54       => ( ( ( times_3573771949741848930nteger @ C @ A )
% 0.32/0.54            = ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_left_cancel
% 0.32/0.54  thf(fact_2276_mult__left__cancel,axiom,
% 0.32/0.54      ! [C: rat,A: rat,B: rat] :
% 0.32/0.54        ( ( C != zero_zero_rat )
% 0.32/0.54       => ( ( ( times_times_rat @ C @ A )
% 0.32/0.54            = ( times_times_rat @ C @ B ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_left_cancel
% 0.32/0.54  thf(fact_2277_mult__left__cancel,axiom,
% 0.32/0.54      ! [C: nat,A: nat,B: nat] :
% 0.32/0.54        ( ( C != zero_zero_nat )
% 0.32/0.54       => ( ( ( times_times_nat @ C @ A )
% 0.32/0.54            = ( times_times_nat @ C @ B ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_left_cancel
% 0.32/0.54  thf(fact_2278_mult__left__cancel,axiom,
% 0.32/0.54      ! [C: int,A: int,B: int] :
% 0.32/0.54        ( ( C != zero_zero_int )
% 0.32/0.54       => ( ( ( times_times_int @ C @ A )
% 0.32/0.54            = ( times_times_int @ C @ B ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_left_cancel
% 0.32/0.54  thf(fact_2279_mult__right__cancel,axiom,
% 0.32/0.54      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.32/0.54        ( ( C != zero_z2226904508553997617atural )
% 0.32/0.54       => ( ( ( times_2397367101498566445atural @ A @ C )
% 0.32/0.54            = ( times_2397367101498566445atural @ B @ C ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_right_cancel
% 0.32/0.54  thf(fact_2280_mult__right__cancel,axiom,
% 0.32/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( C != zero_z3403309356797280102nteger )
% 0.32/0.54       => ( ( ( times_3573771949741848930nteger @ A @ C )
% 0.32/0.54            = ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_right_cancel
% 0.32/0.54  thf(fact_2281_mult__right__cancel,axiom,
% 0.32/0.54      ! [C: rat,A: rat,B: rat] :
% 0.32/0.54        ( ( C != zero_zero_rat )
% 0.32/0.54       => ( ( ( times_times_rat @ A @ C )
% 0.32/0.54            = ( times_times_rat @ B @ C ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_right_cancel
% 0.32/0.54  thf(fact_2282_mult__right__cancel,axiom,
% 0.32/0.54      ! [C: nat,A: nat,B: nat] :
% 0.32/0.54        ( ( C != zero_zero_nat )
% 0.32/0.54       => ( ( ( times_times_nat @ A @ C )
% 0.32/0.54            = ( times_times_nat @ B @ C ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_right_cancel
% 0.32/0.54  thf(fact_2283_mult__right__cancel,axiom,
% 0.32/0.54      ! [C: int,A: int,B: int] :
% 0.32/0.54        ( ( C != zero_zero_int )
% 0.32/0.54       => ( ( ( times_times_int @ A @ C )
% 0.32/0.54            = ( times_times_int @ B @ C ) )
% 0.32/0.54          = ( A = B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_right_cancel
% 0.32/0.54  thf(fact_2284_crossproduct__eq,axiom,
% 0.32/0.54      ! [W2: code_integer,Y: code_integer,X2: code_integer,Z2: code_integer] :
% 0.32/0.54        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W2 @ Y ) @ ( times_3573771949741848930nteger @ X2 @ Z2 ) )
% 0.32/0.54          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W2 @ Z2 ) @ ( times_3573771949741848930nteger @ X2 @ Y ) ) )
% 0.32/0.54        = ( ( W2 = X2 )
% 0.32/0.54          | ( Y = Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % crossproduct_eq
% 0.32/0.54  thf(fact_2285_crossproduct__eq,axiom,
% 0.32/0.54      ! [W2: rat,Y: rat,X2: rat,Z2: rat] :
% 0.32/0.54        ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y ) @ ( times_times_rat @ X2 @ Z2 ) )
% 0.32/0.54          = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z2 ) @ ( times_times_rat @ X2 @ Y ) ) )
% 0.32/0.54        = ( ( W2 = X2 )
% 0.32/0.54          | ( Y = Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % crossproduct_eq
% 0.32/0.54  thf(fact_2286_crossproduct__eq,axiom,
% 0.32/0.54      ! [W2: nat,Y: nat,X2: nat,Z2: nat] :
% 0.32/0.54        ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X2 @ Z2 ) )
% 0.32/0.54          = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z2 ) @ ( times_times_nat @ X2 @ Y ) ) )
% 0.32/0.54        = ( ( W2 = X2 )
% 0.32/0.54          | ( Y = Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % crossproduct_eq
% 0.32/0.54  thf(fact_2287_crossproduct__eq,axiom,
% 0.32/0.54      ! [W2: int,Y: int,X2: int,Z2: int] :
% 0.32/0.54        ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X2 @ Z2 ) )
% 0.32/0.54          = ( plus_plus_int @ ( times_times_int @ W2 @ Z2 ) @ ( times_times_int @ X2 @ Y ) ) )
% 0.32/0.54        = ( ( W2 = X2 )
% 0.32/0.54          | ( Y = Z2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % crossproduct_eq
% 0.32/0.54  thf(fact_2288_crossproduct__noteq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.54        ( ( ( A != B )
% 0.32/0.54          & ( C != D ) )
% 0.32/0.54        = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) )
% 0.32/0.54         != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ D ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % crossproduct_noteq
% 0.32/0.54  thf(fact_2289_crossproduct__noteq,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.54        ( ( ( A != B )
% 0.32/0.54          & ( C != D ) )
% 0.32/0.54        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 0.32/0.54         != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % crossproduct_noteq
% 0.32/0.54  thf(fact_2290_crossproduct__noteq,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.54        ( ( ( A != B )
% 0.32/0.54          & ( C != D ) )
% 0.32/0.54        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 0.32/0.54         != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % crossproduct_noteq
% 0.32/0.54  thf(fact_2291_crossproduct__noteq,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.54        ( ( ( A != B )
% 0.32/0.54          & ( C != D ) )
% 0.32/0.54        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 0.32/0.54         != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % crossproduct_noteq
% 0.32/0.54  thf(fact_2292_ring__class_Oring__distribs_I2_J,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.54        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ring_class.ring_distribs(2)
% 0.32/0.54  thf(fact_2293_ring__class_Oring__distribs_I2_J,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.32/0.54        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ring_class.ring_distribs(2)
% 0.32/0.54  thf(fact_2294_ring__class_Oring__distribs_I2_J,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.54        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ring_class.ring_distribs(2)
% 0.32/0.54  thf(fact_2295_ring__class_Oring__distribs_I1_J,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.54        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ring_class.ring_distribs(1)
% 0.32/0.54  thf(fact_2296_ring__class_Oring__distribs_I1_J,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.54        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ring_class.ring_distribs(1)
% 0.32/0.54  thf(fact_2297_ring__class_Oring__distribs_I1_J,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.32/0.54        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ring_class.ring_distribs(1)
% 0.32/0.54  thf(fact_2298_comm__semiring__class_Odistrib,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.54        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % comm_semiring_class.distrib
% 0.32/0.54  thf(fact_2299_comm__semiring__class_Odistrib,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.32/0.54        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % comm_semiring_class.distrib
% 0.32/0.54  thf(fact_2300_comm__semiring__class_Odistrib,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.32/0.54        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % comm_semiring_class.distrib
% 0.32/0.54  thf(fact_2301_comm__semiring__class_Odistrib,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.54        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % comm_semiring_class.distrib
% 0.32/0.54  thf(fact_2302_distrib__left,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.54        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % distrib_left
% 0.32/0.54  thf(fact_2303_distrib__left,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.54        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % distrib_left
% 0.32/0.54  thf(fact_2304_distrib__left,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.54        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % distrib_left
% 0.32/0.54  thf(fact_2305_distrib__left,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.32/0.54        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % distrib_left
% 0.32/0.54  thf(fact_2306_distrib__right,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.54        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % distrib_right
% 0.32/0.54  thf(fact_2307_distrib__right,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.32/0.54        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % distrib_right
% 0.32/0.54  thf(fact_2308_distrib__right,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.32/0.54        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % distrib_right
% 0.32/0.54  thf(fact_2309_distrib__right,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.54        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % distrib_right
% 0.32/0.54  thf(fact_2310_combine__common__factor,axiom,
% 0.32/0.54      ! [A: code_integer,E: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ C ) )
% 0.32/0.54        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ E ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % combine_common_factor
% 0.32/0.54  thf(fact_2311_combine__common__factor,axiom,
% 0.32/0.54      ! [A: rat,E: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 0.32/0.54        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % combine_common_factor
% 0.32/0.54  thf(fact_2312_combine__common__factor,axiom,
% 0.32/0.54      ! [A: nat,E: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 0.32/0.54        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % combine_common_factor
% 0.32/0.54  thf(fact_2313_combine__common__factor,axiom,
% 0.32/0.54      ! [A: int,E: int,B: int,C: int] :
% 0.32/0.54        ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 0.32/0.54        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % combine_common_factor
% 0.32/0.54  thf(fact_2314_mult_Ocomm__neutral,axiom,
% 0.32/0.54      ! [A: code_natural] :
% 0.32/0.54        ( ( times_2397367101498566445atural @ A @ one_one_Code_natural )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.comm_neutral
% 0.32/0.54  thf(fact_2315_mult_Ocomm__neutral,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.comm_neutral
% 0.32/0.54  thf(fact_2316_mult_Ocomm__neutral,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( times_times_rat @ A @ one_one_rat )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.comm_neutral
% 0.32/0.54  thf(fact_2317_mult_Ocomm__neutral,axiom,
% 0.32/0.54      ! [A: nat] :
% 0.32/0.54        ( ( times_times_nat @ A @ one_one_nat )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.comm_neutral
% 0.32/0.54  thf(fact_2318_mult_Ocomm__neutral,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( times_times_int @ A @ one_one_int )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % mult.comm_neutral
% 0.32/0.54  thf(fact_2319_comm__monoid__mult__class_Omult__1,axiom,
% 0.32/0.54      ! [A: code_natural] :
% 0.32/0.54        ( ( times_2397367101498566445atural @ one_one_Code_natural @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % comm_monoid_mult_class.mult_1
% 0.32/0.54  thf(fact_2320_comm__monoid__mult__class_Omult__1,axiom,
% 0.32/0.54      ! [A: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % comm_monoid_mult_class.mult_1
% 0.32/0.54  thf(fact_2321_comm__monoid__mult__class_Omult__1,axiom,
% 0.32/0.54      ! [A: rat] :
% 0.32/0.54        ( ( times_times_rat @ one_one_rat @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % comm_monoid_mult_class.mult_1
% 0.32/0.54  thf(fact_2322_comm__monoid__mult__class_Omult__1,axiom,
% 0.32/0.54      ! [A: nat] :
% 0.32/0.54        ( ( times_times_nat @ one_one_nat @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % comm_monoid_mult_class.mult_1
% 0.32/0.54  thf(fact_2323_comm__monoid__mult__class_Omult__1,axiom,
% 0.32/0.54      ! [A: int] :
% 0.32/0.54        ( ( times_times_int @ one_one_int @ A )
% 0.32/0.54        = A ) ).
% 0.32/0.54  
% 0.32/0.54  % comm_monoid_mult_class.mult_1
% 0.32/0.54  thf(fact_2324_diffs0__imp__equal,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( ( minus_minus_nat @ M @ N )
% 0.32/0.54          = zero_zero_nat )
% 0.32/0.54       => ( ( ( minus_minus_nat @ N @ M )
% 0.32/0.54            = zero_zero_nat )
% 0.32/0.54         => ( M = N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diffs0_imp_equal
% 0.32/0.54  thf(fact_2325_minus__nat_Odiff__0,axiom,
% 0.32/0.54      ! [M: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.32/0.54        = M ) ).
% 0.32/0.54  
% 0.32/0.54  % minus_nat.diff_0
% 0.32/0.54  thf(fact_2326_minus__int__code_I1_J,axiom,
% 0.32/0.54      ! [K: int] :
% 0.32/0.54        ( ( minus_minus_int @ K @ zero_zero_int )
% 0.32/0.54        = K ) ).
% 0.32/0.54  
% 0.32/0.54  % minus_int_code(1)
% 0.32/0.54  thf(fact_2327_zero__induct__lemma,axiom,
% 0.32/0.54      ! [P: nat > $o,K: nat,I: nat] :
% 0.32/0.54        ( ( P @ K )
% 0.32/0.54       => ( ! [N2: nat] :
% 0.32/0.54              ( ( P @ ( suc @ N2 ) )
% 0.32/0.54             => ( P @ N2 ) )
% 0.32/0.54         => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_induct_lemma
% 0.32/0.54  thf(fact_2328_diff__less__mono2,axiom,
% 0.32/0.54      ! [M: nat,N: nat,L: nat] :
% 0.32/0.54        ( ( ord_less_nat @ M @ N )
% 0.32/0.54       => ( ( ord_less_nat @ M @ L )
% 0.32/0.54         => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_less_mono2
% 0.32/0.54  thf(fact_2329_less__imp__diff__less,axiom,
% 0.32/0.54      ! [J: nat,K: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_nat @ J @ K )
% 0.32/0.54       => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_imp_diff_less
% 0.32/0.54  thf(fact_2330_diff__le__mono2,axiom,
% 0.32/0.54      ! [M: nat,N: nat,L: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.54       => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_le_mono2
% 0.32/0.54  thf(fact_2331_le__diff__iff_H,axiom,
% 0.32/0.54      ! [A: nat,C: nat,B: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ C )
% 0.32/0.54       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.54         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.32/0.54            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_diff_iff'
% 0.32/0.54  thf(fact_2332_diff__le__self,axiom,
% 0.32/0.54      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_le_self
% 0.32/0.54  thf(fact_2333_diff__le__mono,axiom,
% 0.32/0.54      ! [M: nat,N: nat,L: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.54       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_le_mono
% 0.32/0.54  thf(fact_2334_Nat_Odiff__diff__eq,axiom,
% 0.32/0.54      ! [K: nat,M: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.54       => ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.54         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.32/0.54            = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Nat.diff_diff_eq
% 0.32/0.54  thf(fact_2335_le__diff__iff,axiom,
% 0.32/0.54      ! [K: nat,M: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.54       => ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.54         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.32/0.54            = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_diff_iff
% 0.32/0.54  thf(fact_2336_eq__diff__iff,axiom,
% 0.32/0.54      ! [K: nat,M: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.54       => ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.54         => ( ( ( minus_minus_nat @ M @ K )
% 0.32/0.54              = ( minus_minus_nat @ N @ K ) )
% 0.32/0.54            = ( M = N ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % eq_diff_iff
% 0.32/0.54  thf(fact_2337_diff__add__inverse2,axiom,
% 0.32/0.54      ! [M: nat,N: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.32/0.54        = M ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_inverse2
% 0.32/0.54  thf(fact_2338_diff__add__inverse,axiom,
% 0.32/0.54      ! [N: nat,M: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.32/0.54        = M ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_add_inverse
% 0.32/0.54  thf(fact_2339_diff__cancel2,axiom,
% 0.32/0.54      ! [M: nat,K: nat,N: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.32/0.54        = ( minus_minus_nat @ M @ N ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_cancel2
% 0.32/0.54  thf(fact_2340_Nat_Odiff__cancel,axiom,
% 0.32/0.54      ! [K: nat,M: nat,N: nat] :
% 0.32/0.54        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.32/0.54        = ( minus_minus_nat @ M @ N ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Nat.diff_cancel
% 0.32/0.54  thf(fact_2341_mult__0,axiom,
% 0.32/0.54      ! [N: nat] :
% 0.32/0.54        ( ( times_times_nat @ zero_zero_nat @ N )
% 0.32/0.54        = zero_zero_nat ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_0
% 0.32/0.54  thf(fact_2342_Suc__mult__cancel1,axiom,
% 0.32/0.54      ! [K: nat,M: nat,N: nat] :
% 0.32/0.54        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.32/0.54          = ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.32/0.54        = ( M = N ) ) ).
% 0.32/0.54  
% 0.32/0.54  % Suc_mult_cancel1
% 0.32/0.54  thf(fact_2343_mult__of__nat__commute,axiom,
% 0.32/0.54      ! [X2: nat,Y: int] :
% 0.32/0.54        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X2 ) @ Y )
% 0.32/0.54        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_of_nat_commute
% 0.32/0.54  thf(fact_2344_mult__of__nat__commute,axiom,
% 0.32/0.54      ! [X2: nat,Y: nat] :
% 0.32/0.54        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ Y )
% 0.32/0.54        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_of_nat_commute
% 0.32/0.54  thf(fact_2345_mult__of__nat__commute,axiom,
% 0.32/0.54      ! [X2: nat,Y: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X2 ) @ Y )
% 0.32/0.54        = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_of_nat_commute
% 0.32/0.54  thf(fact_2346_mult__of__nat__commute,axiom,
% 0.32/0.54      ! [X2: nat,Y: rat] :
% 0.32/0.54        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X2 ) @ Y )
% 0.32/0.54        = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_of_nat_commute
% 0.32/0.54  thf(fact_2347_mult__of__nat__commute,axiom,
% 0.32/0.54      ! [X2: nat,Y: code_natural] :
% 0.32/0.54        ( ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ X2 ) @ Y )
% 0.32/0.54        = ( times_2397367101498566445atural @ Y @ ( semiri3763490453095760265atural @ X2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_of_nat_commute
% 0.32/0.54  thf(fact_2348_times__int__code_I2_J,axiom,
% 0.32/0.54      ! [L: int] :
% 0.32/0.54        ( ( times_times_int @ zero_zero_int @ L )
% 0.32/0.54        = zero_zero_int ) ).
% 0.32/0.54  
% 0.32/0.54  % times_int_code(2)
% 0.32/0.54  thf(fact_2349_times__int__code_I1_J,axiom,
% 0.32/0.54      ! [K: int] :
% 0.32/0.54        ( ( times_times_int @ K @ zero_zero_int )
% 0.32/0.54        = zero_zero_int ) ).
% 0.32/0.54  
% 0.32/0.54  % times_int_code(1)
% 0.32/0.54  thf(fact_2350_mult__le__mono2,axiom,
% 0.32/0.54      ! [I: nat,J: nat,K: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.54       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_le_mono2
% 0.32/0.54  thf(fact_2351_mult__le__mono1,axiom,
% 0.32/0.54      ! [I: nat,J: nat,K: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.54       => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_le_mono1
% 0.32/0.54  thf(fact_2352_mult__le__mono,axiom,
% 0.32/0.54      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.54       => ( ( ord_less_eq_nat @ K @ L )
% 0.32/0.54         => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_le_mono
% 0.32/0.54  thf(fact_2353_le__square,axiom,
% 0.32/0.54      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_square
% 0.32/0.54  thf(fact_2354_le__cube,axiom,
% 0.32/0.54      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_cube
% 0.32/0.54  thf(fact_2355_int__diff__cases,axiom,
% 0.32/0.54      ! [Z2: int] :
% 0.32/0.54        ~ ! [M4: nat,N2: nat] :
% 0.32/0.54            ( Z2
% 0.32/0.54           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % int_diff_cases
% 0.32/0.54  thf(fact_2356_add__mult__distrib2,axiom,
% 0.32/0.54      ! [K: nat,M: nat,N: nat] :
% 0.32/0.54        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.54        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_mult_distrib2
% 0.32/0.54  thf(fact_2357_add__mult__distrib,axiom,
% 0.32/0.54      ! [M: nat,N: nat,K: nat] :
% 0.32/0.54        ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.32/0.54        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_mult_distrib
% 0.32/0.54  thf(fact_2358_nat__minus__as__int,axiom,
% 0.32/0.54      ( minus_minus_nat
% 0.32/0.54      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_minus_as_int
% 0.32/0.54  thf(fact_2359_nat__mult__1,axiom,
% 0.32/0.54      ! [N: nat] :
% 0.32/0.54        ( ( times_times_nat @ one_one_nat @ N )
% 0.32/0.54        = N ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_mult_1
% 0.32/0.54  thf(fact_2360_nat__mult__1__right,axiom,
% 0.32/0.54      ! [N: nat] :
% 0.32/0.54        ( ( times_times_nat @ N @ one_one_nat )
% 0.32/0.54        = N ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_mult_1_right
% 0.32/0.54  thf(fact_2361_mult__of__int__commute,axiom,
% 0.32/0.54      ! [X2: int,Y: code_integer] :
% 0.32/0.54        ( ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ X2 ) @ Y )
% 0.32/0.54        = ( times_3573771949741848930nteger @ Y @ ( ring_18347121197199848620nteger @ X2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_of_int_commute
% 0.32/0.54  thf(fact_2362_mult__of__int__commute,axiom,
% 0.32/0.54      ! [X2: int,Y: rat] :
% 0.32/0.54        ( ( times_times_rat @ ( ring_1_of_int_rat @ X2 ) @ Y )
% 0.32/0.54        = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_of_int_commute
% 0.32/0.54  thf(fact_2363_mult__of__int__commute,axiom,
% 0.32/0.54      ! [X2: int,Y: int] :
% 0.32/0.54        ( ( times_times_int @ ( ring_1_of_int_int @ X2 ) @ Y )
% 0.32/0.54        = ( times_times_int @ Y @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_of_int_commute
% 0.32/0.54  thf(fact_2364_int__distrib_I2_J,axiom,
% 0.32/0.54      ! [W2: int,Z1: int,Z22: int] :
% 0.32/0.54        ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 0.32/0.54        = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % int_distrib(2)
% 0.32/0.54  thf(fact_2365_int__distrib_I1_J,axiom,
% 0.32/0.54      ! [Z1: int,Z22: int,W2: int] :
% 0.32/0.54        ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 0.32/0.54        = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % int_distrib(1)
% 0.32/0.54  thf(fact_2366_nat__times__as__int,axiom,
% 0.32/0.54      ( times_times_nat
% 0.32/0.54      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_times_as_int
% 0.32/0.54  thf(fact_2367_power__int__mult__distrib,axiom,
% 0.32/0.54      ! [X2: rat,Y: rat,M: int] :
% 0.32/0.54        ( ( power_int_rat @ ( times_times_rat @ X2 @ Y ) @ M )
% 0.32/0.54        = ( times_times_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ Y @ M ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % power_int_mult_distrib
% 0.32/0.54  thf(fact_2368_power__int__commutes,axiom,
% 0.32/0.54      ! [X2: rat,N: int] :
% 0.32/0.54        ( ( times_times_rat @ ( power_int_rat @ X2 @ N ) @ X2 )
% 0.32/0.54        = ( times_times_rat @ X2 @ ( power_int_rat @ X2 @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % power_int_commutes
% 0.32/0.54  thf(fact_2369_int__ops_I6_J,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.32/0.54         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.54            = zero_zero_int ) )
% 0.32/0.54        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.32/0.54         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.54            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % int_ops(6)
% 0.32/0.54  thf(fact_2370_mult__eq__if,axiom,
% 0.32/0.54      ( times_times_nat
% 0.32/0.54      = ( ^ [M2: nat,N3: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N3 @ ( times_times_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_eq_if
% 0.32/0.54  thf(fact_2371_decr__mult__lemma,axiom,
% 0.32/0.54      ! [D: int,P: int > $o,K: int] :
% 0.32/0.54        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.54       => ( ! [X3: int] :
% 0.32/0.54              ( ( P @ X3 )
% 0.32/0.54             => ( P @ ( minus_minus_int @ X3 @ D ) ) )
% 0.32/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.54           => ! [X4: int] :
% 0.32/0.54                ( ( P @ X4 )
% 0.32/0.54               => ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % decr_mult_lemma
% 0.32/0.54  thf(fact_2372_nat__diff__distrib_H,axiom,
% 0.32/0.54      ! [X2: int,Y: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.32/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.54         => ( ( nat2 @ ( minus_minus_int @ X2 @ Y ) )
% 0.32/0.54            = ( minus_minus_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_diff_distrib'
% 0.32/0.54  thf(fact_2373_nat__diff__distrib,axiom,
% 0.32/0.54      ! [Z6: int,Z2: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 0.32/0.54       => ( ( ord_less_eq_int @ Z6 @ Z2 )
% 0.32/0.54         => ( ( nat2 @ ( minus_minus_int @ Z2 @ Z6 ) )
% 0.32/0.54            = ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_diff_distrib
% 0.32/0.54  thf(fact_2374_lambda__zero,axiom,
% 0.32/0.54      ( ( ^ [H3: code_natural] : zero_z2226904508553997617atural )
% 0.32/0.54      = ( times_2397367101498566445atural @ zero_z2226904508553997617atural ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_zero
% 0.32/0.54  thf(fact_2375_lambda__zero,axiom,
% 0.32/0.54      ( ( ^ [H3: code_integer] : zero_z3403309356797280102nteger )
% 0.32/0.54      = ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_zero
% 0.32/0.54  thf(fact_2376_lambda__zero,axiom,
% 0.32/0.54      ( ( ^ [H3: rat] : zero_zero_rat )
% 0.32/0.54      = ( times_times_rat @ zero_zero_rat ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_zero
% 0.32/0.54  thf(fact_2377_lambda__zero,axiom,
% 0.32/0.54      ( ( ^ [H3: nat] : zero_zero_nat )
% 0.32/0.54      = ( times_times_nat @ zero_zero_nat ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_zero
% 0.32/0.54  thf(fact_2378_lambda__zero,axiom,
% 0.32/0.54      ( ( ^ [H3: int] : zero_zero_int )
% 0.32/0.54      = ( times_times_int @ zero_zero_int ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_zero
% 0.32/0.54  thf(fact_2379_lambda__one,axiom,
% 0.32/0.54      ( ( ^ [X: code_natural] : X )
% 0.32/0.54      = ( times_2397367101498566445atural @ one_one_Code_natural ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_one
% 0.32/0.54  thf(fact_2380_lambda__one,axiom,
% 0.32/0.54      ( ( ^ [X: code_integer] : X )
% 0.32/0.54      = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_one
% 0.32/0.54  thf(fact_2381_lambda__one,axiom,
% 0.32/0.54      ( ( ^ [X: rat] : X )
% 0.32/0.54      = ( times_times_rat @ one_one_rat ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_one
% 0.32/0.54  thf(fact_2382_lambda__one,axiom,
% 0.32/0.54      ( ( ^ [X: nat] : X )
% 0.32/0.54      = ( times_times_nat @ one_one_nat ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_one
% 0.32/0.54  thf(fact_2383_lambda__one,axiom,
% 0.32/0.54      ( ( ^ [X: int] : X )
% 0.32/0.54      = ( times_times_int @ one_one_int ) ) ).
% 0.32/0.54  
% 0.32/0.54  % lambda_one
% 0.32/0.54  thf(fact_2384_nat__mult__distrib,axiom,
% 0.32/0.54      ! [Z2: int,Z6: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.32/0.54       => ( ( nat2 @ ( times_times_int @ Z2 @ Z6 ) )
% 0.32/0.54          = ( times_times_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_mult_distrib
% 0.32/0.54  thf(fact_2385_zdiff__int__split,axiom,
% 0.32/0.54      ! [P: int > $o,X2: nat,Y: nat] :
% 0.32/0.54        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X2 @ Y ) ) )
% 0.32/0.54        = ( ( ( ord_less_eq_nat @ Y @ X2 )
% 0.32/0.54           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 0.32/0.54          & ( ( ord_less_nat @ X2 @ Y )
% 0.32/0.54           => ( P @ zero_zero_int ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zdiff_int_split
% 0.32/0.54  thf(fact_2386_le__iff__diff__le__0,axiom,
% 0.32/0.54      ( ord_le3102999989581377725nteger
% 0.32/0.54      = ( ^ [A2: code_integer,B2: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_iff_diff_le_0
% 0.32/0.54  thf(fact_2387_le__iff__diff__le__0,axiom,
% 0.32/0.54      ( ord_less_eq_rat
% 0.32/0.54      = ( ^ [A2: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_iff_diff_le_0
% 0.32/0.54  thf(fact_2388_le__iff__diff__le__0,axiom,
% 0.32/0.54      ( ord_less_eq_int
% 0.32/0.54      = ( ^ [A2: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_iff_diff_le_0
% 0.32/0.54  thf(fact_2389_power__int__minus__mult,axiom,
% 0.32/0.54      ! [X2: rat,N: int] :
% 0.32/0.54        ( ( ( X2 != zero_zero_rat )
% 0.32/0.54          | ( N != zero_zero_int ) )
% 0.32/0.54       => ( ( times_times_rat @ ( power_int_rat @ X2 @ ( minus_minus_int @ N @ one_one_int ) ) @ X2 )
% 0.32/0.54          = ( power_int_rat @ X2 @ N ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % power_int_minus_mult
% 0.32/0.54  thf(fact_2390_less__iff__diff__less__0,axiom,
% 0.32/0.54      ( ord_le6747313008572928689nteger
% 0.32/0.54      = ( ^ [A2: code_integer,B2: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_iff_diff_less_0
% 0.32/0.54  thf(fact_2391_less__iff__diff__less__0,axiom,
% 0.32/0.54      ( ord_less_rat
% 0.32/0.54      = ( ^ [A2: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_iff_diff_less_0
% 0.32/0.54  thf(fact_2392_less__iff__diff__less__0,axiom,
% 0.32/0.54      ( ord_less_int
% 0.32/0.54      = ( ^ [A2: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_iff_diff_less_0
% 0.32/0.54  thf(fact_2393_le__mult__floor,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.54         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_mult_floor
% 0.32/0.54  thf(fact_2394_diff__le__eq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.32/0.54        = ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_le_eq
% 0.32/0.54  thf(fact_2395_diff__le__eq,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.32/0.54        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_le_eq
% 0.32/0.54  thf(fact_2396_diff__le__eq,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.32/0.54        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_le_eq
% 0.32/0.54  thf(fact_2397_le__diff__eq,axiom,
% 0.32/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 0.32/0.54        = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_diff_eq
% 0.32/0.54  thf(fact_2398_le__diff__eq,axiom,
% 0.32/0.54      ! [A: rat,C: rat,B: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.32/0.54        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_diff_eq
% 0.32/0.54  thf(fact_2399_le__diff__eq,axiom,
% 0.32/0.54      ! [A: int,C: int,B: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.32/0.54        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_diff_eq
% 0.32/0.54  thf(fact_2400_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.32/0.54          = B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_cancel_comm_monoid_diff_class.diff_add
% 0.32/0.54  thf(fact_2401_le__add__diff,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % le_add_diff
% 0.32/0.54  thf(fact_2402_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.32/0.54          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.32/0.54  thf(fact_2403_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.32/0.54          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.32/0.54  thf(fact_2404_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 0.32/0.54          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.32/0.54  thf(fact_2405_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 0.32/0.54          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.32/0.54  thf(fact_2406_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 0.32/0.54          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.32/0.54  thf(fact_2407_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.32/0.54          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.32/0.54  thf(fact_2408_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.32/0.54          = B ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.32/0.54  thf(fact_2409_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54         => ( ( ( minus_minus_nat @ B @ A )
% 0.32/0.54              = C )
% 0.32/0.54            = ( B
% 0.32/0.54              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.32/0.54  thf(fact_2410_add__le__imp__le__diff,axiom,
% 0.32/0.54      ! [I: code_integer,K: code_integer,N: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N )
% 0.32/0.54       => ( ord_le3102999989581377725nteger @ I @ ( minus_8373710615458151222nteger @ N @ K ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_le_imp_le_diff
% 0.32/0.54  thf(fact_2411_add__le__imp__le__diff,axiom,
% 0.32/0.54      ! [I: rat,K: rat,N: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.32/0.54       => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_le_imp_le_diff
% 0.32/0.54  thf(fact_2412_add__le__imp__le__diff,axiom,
% 0.32/0.54      ! [I: nat,K: nat,N: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.32/0.54       => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_le_imp_le_diff
% 0.32/0.54  thf(fact_2413_add__le__imp__le__diff,axiom,
% 0.32/0.54      ! [I: int,K: int,N: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.32/0.54       => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_le_imp_le_diff
% 0.32/0.54  thf(fact_2414_add__le__add__imp__diff__le,axiom,
% 0.32/0.54      ! [I: code_integer,K: code_integer,N: code_integer,J: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N )
% 0.32/0.54       => ( ( ord_le3102999989581377725nteger @ N @ ( plus_p5714425477246183910nteger @ J @ K ) )
% 0.32/0.54         => ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N )
% 0.32/0.54           => ( ( ord_le3102999989581377725nteger @ N @ ( plus_p5714425477246183910nteger @ J @ K ) )
% 0.32/0.54             => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ N @ K ) @ J ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_le_add_imp_diff_le
% 0.32/0.54  thf(fact_2415_add__le__add__imp__diff__le,axiom,
% 0.32/0.54      ! [I: rat,K: rat,N: rat,J: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.32/0.54       => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.32/0.54         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.32/0.54           => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.32/0.54             => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_le_add_imp_diff_le
% 0.32/0.54  thf(fact_2416_add__le__add__imp__diff__le,axiom,
% 0.32/0.54      ! [I: nat,K: nat,N: nat,J: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.32/0.54       => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.32/0.54         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.32/0.54           => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.32/0.54             => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_le_add_imp_diff_le
% 0.32/0.54  thf(fact_2417_add__le__add__imp__diff__le,axiom,
% 0.32/0.54      ! [I: int,K: int,N: int,J: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.32/0.54       => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.32/0.54         => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.32/0.54           => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.32/0.54             => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % add_le_add_imp_diff_le
% 0.32/0.54  thf(fact_2418_mult__ceiling__le,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.54         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % mult_ceiling_le
% 0.32/0.54  thf(fact_2419_less__diff__eq,axiom,
% 0.32/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ord_le6747313008572928689nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 0.32/0.54        = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_diff_eq
% 0.32/0.54  thf(fact_2420_less__diff__eq,axiom,
% 0.32/0.54      ! [A: rat,C: rat,B: rat] :
% 0.32/0.54        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.32/0.54        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_diff_eq
% 0.32/0.54  thf(fact_2421_less__diff__eq,axiom,
% 0.32/0.54      ! [A: int,C: int,B: int] :
% 0.32/0.54        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.32/0.54        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.32/0.54  
% 0.32/0.54  % less_diff_eq
% 0.32/0.54  thf(fact_2422_diff__less__eq,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.32/0.54        = ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_less_eq
% 0.32/0.54  thf(fact_2423_diff__less__eq,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.32/0.54        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_less_eq
% 0.32/0.54  thf(fact_2424_diff__less__eq,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.32/0.54        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_less_eq
% 0.32/0.54  thf(fact_2425_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ~ ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.54       => ( ( plus_p5714425477246183910nteger @ B @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % linordered_semidom_class.add_diff_inverse
% 0.32/0.54  thf(fact_2426_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ~ ( ord_less_rat @ A @ B )
% 0.32/0.54       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % linordered_semidom_class.add_diff_inverse
% 0.32/0.54  thf(fact_2427_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.32/0.54      ! [A: nat,B: nat] :
% 0.32/0.54        ( ~ ( ord_less_nat @ A @ B )
% 0.32/0.54       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % linordered_semidom_class.add_diff_inverse
% 0.32/0.54  thf(fact_2428_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ~ ( ord_less_int @ A @ B )
% 0.32/0.54       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.32/0.54          = A ) ) ).
% 0.32/0.54  
% 0.32/0.54  % linordered_semidom_class.add_diff_inverse
% 0.32/0.54  thf(fact_2429_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.32/0.54      ( minus_minus_int
% 0.32/0.54      = ( ^ [A2: int,B2: int] : ( plus_plus_int @ A2 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.32/0.54  thf(fact_2430_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.32/0.54      ( minus_8373710615458151222nteger
% 0.32/0.54      = ( ^ [A2: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A2 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.32/0.54  thf(fact_2431_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.32/0.54      ( minus_minus_rat
% 0.32/0.54      = ( ^ [A2: rat,B2: rat] : ( plus_plus_rat @ A2 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.32/0.54  thf(fact_2432_diff__conv__add__uminus,axiom,
% 0.32/0.54      ( minus_minus_int
% 0.32/0.54      = ( ^ [A2: int,B2: int] : ( plus_plus_int @ A2 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_conv_add_uminus
% 0.32/0.54  thf(fact_2433_diff__conv__add__uminus,axiom,
% 0.32/0.54      ( minus_8373710615458151222nteger
% 0.32/0.54      = ( ^ [A2: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A2 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_conv_add_uminus
% 0.32/0.54  thf(fact_2434_diff__conv__add__uminus,axiom,
% 0.32/0.54      ( minus_minus_rat
% 0.32/0.54      = ( ^ [A2: rat,B2: rat] : ( plus_plus_rat @ A2 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % diff_conv_add_uminus
% 0.32/0.54  thf(fact_2435_group__cancel_Osub2,axiom,
% 0.32/0.54      ! [B4: int,K: int,B: int,A: int] :
% 0.32/0.54        ( ( B4
% 0.32/0.54          = ( plus_plus_int @ K @ B ) )
% 0.32/0.54       => ( ( minus_minus_int @ A @ B4 )
% 0.32/0.54          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % group_cancel.sub2
% 0.32/0.54  thf(fact_2436_group__cancel_Osub2,axiom,
% 0.32/0.54      ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.54        ( ( B4
% 0.32/0.54          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 0.32/0.54       => ( ( minus_8373710615458151222nteger @ A @ B4 )
% 0.32/0.54          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % group_cancel.sub2
% 0.32/0.54  thf(fact_2437_group__cancel_Osub2,axiom,
% 0.32/0.54      ! [B4: rat,K: rat,B: rat,A: rat] :
% 0.32/0.54        ( ( B4
% 0.32/0.54          = ( plus_plus_rat @ K @ B ) )
% 0.32/0.54       => ( ( minus_minus_rat @ A @ B4 )
% 0.32/0.54          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % group_cancel.sub2
% 0.32/0.54  thf(fact_2438_nat__mult__distrib__neg,axiom,
% 0.32/0.54      ! [Z2: int,Z6: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 0.32/0.54       => ( ( nat2 @ ( times_times_int @ Z2 @ Z6 ) )
% 0.32/0.54          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z2 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % nat_mult_distrib_neg
% 0.32/0.54  thf(fact_2439_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.32/0.54      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.54        ( ( ord_le1926595141338095240atural @ A @ B )
% 0.32/0.54       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.54         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.32/0.54  thf(fact_2440_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.54       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.54         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.32/0.54  thf(fact_2441_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.32/0.54      ! [A: rat,B: rat,C: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.54         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.32/0.54  thf(fact_2442_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.32/0.54      ! [A: nat,B: nat,C: nat] :
% 0.32/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.54         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.32/0.54  thf(fact_2443_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.32/0.54      ! [A: int,B: int,C: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.54         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.32/0.54  thf(fact_2444_zero__le__mult__iff,axiom,
% 0.32/0.54      ! [A: code_integer,B: code_integer] :
% 0.32/0.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.32/0.54        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.54            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 0.32/0.54          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.54            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_le_mult_iff
% 0.32/0.54  thf(fact_2445_zero__le__mult__iff,axiom,
% 0.32/0.54      ! [A: rat,B: rat] :
% 0.32/0.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.54            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.32/0.54          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.54            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_le_mult_iff
% 0.32/0.54  thf(fact_2446_zero__le__mult__iff,axiom,
% 0.32/0.54      ! [A: int,B: int] :
% 0.32/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.32/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.54            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.32/0.54          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.54            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 0.32/0.54  
% 0.32/0.54  % zero_le_mult_iff
% 0.32/0.54  thf(fact_2447_mult__nonneg__nonpos2,axiom,
% 0.32/0.54      ! [A: code_natural,B: code_natural] :
% 0.32/0.54        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.54       => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 0.32/0.54         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ B @ A ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos2
% 0.32/0.55  thf(fact_2448_mult__nonneg__nonpos2,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos2
% 0.32/0.55  thf(fact_2449_mult__nonneg__nonpos2,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos2
% 0.32/0.55  thf(fact_2450_mult__nonneg__nonpos2,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.55       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.32/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos2
% 0.32/0.55  thf(fact_2451_mult__nonneg__nonpos2,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.32/0.55         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos2
% 0.32/0.55  thf(fact_2452_mult__nonpos__nonneg,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonpos_nonneg
% 0.32/0.55  thf(fact_2453_mult__nonpos__nonneg,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonpos_nonneg
% 0.32/0.55  thf(fact_2454_mult__nonpos__nonneg,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonpos_nonneg
% 0.32/0.55  thf(fact_2455_mult__nonpos__nonneg,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonpos_nonneg
% 0.32/0.55  thf(fact_2456_mult__nonpos__nonneg,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonpos_nonneg
% 0.32/0.55  thf(fact_2457_mult__nonneg__nonpos,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 0.32/0.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos
% 0.32/0.55  thf(fact_2458_mult__nonneg__nonpos,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos
% 0.32/0.55  thf(fact_2459_mult__nonneg__nonpos,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos
% 0.32/0.55  thf(fact_2460_mult__nonneg__nonpos,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.55       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.32/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos
% 0.32/0.55  thf(fact_2461_mult__nonneg__nonpos,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.32/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonpos
% 0.32/0.55  thf(fact_2462_mult__nonneg__nonneg,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.55         => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonneg
% 0.32/0.55  thf(fact_2463_mult__nonneg__nonneg,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonneg
% 0.32/0.55  thf(fact_2464_mult__nonneg__nonneg,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.55         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonneg
% 0.32/0.55  thf(fact_2465_mult__nonneg__nonneg,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.55         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonneg
% 0.32/0.55  thf(fact_2466_mult__nonneg__nonneg,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.55         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonneg_nonneg
% 0.32/0.55  thf(fact_2467_split__mult__neg__le,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55            & ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural ) )
% 0.32/0.55          | ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.55            & ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B ) ) )
% 0.32/0.55       => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ).
% 0.32/0.55  
% 0.32/0.55  % split_mult_neg_le
% 0.32/0.55  thf(fact_2468_split__mult__neg__le,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 0.32/0.55          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) )
% 0.32/0.55       => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.55  
% 0.32/0.55  % split_mult_neg_le
% 0.32/0.55  thf(fact_2469_split__mult__neg__le,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.32/0.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 0.32/0.55       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % split_mult_neg_le
% 0.32/0.55  thf(fact_2470_split__mult__neg__le,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.55            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 0.32/0.55          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.32/0.55            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 0.32/0.55       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % split_mult_neg_le
% 0.32/0.55  thf(fact_2471_split__mult__neg__le,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.32/0.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.55            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 0.32/0.55       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.32/0.55  
% 0.32/0.55  % split_mult_neg_le
% 0.32/0.55  thf(fact_2472_mult__le__0__iff,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 0.32/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 0.32/0.55          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_0_iff
% 0.32/0.55  thf(fact_2473_mult__le__0__iff,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.32/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.32/0.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_0_iff
% 0.32/0.55  thf(fact_2474_mult__le__0__iff,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.32/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.32/0.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.55            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_0_iff
% 0.32/0.55  thf(fact_2475_mult__right__mono,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_mono
% 0.32/0.55  thf(fact_2476_mult__right__mono,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_mono
% 0.32/0.55  thf(fact_2477_mult__right__mono,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_mono
% 0.32/0.55  thf(fact_2478_mult__right__mono,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_mono
% 0.32/0.55  thf(fact_2479_mult__right__mono,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_mono
% 0.32/0.55  thf(fact_2480_mult__right__mono__neg,axiom,
% 0.32/0.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_mono_neg
% 0.32/0.55  thf(fact_2481_mult__right__mono__neg,axiom,
% 0.32/0.55      ! [B: rat,A: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.55       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_mono_neg
% 0.32/0.55  thf(fact_2482_mult__right__mono__neg,axiom,
% 0.32/0.55      ! [B: int,A: int,C: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.55       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.32/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_mono_neg
% 0.32/0.55  thf(fact_2483_mult__left__mono,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_mono
% 0.32/0.55  thf(fact_2484_mult__left__mono,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_mono
% 0.32/0.55  thf(fact_2485_mult__left__mono,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_mono
% 0.32/0.55  thf(fact_2486_mult__left__mono,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_mono
% 0.32/0.55  thf(fact_2487_mult__left__mono,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_mono
% 0.32/0.55  thf(fact_2488_mult__nonpos__nonpos,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonpos_nonpos
% 0.32/0.55  thf(fact_2489_mult__nonpos__nonpos,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonpos_nonpos
% 0.32/0.55  thf(fact_2490_mult__nonpos__nonpos,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.32/0.55         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_nonpos_nonpos
% 0.32/0.55  thf(fact_2491_mult__left__mono__neg,axiom,
% 0.32/0.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_mono_neg
% 0.32/0.55  thf(fact_2492_mult__left__mono__neg,axiom,
% 0.32/0.55      ! [B: rat,A: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.55       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_mono_neg
% 0.32/0.55  thf(fact_2493_mult__left__mono__neg,axiom,
% 0.32/0.55      ! [B: int,A: int,C: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.55       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.32/0.55         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_mono_neg
% 0.32/0.55  thf(fact_2494_split__mult__pos__le,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 0.32/0.55          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.32/0.55       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % split_mult_pos_le
% 0.32/0.55  thf(fact_2495_split__mult__pos__le,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.32/0.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.32/0.55       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % split_mult_pos_le
% 0.32/0.55  thf(fact_2496_split__mult__pos__le,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.32/0.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.55            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.32/0.55       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % split_mult_pos_le
% 0.32/0.55  thf(fact_2497_zero__le__square,axiom,
% 0.32/0.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_le_square
% 0.32/0.55  thf(fact_2498_zero__le__square,axiom,
% 0.32/0.55      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_le_square
% 0.32/0.55  thf(fact_2499_zero__le__square,axiom,
% 0.32/0.55      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_le_square
% 0.32/0.55  thf(fact_2500_mult__mono_H,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ C @ D )
% 0.32/0.55         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55             => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono'
% 0.32/0.55  thf(fact_2501_mult__mono_H,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 0.32/0.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55             => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono'
% 0.32/0.55  thf(fact_2502_mult__mono_H,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_rat @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono'
% 0.32/0.55  thf(fact_2503_mult__mono_H,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_nat @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.55             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono'
% 0.32/0.55  thf(fact_2504_mult__mono_H,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_int @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono'
% 0.32/0.55  thf(fact_2505_mult__mono,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ C @ D )
% 0.32/0.55         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55             => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono
% 0.32/0.55  thf(fact_2506_mult__mono,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 0.32/0.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55             => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono
% 0.32/0.55  thf(fact_2507_mult__mono,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_rat @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono
% 0.32/0.55  thf(fact_2508_mult__mono,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_nat @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.55             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono
% 0.32/0.55  thf(fact_2509_mult__mono,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_int @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_mono
% 0.32/0.55  thf(fact_2510_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.32/0.55  thf(fact_2511_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.32/0.55  thf(fact_2512_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.32/0.55  thf(fact_2513_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.32/0.55         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.32/0.55  thf(fact_2514_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int] :
% 0.32/0.55        ( ( ord_less_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.32/0.55  thf(fact_2515_mult__less__cancel__right__disj,axiom,
% 0.32/0.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55            & ( ord_le6747313008572928689nteger @ A @ B ) )
% 0.32/0.55          | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55            & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right_disj
% 0.32/0.55  thf(fact_2516_mult__less__cancel__right__disj,axiom,
% 0.32/0.55      ! [A: rat,C: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55            & ( ord_less_rat @ A @ B ) )
% 0.32/0.55          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right_disj
% 0.32/0.55  thf(fact_2517_mult__less__cancel__right__disj,axiom,
% 0.32/0.55      ! [A: int,C: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55            & ( ord_less_int @ A @ B ) )
% 0.32/0.55          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right_disj
% 0.32/0.55  thf(fact_2518_mult__strict__right__mono,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_right_mono
% 0.32/0.55  thf(fact_2519_mult__strict__right__mono,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_right_mono
% 0.32/0.55  thf(fact_2520_mult__strict__right__mono,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_right_mono
% 0.32/0.55  thf(fact_2521_mult__strict__right__mono,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.32/0.55         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_right_mono
% 0.32/0.55  thf(fact_2522_mult__strict__right__mono,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int] :
% 0.32/0.55        ( ( ord_less_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_right_mono
% 0.32/0.55  thf(fact_2523_mult__strict__right__mono__neg,axiom,
% 0.32/0.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_right_mono_neg
% 0.32/0.55  thf(fact_2524_mult__strict__right__mono__neg,axiom,
% 0.32/0.55      ! [B: rat,A: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_rat @ B @ A )
% 0.32/0.55       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_right_mono_neg
% 0.32/0.55  thf(fact_2525_mult__strict__right__mono__neg,axiom,
% 0.32/0.55      ! [B: int,A: int,C: int] :
% 0.32/0.55        ( ( ord_less_int @ B @ A )
% 0.32/0.55       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_right_mono_neg
% 0.32/0.55  thf(fact_2526_mult__less__cancel__left__disj,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55            & ( ord_le6747313008572928689nteger @ A @ B ) )
% 0.32/0.55          | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55            & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left_disj
% 0.32/0.55  thf(fact_2527_mult__less__cancel__left__disj,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55            & ( ord_less_rat @ A @ B ) )
% 0.32/0.55          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left_disj
% 0.32/0.55  thf(fact_2528_mult__less__cancel__left__disj,axiom,
% 0.32/0.55      ! [C: int,A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55            & ( ord_less_int @ A @ B ) )
% 0.32/0.55          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left_disj
% 0.32/0.55  thf(fact_2529_mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_left_mono
% 0.32/0.55  thf(fact_2530_mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_left_mono
% 0.32/0.55  thf(fact_2531_mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_left_mono
% 0.32/0.55  thf(fact_2532_mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.32/0.55         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_left_mono
% 0.32/0.55  thf(fact_2533_mult__strict__left__mono,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int] :
% 0.32/0.55        ( ( ord_less_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_left_mono
% 0.32/0.55  thf(fact_2534_mult__strict__left__mono__neg,axiom,
% 0.32/0.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_left_mono_neg
% 0.32/0.55  thf(fact_2535_mult__strict__left__mono__neg,axiom,
% 0.32/0.55      ! [B: rat,A: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_rat @ B @ A )
% 0.32/0.55       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_left_mono_neg
% 0.32/0.55  thf(fact_2536_mult__strict__left__mono__neg,axiom,
% 0.32/0.55      ! [B: int,A: int,C: int] :
% 0.32/0.55        ( ( ord_less_int @ B @ A )
% 0.32/0.55       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_left_mono_neg
% 0.32/0.55  thf(fact_2537_mult__less__cancel__left__pos,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55          = ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left_pos
% 0.32/0.55  thf(fact_2538_mult__less__cancel__left__pos,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.55          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left_pos
% 0.32/0.55  thf(fact_2539_mult__less__cancel__left__pos,axiom,
% 0.32/0.55      ! [C: int,A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.55          = ( ord_less_int @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left_pos
% 0.32/0.55  thf(fact_2540_mult__less__cancel__left__neg,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55          = ( ord_le6747313008572928689nteger @ B @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left_neg
% 0.32/0.55  thf(fact_2541_mult__less__cancel__left__neg,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.55          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left_neg
% 0.32/0.55  thf(fact_2542_mult__less__cancel__left__neg,axiom,
% 0.32/0.55      ! [C: int,A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.55          = ( ord_less_int @ B @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left_neg
% 0.32/0.55  thf(fact_2543_zero__less__mult__pos2,axiom,
% 0.32/0.55      ! [B: code_natural,A: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ B @ A ) )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos2
% 0.32/0.55  thf(fact_2544_zero__less__mult__pos2,axiom,
% 0.32/0.55      ! [B: code_integer,A: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B @ A ) )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos2
% 0.32/0.55  thf(fact_2545_zero__less__mult__pos2,axiom,
% 0.32/0.55      ! [B: rat,A: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 0.32/0.55       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.55         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos2
% 0.32/0.55  thf(fact_2546_zero__less__mult__pos2,axiom,
% 0.32/0.55      ! [B: nat,A: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.55         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos2
% 0.32/0.55  thf(fact_2547_zero__less__mult__pos2,axiom,
% 0.32/0.55      ! [B: int,A: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.55         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos2
% 0.32/0.55  thf(fact_2548_zero__less__mult__pos,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ A @ B ) )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos
% 0.32/0.55  thf(fact_2549_zero__less__mult__pos,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos
% 0.32/0.55  thf(fact_2550_zero__less__mult__pos,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.55       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.55         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos
% 0.32/0.55  thf(fact_2551_zero__less__mult__pos,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.55         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos
% 0.32/0.55  thf(fact_2552_zero__less__mult__pos,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.55         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_pos
% 0.32/0.55  thf(fact_2553_zero__less__mult__iff,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55            & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) )
% 0.32/0.55          | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55            & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_iff
% 0.32/0.55  thf(fact_2554_zero__less__mult__iff,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.55            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.32/0.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.55            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_iff
% 0.32/0.55  thf(fact_2555_zero__less__mult__iff,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.55            & ( ord_less_int @ zero_zero_int @ B ) )
% 0.32/0.55          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.55            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_less_mult_iff
% 0.32/0.55  thf(fact_2556_mult__pos__neg2,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ B @ A ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg2
% 0.32/0.55  thf(fact_2557_mult__pos__neg2,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg2
% 0.32/0.55  thf(fact_2558_mult__pos__neg2,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg2
% 0.32/0.55  thf(fact_2559_mult__pos__neg2,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.55       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.32/0.55         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg2
% 0.32/0.55  thf(fact_2560_mult__pos__neg2,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg2
% 0.32/0.55  thf(fact_2561_mult__pos__pos,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_pos
% 0.32/0.55  thf(fact_2562_mult__pos__pos,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_pos
% 0.32/0.55  thf(fact_2563_mult__pos__pos,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.32/0.55         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_pos
% 0.32/0.55  thf(fact_2564_mult__pos__pos,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.32/0.55         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_pos
% 0.32/0.55  thf(fact_2565_mult__pos__pos,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.55         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_pos
% 0.32/0.55  thf(fact_2566_mult__pos__neg,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg
% 0.32/0.55  thf(fact_2567_mult__pos__neg,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg
% 0.32/0.55  thf(fact_2568_mult__pos__neg,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg
% 0.32/0.55  thf(fact_2569_mult__pos__neg,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.55       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.32/0.55         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg
% 0.32/0.55  thf(fact_2570_mult__pos__neg,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_pos_neg
% 0.32/0.55  thf(fact_2571_mult__neg__pos,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_neg_pos
% 0.32/0.55  thf(fact_2572_mult__neg__pos,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_neg_pos
% 0.32/0.55  thf(fact_2573_mult__neg__pos,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.32/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_neg_pos
% 0.32/0.55  thf(fact_2574_mult__neg__pos,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.32/0.55         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_neg_pos
% 0.32/0.55  thf(fact_2575_mult__neg__pos,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_neg_pos
% 0.32/0.55  thf(fact_2576_mult__less__0__iff,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55            & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) )
% 0.32/0.55          | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55            & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_0_iff
% 0.32/0.55  thf(fact_2577_mult__less__0__iff,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.55            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.32/0.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.55            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_0_iff
% 0.32/0.55  thf(fact_2578_mult__less__0__iff,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.55            & ( ord_less_int @ B @ zero_zero_int ) )
% 0.32/0.55          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.55            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_0_iff
% 0.32/0.55  thf(fact_2579_not__square__less__zero,axiom,
% 0.32/0.55      ! [A: code_integer] :
% 0.32/0.55        ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.55  
% 0.32/0.55  % not_square_less_zero
% 0.32/0.55  thf(fact_2580_not__square__less__zero,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 0.32/0.55  
% 0.32/0.55  % not_square_less_zero
% 0.32/0.55  thf(fact_2581_not__square__less__zero,axiom,
% 0.32/0.55      ! [A: int] :
% 0.32/0.55        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 0.32/0.55  
% 0.32/0.55  % not_square_less_zero
% 0.32/0.55  thf(fact_2582_mult__neg__neg,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_neg_neg
% 0.32/0.55  thf(fact_2583_mult__neg__neg,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.32/0.55         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_neg_neg
% 0.32/0.55  thf(fact_2584_mult__neg__neg,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.32/0.55         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_neg_neg
% 0.32/0.55  thf(fact_2585_add__scale__eq__noteq,axiom,
% 0.32/0.55      ! [R: code_integer,A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.55        ( ( R != zero_z3403309356797280102nteger )
% 0.32/0.55       => ( ( ( A = B )
% 0.32/0.55            & ( C != D ) )
% 0.32/0.55         => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R @ C ) )
% 0.32/0.55           != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R @ D ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % add_scale_eq_noteq
% 0.32/0.55  thf(fact_2586_add__scale__eq__noteq,axiom,
% 0.32/0.55      ! [R: rat,A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.55        ( ( R != zero_zero_rat )
% 0.32/0.55       => ( ( ( A = B )
% 0.32/0.55            & ( C != D ) )
% 0.32/0.55         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 0.32/0.55           != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % add_scale_eq_noteq
% 0.32/0.55  thf(fact_2587_add__scale__eq__noteq,axiom,
% 0.32/0.55      ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.55        ( ( R != zero_zero_nat )
% 0.32/0.55       => ( ( ( A = B )
% 0.32/0.55            & ( C != D ) )
% 0.32/0.55         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 0.32/0.55           != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % add_scale_eq_noteq
% 0.32/0.55  thf(fact_2588_add__scale__eq__noteq,axiom,
% 0.32/0.55      ! [R: int,A: int,B: int,C: int,D: int] :
% 0.32/0.55        ( ( R != zero_zero_int )
% 0.32/0.55       => ( ( ( A = B )
% 0.32/0.55            & ( C != D ) )
% 0.32/0.55         => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 0.32/0.55           != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % add_scale_eq_noteq
% 0.32/0.55  thf(fact_2589_less__1__mult,axiom,
% 0.32/0.55      ! [M: code_natural,N: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ M )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ N )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_1_mult
% 0.32/0.55  thf(fact_2590_less__1__mult,axiom,
% 0.32/0.55      ! [M: code_integer,N: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_1_mult
% 0.32/0.55  thf(fact_2591_less__1__mult,axiom,
% 0.32/0.55      ! [M: rat,N: rat] :
% 0.32/0.55        ( ( ord_less_rat @ one_one_rat @ M )
% 0.32/0.55       => ( ( ord_less_rat @ one_one_rat @ N )
% 0.32/0.55         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_1_mult
% 0.32/0.55  thf(fact_2592_less__1__mult,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ one_one_nat @ M )
% 0.32/0.55       => ( ( ord_less_nat @ one_one_nat @ N )
% 0.32/0.55         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_1_mult
% 0.32/0.55  thf(fact_2593_less__1__mult,axiom,
% 0.32/0.55      ! [M: int,N: int] :
% 0.32/0.55        ( ( ord_less_int @ one_one_int @ M )
% 0.32/0.55       => ( ( ord_less_int @ one_one_int @ N )
% 0.32/0.55         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_1_mult
% 0.32/0.55  thf(fact_2594_Suc__to__right,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ( suc @ N )
% 0.32/0.55          = M )
% 0.32/0.55       => ( N
% 0.32/0.55          = ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_to_right
% 0.32/0.55  thf(fact_2595_diff__less,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.55         => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_less
% 0.32/0.55  thf(fact_2596_Suc__diff__Suc,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ N @ M )
% 0.32/0.55       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 0.32/0.55          = ( minus_minus_nat @ M @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_diff_Suc
% 0.32/0.55  thf(fact_2597_diff__less__Suc,axiom,
% 0.32/0.55      ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_less_Suc
% 0.32/0.55  thf(fact_2598_square__eq__1__iff,axiom,
% 0.32/0.55      ! [X2: int] :
% 0.32/0.55        ( ( ( times_times_int @ X2 @ X2 )
% 0.32/0.55          = one_one_int )
% 0.32/0.55        = ( ( X2 = one_one_int )
% 0.32/0.55          | ( X2
% 0.32/0.55            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % square_eq_1_iff
% 0.32/0.55  thf(fact_2599_square__eq__1__iff,axiom,
% 0.32/0.55      ! [X2: code_integer] :
% 0.32/0.55        ( ( ( times_3573771949741848930nteger @ X2 @ X2 )
% 0.32/0.55          = one_one_Code_integer )
% 0.32/0.55        = ( ( X2 = one_one_Code_integer )
% 0.32/0.55          | ( X2
% 0.32/0.55            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % square_eq_1_iff
% 0.32/0.55  thf(fact_2600_square__eq__1__iff,axiom,
% 0.32/0.55      ! [X2: rat] :
% 0.32/0.55        ( ( ( times_times_rat @ X2 @ X2 )
% 0.32/0.55          = one_one_rat )
% 0.32/0.55        = ( ( X2 = one_one_rat )
% 0.32/0.55          | ( X2
% 0.32/0.55            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % square_eq_1_iff
% 0.32/0.55  thf(fact_2601_Suc__diff__le,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.55       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.32/0.55          = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_diff_le
% 0.32/0.55  thf(fact_2602_diff__add__0,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.32/0.55        = zero_zero_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_add_0
% 0.32/0.55  thf(fact_2603_less__diff__iff,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.55       => ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.55         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.32/0.55            = ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_diff_iff
% 0.32/0.55  thf(fact_2604_diff__less__mono,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_nat @ C @ A )
% 0.32/0.55         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_less_mono
% 0.32/0.55  thf(fact_2605_add__diff__inverse__nat,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ~ ( ord_less_nat @ M @ N )
% 0.32/0.55       => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.55          = M ) ) ).
% 0.32/0.55  
% 0.32/0.55  % add_diff_inverse_nat
% 0.32/0.55  thf(fact_2606_less__diff__conv,axiom,
% 0.32/0.55      ! [I: nat,J: nat,K: nat] :
% 0.32/0.55        ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.32/0.55        = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_diff_conv
% 0.32/0.55  thf(fact_2607_le__diff__conv,axiom,
% 0.32/0.55      ! [J: nat,K: nat,I: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.32/0.55        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % le_diff_conv
% 0.32/0.55  thf(fact_2608_Nat_Ole__diff__conv2,axiom,
% 0.32/0.55      ! [K: nat,J: nat,I: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.55       => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.32/0.55          = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Nat.le_diff_conv2
% 0.32/0.55  thf(fact_2609_Nat_Odiff__add__assoc,axiom,
% 0.32/0.55      ! [K: nat,J: nat,I: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.55       => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.32/0.55          = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Nat.diff_add_assoc
% 0.32/0.55  thf(fact_2610_Nat_Odiff__add__assoc2,axiom,
% 0.32/0.55      ! [K: nat,J: nat,I: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.55       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 0.32/0.55          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Nat.diff_add_assoc2
% 0.32/0.55  thf(fact_2611_Nat_Ole__imp__diff__is__add,axiom,
% 0.32/0.55      ! [I: nat,J: nat,K: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.55       => ( ( ( minus_minus_nat @ J @ I )
% 0.32/0.55            = K )
% 0.32/0.55          = ( J
% 0.32/0.55            = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Nat.le_imp_diff_is_add
% 0.32/0.55  thf(fact_2612_minus__int__code_I2_J,axiom,
% 0.32/0.55      ! [L: int] :
% 0.32/0.55        ( ( minus_minus_int @ zero_zero_int @ L )
% 0.32/0.55        = ( uminus_uminus_int @ L ) ) ).
% 0.32/0.55  
% 0.32/0.55  % minus_int_code(2)
% 0.32/0.55  thf(fact_2613_mult__less__mono2,axiom,
% 0.32/0.55      ! [I: nat,J: nat,K: nat] :
% 0.32/0.55        ( ( ord_less_nat @ I @ J )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.55         => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_mono2
% 0.32/0.55  thf(fact_2614_mult__less__mono1,axiom,
% 0.32/0.55      ! [I: nat,J: nat,K: nat] :
% 0.32/0.55        ( ( ord_less_nat @ I @ J )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.55         => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_mono1
% 0.32/0.55  thf(fact_2615_int__le__induct,axiom,
% 0.32/0.55      ! [I: int,K: int,P: int > $o] :
% 0.32/0.55        ( ( ord_less_eq_int @ I @ K )
% 0.32/0.55       => ( ( P @ K )
% 0.32/0.55         => ( ! [I3: int] :
% 0.32/0.55                ( ( ord_less_eq_int @ I3 @ K )
% 0.32/0.55               => ( ( P @ I3 )
% 0.32/0.55                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 0.32/0.55           => ( P @ I ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % int_le_induct
% 0.32/0.55  thf(fact_2616_Suc__mult__less__cancel1,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.32/0.55        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_mult_less_cancel1
% 0.32/0.55  thf(fact_2617_diff__Suc__eq__diff__pred,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.32/0.55        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_Suc_eq_diff_pred
% 0.32/0.55  thf(fact_2618_diff__nat__eq__if,axiom,
% 0.32/0.55      ! [Z6: int,Z2: int] :
% 0.32/0.55        ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 0.32/0.55         => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) )
% 0.32/0.55            = ( nat2 @ Z2 ) ) )
% 0.32/0.55        & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 0.32/0.55         => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) )
% 0.32/0.55            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z2 @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z2 @ Z6 ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_nat_eq_if
% 0.32/0.55  thf(fact_2619_int__less__induct,axiom,
% 0.32/0.55      ! [I: int,K: int,P: int > $o] :
% 0.32/0.55        ( ( ord_less_int @ I @ K )
% 0.32/0.55       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 0.32/0.55         => ( ! [I3: int] :
% 0.32/0.55                ( ( ord_less_int @ I3 @ K )
% 0.32/0.55               => ( ( P @ I3 )
% 0.32/0.55                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 0.32/0.55           => ( P @ I ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % int_less_induct
% 0.32/0.55  thf(fact_2620_Suc__mult__le__cancel1,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.32/0.55        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_mult_le_cancel1
% 0.32/0.55  thf(fact_2621_mult__Suc,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( times_times_nat @ ( suc @ M ) @ N )
% 0.32/0.55        = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_Suc
% 0.32/0.55  thf(fact_2622_mlex__snd__decrI,axiom,
% 0.32/0.55      ! [A: nat,A5: nat,B: nat,B5: nat,N4: nat] :
% 0.32/0.55        ( ( A = A5 )
% 0.32/0.55       => ( ( ord_less_nat @ B @ B5 )
% 0.32/0.55         => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A5 @ N4 ) @ B5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mlex_snd_decrI
% 0.32/0.55  thf(fact_2623_mlex__fst__decrI,axiom,
% 0.32/0.55      ! [A: nat,A5: nat,B: nat,N4: nat,B5: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ A5 )
% 0.32/0.55       => ( ( ord_less_nat @ B @ N4 )
% 0.32/0.55         => ( ( ord_less_nat @ B5 @ N4 )
% 0.32/0.55           => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A5 @ N4 ) @ B5 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mlex_fst_decrI
% 0.32/0.55  thf(fact_2624_mlex__bound,axiom,
% 0.32/0.55      ! [A: nat,A4: nat,B: nat,N4: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ A4 )
% 0.32/0.55       => ( ( ord_less_nat @ B @ N4 )
% 0.32/0.55         => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( times_times_nat @ A4 @ N4 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mlex_bound
% 0.32/0.55  thf(fact_2625_mlex__leI,axiom,
% 0.32/0.55      ! [A: nat,A5: nat,B: nat,B5: nat,N4: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ A @ A5 )
% 0.32/0.55       => ( ( ord_less_eq_nat @ B @ B5 )
% 0.32/0.55         => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A5 @ N4 ) @ B5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mlex_leI
% 0.32/0.55  thf(fact_2626_mult__eq__self__implies__10,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( M
% 0.32/0.55          = ( times_times_nat @ M @ N ) )
% 0.32/0.55       => ( ( N = one_one_nat )
% 0.32/0.55          | ( M = zero_zero_nat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_eq_self_implies_10
% 0.32/0.55  thf(fact_2627_zmult__zless__mono2,axiom,
% 0.32/0.55      ! [I: int,J: int,K: int] :
% 0.32/0.55        ( ( ord_less_int @ I @ J )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zmult_zless_mono2
% 0.32/0.55  thf(fact_2628_zmult__eq__1__iff,axiom,
% 0.32/0.55      ! [M: int,N: int] :
% 0.32/0.55        ( ( ( times_times_int @ M @ N )
% 0.32/0.55          = one_one_int )
% 0.32/0.55        = ( ( ( M = one_one_int )
% 0.32/0.55            & ( N = one_one_int ) )
% 0.32/0.55          | ( ( M
% 0.32/0.55              = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.55            & ( N
% 0.32/0.55              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zmult_eq_1_iff
% 0.32/0.55  thf(fact_2629_pos__zmult__eq__1__iff__lemma,axiom,
% 0.32/0.55      ! [M: int,N: int] :
% 0.32/0.55        ( ( ( times_times_int @ M @ N )
% 0.32/0.55          = one_one_int )
% 0.32/0.55       => ( ( M = one_one_int )
% 0.32/0.55          | ( M
% 0.32/0.55            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % pos_zmult_eq_1_iff_lemma
% 0.32/0.55  thf(fact_2630_list_Osize_I3_J,axiom,
% 0.32/0.55      ( ( size_size_list_char @ nil_char )
% 0.32/0.55      = zero_zero_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % list.size(3)
% 0.32/0.55  thf(fact_2631_list_Osize_I3_J,axiom,
% 0.32/0.55      ( ( size_size_list_nat @ nil_nat )
% 0.32/0.55      = zero_zero_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % list.size(3)
% 0.32/0.55  thf(fact_2632_list_Osize_I3_J,axiom,
% 0.32/0.55      ( ( size_size_list_int @ nil_int )
% 0.32/0.55      = zero_zero_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % list.size(3)
% 0.32/0.55  thf(fact_2633_list_Osize_I3_J,axiom,
% 0.32/0.55      ( ( size_size_list_o @ nil_o )
% 0.32/0.55      = zero_zero_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % list.size(3)
% 0.32/0.55  thf(fact_2634_len__greater__imp__nonempty,axiom,
% 0.32/0.55      ! [X2: nat,L: list_char] :
% 0.32/0.55        ( ( ord_less_nat @ X2 @ ( size_size_list_char @ L ) )
% 0.32/0.55       => ( L != nil_char ) ) ).
% 0.32/0.55  
% 0.32/0.55  % len_greater_imp_nonempty
% 0.32/0.55  thf(fact_2635_len__greater__imp__nonempty,axiom,
% 0.32/0.55      ! [X2: nat,L: list_nat] :
% 0.32/0.55        ( ( ord_less_nat @ X2 @ ( size_size_list_nat @ L ) )
% 0.32/0.55       => ( L != nil_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % len_greater_imp_nonempty
% 0.32/0.55  thf(fact_2636_len__greater__imp__nonempty,axiom,
% 0.32/0.55      ! [X2: nat,L: list_int] :
% 0.32/0.55        ( ( ord_less_nat @ X2 @ ( size_size_list_int @ L ) )
% 0.32/0.55       => ( L != nil_int ) ) ).
% 0.32/0.55  
% 0.32/0.55  % len_greater_imp_nonempty
% 0.32/0.55  thf(fact_2637_len__greater__imp__nonempty,axiom,
% 0.32/0.55      ! [X2: nat,L: list_o] :
% 0.32/0.55        ( ( ord_less_nat @ X2 @ ( size_size_list_o @ L ) )
% 0.32/0.55       => ( L != nil_o ) ) ).
% 0.32/0.55  
% 0.32/0.55  % len_greater_imp_nonempty
% 0.32/0.55  thf(fact_2638_mult__less__le__imp__less,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ C @ D )
% 0.32/0.55         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55           => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55             => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_le_imp_less
% 0.32/0.55  thf(fact_2639_mult__less__le__imp__less,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 0.32/0.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55           => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_le_imp_less
% 0.32/0.55  thf(fact_2640_mult__less__le__imp__less,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.55        ( ( ord_less_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_rat @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_le_imp_less
% 0.32/0.55  thf(fact_2641_mult__less__le__imp__less,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_nat @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.55           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.32/0.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_le_imp_less
% 0.32/0.55  thf(fact_2642_mult__less__le__imp__less,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.55        ( ( ord_less_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_eq_int @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55           => ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_le_imp_less
% 0.32/0.55  thf(fact_2643_mult__le__less__imp__less,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ C @ D )
% 0.32/0.55         => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55             => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_less_imp_less
% 0.32/0.55  thf(fact_2644_mult__le__less__imp__less,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 0.32/0.55         => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_less_imp_less
% 0.32/0.55  thf(fact_2645_mult__le__less__imp__less,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_rat @ C @ D )
% 0.32/0.55         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_less_imp_less
% 0.32/0.55  thf(fact_2646_mult__le__less__imp__less,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_nat @ C @ D )
% 0.32/0.55         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_less_imp_less
% 0.32/0.55  thf(fact_2647_mult__le__less__imp__less,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_int @ C @ D )
% 0.32/0.55         => ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_less_imp_less
% 0.32/0.55  thf(fact_2648_mult__right__le__imp__le,axiom,
% 0.32/0.55      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55         => ( ord_le1926595141338095240atural @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_le_imp_le
% 0.32/0.55  thf(fact_2649_mult__right__le__imp__le,axiom,
% 0.32/0.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_le_imp_le
% 0.32/0.55  thf(fact_2650_mult__right__le__imp__le,axiom,
% 0.32/0.55      ! [A: rat,C: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.32/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_le_imp_le
% 0.32/0.55  thf(fact_2651_mult__right__le__imp__le,axiom,
% 0.32/0.55      ! [A: nat,C: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.32/0.55         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_le_imp_le
% 0.32/0.55  thf(fact_2652_mult__right__le__imp__le,axiom,
% 0.32/0.55      ! [A: int,C: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_le_imp_le
% 0.32/0.55  thf(fact_2653_mult__left__le__imp__le,axiom,
% 0.32/0.55      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55         => ( ord_le1926595141338095240atural @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le_imp_le
% 0.32/0.55  thf(fact_2654_mult__left__le__imp__le,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le_imp_le
% 0.32/0.55  thf(fact_2655_mult__left__le__imp__le,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le_imp_le
% 0.32/0.55  thf(fact_2656_mult__left__le__imp__le,axiom,
% 0.32/0.55      ! [C: nat,A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.32/0.55         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le_imp_le
% 0.32/0.55  thf(fact_2657_mult__left__le__imp__le,axiom,
% 0.32/0.55      ! [C: int,A: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le_imp_le
% 0.32/0.55  thf(fact_2658_mult__le__cancel__left__pos,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55          = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left_pos
% 0.32/0.55  thf(fact_2659_mult__le__cancel__left__pos,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.55          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left_pos
% 0.32/0.55  thf(fact_2660_mult__le__cancel__left__pos,axiom,
% 0.32/0.55      ! [C: int,A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.55          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left_pos
% 0.32/0.55  thf(fact_2661_mult__le__cancel__left__neg,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55          = ( ord_le3102999989581377725nteger @ B @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left_neg
% 0.32/0.55  thf(fact_2662_mult__le__cancel__left__neg,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.55          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left_neg
% 0.32/0.55  thf(fact_2663_mult__le__cancel__left__neg,axiom,
% 0.32/0.55      ! [C: int,A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.55          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left_neg
% 0.32/0.55  thf(fact_2664_mult__less__cancel__right,axiom,
% 0.32/0.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ A @ B ) )
% 0.32/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right
% 0.32/0.55  thf(fact_2665_mult__less__cancel__right,axiom,
% 0.32/0.55      ! [A: rat,C: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_rat @ A @ B ) )
% 0.32/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right
% 0.32/0.55  thf(fact_2666_mult__less__cancel__right,axiom,
% 0.32/0.55      ! [A: int,C: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_int @ A @ B ) )
% 0.32/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right
% 0.32/0.55  thf(fact_2667_mult__strict__mono_H,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ C @ D )
% 0.32/0.55         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55             => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono'
% 0.32/0.55  thf(fact_2668_mult__strict__mono_H,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 0.32/0.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono'
% 0.32/0.55  thf(fact_2669_mult__strict__mono_H,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.55        ( ( ord_less_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_rat @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono'
% 0.32/0.55  thf(fact_2670_mult__strict__mono_H,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_nat @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono'
% 0.32/0.55  thf(fact_2671_mult__strict__mono_H,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.55        ( ( ord_less_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_int @ C @ D )
% 0.32/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono'
% 0.32/0.55  thf(fact_2672_mult__right__less__imp__less,axiom,
% 0.32/0.55      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_less_imp_less
% 0.32/0.55  thf(fact_2673_mult__right__less__imp__less,axiom,
% 0.32/0.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_less_imp_less
% 0.32/0.55  thf(fact_2674_mult__right__less__imp__less,axiom,
% 0.32/0.55      ! [A: rat,C: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_less_imp_less
% 0.32/0.55  thf(fact_2675_mult__right__less__imp__less,axiom,
% 0.32/0.55      ! [A: nat,C: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.55         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_less_imp_less
% 0.32/0.55  thf(fact_2676_mult__right__less__imp__less,axiom,
% 0.32/0.55      ! [A: int,C: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55         => ( ord_less_int @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_less_imp_less
% 0.32/0.55  thf(fact_2677_mult__less__cancel__left,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ A @ B ) )
% 0.32/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left
% 0.32/0.55  thf(fact_2678_mult__less__cancel__left,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_rat @ A @ B ) )
% 0.32/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left
% 0.32/0.55  thf(fact_2679_mult__less__cancel__left,axiom,
% 0.32/0.55      ! [C: int,A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_int @ A @ B ) )
% 0.32/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left
% 0.32/0.55  thf(fact_2680_mult__strict__mono,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 0.32/0.55       => ( ( ord_le5570908160329646204atural @ C @ D )
% 0.32/0.55         => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55             => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono
% 0.32/0.55  thf(fact_2681_mult__strict__mono,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 0.32/0.55         => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono
% 0.32/0.55  thf(fact_2682_mult__strict__mono,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.55        ( ( ord_less_rat @ A @ B )
% 0.32/0.55       => ( ( ord_less_rat @ C @ D )
% 0.32/0.55         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.32/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono
% 0.32/0.55  thf(fact_2683_mult__strict__mono,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.55        ( ( ord_less_nat @ A @ B )
% 0.32/0.55       => ( ( ord_less_nat @ C @ D )
% 0.32/0.55         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.32/0.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono
% 0.32/0.55  thf(fact_2684_mult__strict__mono,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.55        ( ( ord_less_int @ A @ B )
% 0.32/0.55       => ( ( ord_less_int @ C @ D )
% 0.32/0.55         => ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_strict_mono
% 0.32/0.55  thf(fact_2685_mult__left__less__imp__less,axiom,
% 0.32/0.55      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 0.32/0.55         => ( ord_le5570908160329646204atural @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_less_imp_less
% 0.32/0.55  thf(fact_2686_mult__left__less__imp__less,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_less_imp_less
% 0.32/0.55  thf(fact_2687_mult__left__less__imp__less,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_less_imp_less
% 0.32/0.55  thf(fact_2688_mult__left__less__imp__less,axiom,
% 0.32/0.55      ! [C: nat,A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.55         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_less_imp_less
% 0.32/0.55  thf(fact_2689_mult__left__less__imp__less,axiom,
% 0.32/0.55      ! [C: int,A: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55         => ( ord_less_int @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_less_imp_less
% 0.32/0.55  thf(fact_2690_mult__le__cancel__right,axiom,
% 0.32/0.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ A @ B ) )
% 0.32/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_right
% 0.32/0.55  thf(fact_2691_mult__le__cancel__right,axiom,
% 0.32/0.55      ! [A: rat,C: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_eq_rat @ A @ B ) )
% 0.32/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_right
% 0.32/0.55  thf(fact_2692_mult__le__cancel__right,axiom,
% 0.32/0.55      ! [A: int,C: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_eq_int @ A @ B ) )
% 0.32/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_right
% 0.32/0.55  thf(fact_2693_mult__le__cancel__left,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ A @ B ) )
% 0.32/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left
% 0.32/0.55  thf(fact_2694_mult__le__cancel__left,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_eq_rat @ A @ B ) )
% 0.32/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left
% 0.32/0.55  thf(fact_2695_mult__le__cancel__left,axiom,
% 0.32/0.55      ! [C: int,A: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_eq_int @ A @ B ) )
% 0.32/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left
% 0.32/0.55  thf(fact_2696_sum__squares__ge__zero,axiom,
% 0.32/0.55      ! [X2: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_ge_zero
% 0.32/0.55  thf(fact_2697_sum__squares__ge__zero,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_ge_zero
% 0.32/0.55  thf(fact_2698_sum__squares__ge__zero,axiom,
% 0.32/0.55      ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_ge_zero
% 0.32/0.55  thf(fact_2699_mult__left__le,axiom,
% 0.32/0.55      ! [C: code_natural,A: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ C @ one_one_Code_natural )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le
% 0.32/0.55  thf(fact_2700_mult__left__le,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le
% 0.32/0.55  thf(fact_2701_mult__left__le,axiom,
% 0.32/0.55      ! [C: rat,A: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le
% 0.32/0.55  thf(fact_2702_mult__left__le,axiom,
% 0.32/0.55      ! [C: nat,A: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le
% 0.32/0.55  thf(fact_2703_mult__left__le,axiom,
% 0.32/0.55      ! [C: int,A: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ C @ one_one_int )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le
% 0.32/0.55  thf(fact_2704_mult__le__one,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 0.32/0.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.55         => ( ( ord_le1926595141338095240atural @ B @ one_one_Code_natural )
% 0.32/0.55           => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ one_one_Code_natural ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_one
% 0.32/0.55  thf(fact_2705_mult__le__one,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.55         => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_one
% 0.32/0.55  thf(fact_2706_mult__le__one,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.55         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.32/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_one
% 0.32/0.55  thf(fact_2707_mult__le__one,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.55         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.32/0.55           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_one
% 0.32/0.55  thf(fact_2708_mult__le__one,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ A @ one_one_int )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.55         => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.32/0.55           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_one
% 0.32/0.55  thf(fact_2709_mult__right__le__one__le,axiom,
% 0.32/0.55      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.32/0.55         => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X2 @ Y ) @ X2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_le_one_le
% 0.32/0.55  thf(fact_2710_mult__right__le__one__le,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.32/0.55         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.32/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Y ) @ X2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_le_one_le
% 0.32/0.55  thf(fact_2711_mult__right__le__one__le,axiom,
% 0.32/0.55      ! [X2: int,Y: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.55         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.32/0.55           => ( ord_less_eq_int @ ( times_times_int @ X2 @ Y ) @ X2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_right_le_one_le
% 0.32/0.55  thf(fact_2712_mult__left__le__one__le,axiom,
% 0.32/0.55      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.32/0.55         => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X2 ) @ X2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le_one_le
% 0.32/0.55  thf(fact_2713_mult__left__le__one__le,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.32/0.55         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.32/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X2 ) @ X2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le_one_le
% 0.32/0.55  thf(fact_2714_mult__left__le__one__le,axiom,
% 0.32/0.55      ! [X2: int,Y: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.55         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.32/0.55           => ( ord_less_eq_int @ ( times_times_int @ Y @ X2 ) @ X2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_left_le_one_le
% 0.32/0.55  thf(fact_2715_not__sum__squares__lt__zero,axiom,
% 0.32/0.55      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.55        ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.55  
% 0.32/0.55  % not_sum_squares_lt_zero
% 0.32/0.55  thf(fact_2716_not__sum__squares__lt__zero,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] :
% 0.32/0.55        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 0.32/0.55  
% 0.32/0.55  % not_sum_squares_lt_zero
% 0.32/0.55  thf(fact_2717_not__sum__squares__lt__zero,axiom,
% 0.32/0.55      ! [X2: int,Y: int] :
% 0.32/0.55        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 0.32/0.55  
% 0.32/0.55  % not_sum_squares_lt_zero
% 0.32/0.55  thf(fact_2718_ex__less__of__nat__mult,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 0.32/0.55       => ? [N2: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X2 ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % ex_less_of_nat_mult
% 0.32/0.55  thf(fact_2719_diff__Suc__less,axiom,
% 0.32/0.55      ! [N: nat,I: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_Suc_less
% 0.32/0.55  thf(fact_2720_nat__diff__split__asm,axiom,
% 0.32/0.55      ! [P: nat > $o,A: nat,B: nat] :
% 0.32/0.55        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.55        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 0.32/0.55                & ~ ( P @ zero_zero_nat ) )
% 0.32/0.55              | ? [D4: nat] :
% 0.32/0.55                  ( ( A
% 0.32/0.55                    = ( plus_plus_nat @ B @ D4 ) )
% 0.32/0.55                  & ~ ( P @ D4 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_diff_split_asm
% 0.32/0.55  thf(fact_2721_nat__diff__split,axiom,
% 0.32/0.55      ! [P: nat > $o,A: nat,B: nat] :
% 0.32/0.55        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.55        = ( ( ( ord_less_nat @ A @ B )
% 0.32/0.55           => ( P @ zero_zero_nat ) )
% 0.32/0.55          & ! [D4: nat] :
% 0.32/0.55              ( ( A
% 0.32/0.55                = ( plus_plus_nat @ B @ D4 ) )
% 0.32/0.55             => ( P @ D4 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_diff_split
% 0.32/0.55  thf(fact_2722_less__diff__conv2,axiom,
% 0.32/0.55      ! [K: nat,J: nat,I: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.55       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.32/0.55          = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_diff_conv2
% 0.32/0.55  thf(fact_2723_power__int__minus__one__diff__commute,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_int @ A @ B ) )
% 0.32/0.55        = ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_int_minus_one_diff_commute
% 0.32/0.55  thf(fact_2724_n__less__n__mult__m,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.32/0.55         => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % n_less_n_mult_m
% 0.32/0.55  thf(fact_2725_n__less__m__mult__n,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.32/0.55         => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % n_less_m_mult_n
% 0.32/0.55  thf(fact_2726_one__less__mult,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.55       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.32/0.55         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % one_less_mult
% 0.32/0.55  thf(fact_2727_int__induct,axiom,
% 0.32/0.55      ! [P: int > $o,K: int,I: int] :
% 0.32/0.55        ( ( P @ K )
% 0.32/0.55       => ( ! [I3: int] :
% 0.32/0.55              ( ( ord_less_eq_int @ K @ I3 )
% 0.32/0.55             => ( ( P @ I3 )
% 0.32/0.55               => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 0.32/0.55         => ( ! [I3: int] :
% 0.32/0.55                ( ( ord_less_eq_int @ I3 @ K )
% 0.32/0.55               => ( ( P @ I3 )
% 0.32/0.55                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 0.32/0.55           => ( P @ I ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % int_induct
% 0.32/0.55  thf(fact_2728_pos__zmult__eq__1__iff,axiom,
% 0.32/0.55      ! [M: int,N: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ M )
% 0.32/0.55       => ( ( ( times_times_int @ M @ N )
% 0.32/0.55            = one_one_int )
% 0.32/0.55          = ( ( M = one_one_int )
% 0.32/0.55            & ( N = one_one_int ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % pos_zmult_eq_1_iff
% 0.32/0.55  thf(fact_2729_frac__def,axiom,
% 0.32/0.55      ( archimedean_frac_rat
% 0.32/0.55      = ( ^ [X: rat] : ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % frac_def
% 0.32/0.55  thf(fact_2730_dbl__dec__def,axiom,
% 0.32/0.55      ( neg_nu7757733837767384882nteger
% 0.32/0.55      = ( ^ [X: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X @ X ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % dbl_dec_def
% 0.32/0.55  thf(fact_2731_dbl__dec__def,axiom,
% 0.32/0.55      ( neg_nu3179335615603231917ec_rat
% 0.32/0.55      = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % dbl_dec_def
% 0.32/0.55  thf(fact_2732_dbl__dec__def,axiom,
% 0.32/0.55      ( neg_nu3811975205180677377ec_int
% 0.32/0.55      = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % dbl_dec_def
% 0.32/0.55  thf(fact_2733_field__le__mult__one__interval,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] :
% 0.32/0.55        ( ! [Z4: rat] :
% 0.32/0.55            ( ( ord_less_rat @ zero_zero_rat @ Z4 )
% 0.32/0.55           => ( ( ord_less_rat @ Z4 @ one_one_rat )
% 0.32/0.55             => ( ord_less_eq_rat @ ( times_times_rat @ Z4 @ X2 ) @ Y ) ) )
% 0.32/0.55       => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 0.32/0.55  
% 0.32/0.55  % field_le_mult_one_interval
% 0.32/0.55  thf(fact_2734_mult__less__cancel__right2,axiom,
% 0.32/0.55      ! [A: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 0.32/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 0.32/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right2
% 0.32/0.55  thf(fact_2735_mult__less__cancel__right2,axiom,
% 0.32/0.55      ! [A: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.32/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.32/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right2
% 0.32/0.55  thf(fact_2736_mult__less__cancel__right2,axiom,
% 0.32/0.55      ! [A: int,C: int] :
% 0.32/0.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 0.32/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_int @ A @ one_one_int ) )
% 0.32/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right2
% 0.32/0.55  thf(fact_2737_mult__less__cancel__right1,axiom,
% 0.32/0.55      ! [C: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 0.32/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right1
% 0.32/0.55  thf(fact_2738_mult__less__cancel__right1,axiom,
% 0.32/0.55      ! [C: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.32/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right1
% 0.32/0.55  thf(fact_2739_mult__less__cancel__right1,axiom,
% 0.32/0.55      ! [C: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_int @ one_one_int @ B ) )
% 0.32/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_right1
% 0.32/0.55  thf(fact_2740_mult__less__cancel__left2,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 0.32/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 0.32/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left2
% 0.32/0.55  thf(fact_2741_mult__less__cancel__left2,axiom,
% 0.32/0.55      ! [C: rat,A: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.32/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.32/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left2
% 0.32/0.55  thf(fact_2742_mult__less__cancel__left2,axiom,
% 0.32/0.55      ! [C: int,A: int] :
% 0.32/0.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 0.32/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_int @ A @ one_one_int ) )
% 0.32/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left2
% 0.32/0.55  thf(fact_2743_mult__less__cancel__left1,axiom,
% 0.32/0.55      ! [C: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 0.32/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left1
% 0.32/0.55  thf(fact_2744_mult__less__cancel__left1,axiom,
% 0.32/0.55      ! [C: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.32/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left1
% 0.32/0.55  thf(fact_2745_mult__less__cancel__left1,axiom,
% 0.32/0.55      ! [C: int,B: int] :
% 0.32/0.55        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_int @ one_one_int @ B ) )
% 0.32/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_cancel_left1
% 0.32/0.55  thf(fact_2746_mult__le__cancel__right2,axiom,
% 0.32/0.55      ! [A: code_integer,C: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 0.32/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_right2
% 0.32/0.55  thf(fact_2747_mult__le__cancel__right2,axiom,
% 0.32/0.55      ! [A: rat,C: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.32/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_right2
% 0.32/0.55  thf(fact_2748_mult__le__cancel__right2,axiom,
% 0.32/0.55      ! [A: int,C: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.32/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_right2
% 0.32/0.55  thf(fact_2749_mult__le__cancel__right1,axiom,
% 0.32/0.55      ! [C: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 0.32/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_right1
% 0.32/0.55  thf(fact_2750_mult__le__cancel__right1,axiom,
% 0.32/0.55      ! [C: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.32/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_right1
% 0.32/0.55  thf(fact_2751_mult__le__cancel__right1,axiom,
% 0.32/0.55      ! [C: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.32/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_right1
% 0.32/0.55  thf(fact_2752_mult__le__cancel__left2,axiom,
% 0.32/0.55      ! [C: code_integer,A: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 0.32/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left2
% 0.32/0.55  thf(fact_2753_mult__le__cancel__left2,axiom,
% 0.32/0.55      ! [C: rat,A: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.32/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left2
% 0.32/0.55  thf(fact_2754_mult__le__cancel__left2,axiom,
% 0.32/0.55      ! [C: int,A: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.32/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left2
% 0.32/0.55  thf(fact_2755_mult__le__cancel__left1,axiom,
% 0.32/0.55      ! [C: code_integer,B: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 0.32/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.32/0.55           => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left1
% 0.32/0.55  thf(fact_2756_mult__le__cancel__left1,axiom,
% 0.32/0.55      ! [C: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.55           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.32/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.55           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left1
% 0.32/0.55  thf(fact_2757_mult__le__cancel__left1,axiom,
% 0.32/0.55      ! [C: int,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 0.32/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.32/0.55           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.32/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.32/0.55           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_left1
% 0.32/0.55  thf(fact_2758_convex__bound__le,axiom,
% 0.32/0.55      ! [X2: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ X2 @ A )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 0.32/0.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.32/0.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 0.32/0.55             => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 0.32/0.55                  = one_one_Code_integer )
% 0.32/0.55               => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X2 ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % convex_bound_le
% 0.32/0.55  thf(fact_2759_convex__bound__le,axiom,
% 0.32/0.55      ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ X2 @ A )
% 0.32/0.55       => ( ( ord_less_eq_rat @ Y @ A )
% 0.32/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.32/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.32/0.55             => ( ( ( plus_plus_rat @ U @ V )
% 0.32/0.55                  = one_one_rat )
% 0.32/0.55               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % convex_bound_le
% 0.32/0.55  thf(fact_2760_convex__bound__le,axiom,
% 0.32/0.55      ! [X2: int,A: int,Y: int,U: int,V: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ X2 @ A )
% 0.32/0.55       => ( ( ord_less_eq_int @ Y @ A )
% 0.32/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.32/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.32/0.55             => ( ( ( plus_plus_int @ U @ V )
% 0.32/0.55                  = one_one_int )
% 0.32/0.55               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % convex_bound_le
% 0.32/0.55  thf(fact_2761_nz__le__conv__less,axiom,
% 0.32/0.55      ! [K: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.55       => ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.55         => ( ord_less_nat @ ( minus_minus_nat @ K @ ( suc @ zero_zero_nat ) ) @ M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nz_le_conv_less
% 0.32/0.55  thf(fact_2762_Suc__diff__eq__diff__pred,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.32/0.55          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_diff_eq_diff_pred
% 0.32/0.55  thf(fact_2763_Suc__pred_H,axiom,
% 0.32/0.55      ! [N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( N
% 0.32/0.55          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_pred'
% 0.32/0.55  thf(fact_2764_frac__add,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] :
% 0.32/0.55        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.32/0.55         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 0.32/0.55            = ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 0.32/0.55        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.32/0.55         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 0.32/0.55            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % frac_add
% 0.32/0.55  thf(fact_2765_add__eq__if,axiom,
% 0.32/0.55      ( plus_plus_nat
% 0.32/0.55      = ( ^ [M2: nat,N3: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % add_eq_if
% 0.32/0.55  thf(fact_2766_Suc__n__minus__m__eq,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.55       => ( ( ord_less_nat @ one_one_nat @ M )
% 0.32/0.55         => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 0.32/0.55            = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_n_minus_m_eq
% 0.32/0.55  thf(fact_2767_foldr__length__aux,axiom,
% 0.32/0.55      ! [L: list_nat,A: nat] :
% 0.32/0.55        ( ( foldr_nat_nat
% 0.32/0.55          @ ^ [X: nat] : suc
% 0.32/0.55          @ L
% 0.32/0.55          @ A )
% 0.32/0.55        = ( plus_plus_nat @ A @ ( size_size_list_nat @ L ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % foldr_length_aux
% 0.32/0.55  thf(fact_2768_foldr__length__aux,axiom,
% 0.32/0.55      ! [L: list_int,A: nat] :
% 0.32/0.55        ( ( foldr_int_nat
% 0.32/0.55          @ ^ [X: int] : suc
% 0.32/0.55          @ L
% 0.32/0.55          @ A )
% 0.32/0.55        = ( plus_plus_nat @ A @ ( size_size_list_int @ L ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % foldr_length_aux
% 0.32/0.55  thf(fact_2769_foldr__length__aux,axiom,
% 0.32/0.55      ! [L: list_o,A: nat] :
% 0.32/0.55        ( ( foldr_o_nat
% 0.32/0.55          @ ^ [X: $o] : suc
% 0.32/0.55          @ L
% 0.32/0.55          @ A )
% 0.32/0.55        = ( plus_plus_nat @ A @ ( size_size_list_o @ L ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % foldr_length_aux
% 0.32/0.55  thf(fact_2770_zmult__zless__mono2__lemma,axiom,
% 0.32/0.55      ! [I: int,J: int,K: nat] :
% 0.32/0.55        ( ( ord_less_int @ I @ J )
% 0.32/0.55       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.55         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zmult_zless_mono2_lemma
% 0.32/0.55  thf(fact_2771_power__int__add,axiom,
% 0.32/0.55      ! [X2: rat,M: int,N: int] :
% 0.32/0.55        ( ( ( X2 != zero_zero_rat )
% 0.32/0.55          | ( ( plus_plus_int @ M @ N )
% 0.32/0.55           != zero_zero_int ) )
% 0.32/0.55       => ( ( power_int_rat @ X2 @ ( plus_plus_int @ M @ N ) )
% 0.32/0.55          = ( times_times_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ X2 @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_int_add
% 0.32/0.55  thf(fact_2772_unique__quotient__lemma__neg,axiom,
% 0.32/0.55      ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.32/0.55       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.32/0.55         => ( ( ord_less_int @ B @ R )
% 0.32/0.55           => ( ( ord_less_int @ B @ R4 )
% 0.32/0.55             => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % unique_quotient_lemma_neg
% 0.32/0.55  thf(fact_2773_unique__quotient__lemma,axiom,
% 0.32/0.55      ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.32/0.55         => ( ( ord_less_int @ R4 @ B )
% 0.32/0.55           => ( ( ord_less_int @ R @ B )
% 0.32/0.55             => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % unique_quotient_lemma
% 0.32/0.55  thf(fact_2774_zdiv__mono2__neg__lemma,axiom,
% 0.32/0.55      ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 0.32/0.55        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 0.32/0.55          = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 0.32/0.55       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) @ zero_zero_int )
% 0.32/0.55         => ( ( ord_less_int @ R @ B )
% 0.32/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 0.32/0.55             => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.32/0.55               => ( ( ord_less_eq_int @ B5 @ B )
% 0.32/0.55                 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zdiv_mono2_neg_lemma
% 0.32/0.55  thf(fact_2775_zdiv__mono2__lemma,axiom,
% 0.32/0.55      ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 0.32/0.55        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 0.32/0.55          = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 0.32/0.55         => ( ( ord_less_int @ R4 @ B5 )
% 0.32/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.32/0.55             => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.32/0.55               => ( ( ord_less_eq_int @ B5 @ B )
% 0.32/0.55                 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zdiv_mono2_lemma
% 0.32/0.55  thf(fact_2776_q__pos__lemma,axiom,
% 0.32/0.55      ! [B5: int,Q5: int,R4: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 0.32/0.55       => ( ( ord_less_int @ R4 @ B5 )
% 0.32/0.55         => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.32/0.55           => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % q_pos_lemma
% 0.32/0.55  thf(fact_2777_incr__mult__lemma,axiom,
% 0.32/0.55      ! [D: int,P: int > $o,K: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.55       => ( ! [X3: int] :
% 0.32/0.55              ( ( P @ X3 )
% 0.32/0.55             => ( P @ ( plus_plus_int @ X3 @ D ) ) )
% 0.32/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.55           => ! [X4: int] :
% 0.32/0.55                ( ( P @ X4 )
% 0.32/0.55               => ( P @ ( plus_plus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % incr_mult_lemma
% 0.32/0.55  thf(fact_2778_ceiling__diff__floor__le__1,axiom,
% 0.32/0.55      ! [X2: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim3151403230148437115or_rat @ X2 ) ) @ one_one_int ) ).
% 0.32/0.55  
% 0.32/0.55  % ceiling_diff_floor_le_1
% 0.32/0.55  thf(fact_2779_convex__bound__lt,axiom,
% 0.32/0.55      ! [X2: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ X2 @ A )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 0.32/0.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.32/0.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 0.32/0.55             => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 0.32/0.55                  = one_one_Code_integer )
% 0.32/0.55               => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X2 ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % convex_bound_lt
% 0.32/0.55  thf(fact_2780_convex__bound__lt,axiom,
% 0.32/0.55      ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.32/0.55        ( ( ord_less_rat @ X2 @ A )
% 0.32/0.55       => ( ( ord_less_rat @ Y @ A )
% 0.32/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.32/0.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.32/0.55             => ( ( ( plus_plus_rat @ U @ V )
% 0.32/0.55                  = one_one_rat )
% 0.32/0.55               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % convex_bound_lt
% 0.32/0.55  thf(fact_2781_convex__bound__lt,axiom,
% 0.32/0.55      ! [X2: int,A: int,Y: int,U: int,V: int] :
% 0.32/0.55        ( ( ord_less_int @ X2 @ A )
% 0.32/0.55       => ( ( ord_less_int @ Y @ A )
% 0.32/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.32/0.55           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.32/0.55             => ( ( ( plus_plus_int @ U @ V )
% 0.32/0.55                  = one_one_int )
% 0.32/0.55               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % convex_bound_lt
% 0.32/0.55  thf(fact_2782_ceiling__correct,axiom,
% 0.32/0.55      ! [X2: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) @ one_one_rat ) @ X2 )
% 0.32/0.55        & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % ceiling_correct
% 0.32/0.55  thf(fact_2783_ceiling__unique,axiom,
% 0.32/0.55      ! [Z2: int,X2: rat] :
% 0.32/0.55        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) @ X2 )
% 0.32/0.55       => ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) )
% 0.32/0.55         => ( ( archim2889992004027027881ng_rat @ X2 )
% 0.32/0.55            = Z2 ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % ceiling_unique
% 0.32/0.55  thf(fact_2784_ceiling__eq__iff,axiom,
% 0.32/0.55      ! [X2: rat,A: int] :
% 0.32/0.55        ( ( ( archim2889992004027027881ng_rat @ X2 )
% 0.32/0.55          = A )
% 0.32/0.55        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X2 )
% 0.32/0.55          & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % ceiling_eq_iff
% 0.32/0.55  thf(fact_2785_ceiling__split,axiom,
% 0.32/0.55      ! [P: int > $o,T: rat] :
% 0.32/0.55        ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 0.32/0.55        = ( ! [I2: int] :
% 0.32/0.55              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) @ T )
% 0.32/0.55                & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I2 ) ) )
% 0.32/0.55             => ( P @ I2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % ceiling_split
% 0.32/0.55  thf(fact_2786_ceiling__less__iff,axiom,
% 0.32/0.55      ! [X2: rat,Z2: int] :
% 0.32/0.55        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z2 )
% 0.32/0.55        = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % ceiling_less_iff
% 0.32/0.55  thf(fact_2787_nat__mult__le__cancel__disj,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.55        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.55         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_mult_le_cancel_disj
% 0.32/0.55  thf(fact_2788_nat__mult__less__cancel__disj,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.55        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.55          & ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_mult_less_cancel_disj
% 0.32/0.55  thf(fact_2789_sum__squares__gt__zero__iff,axiom,
% 0.32/0.55      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 0.32/0.55        = ( ( X2 != zero_z3403309356797280102nteger )
% 0.32/0.55          | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_gt_zero_iff
% 0.32/0.55  thf(fact_2790_sum__squares__gt__zero__iff,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) )
% 0.32/0.55        = ( ( X2 != zero_zero_rat )
% 0.32/0.55          | ( Y != zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_gt_zero_iff
% 0.32/0.55  thf(fact_2791_sum__squares__gt__zero__iff,axiom,
% 0.32/0.55      ! [X2: int,Y: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) )
% 0.32/0.55        = ( ( X2 != zero_zero_int )
% 0.32/0.55          | ( Y != zero_zero_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_gt_zero_iff
% 0.32/0.55  thf(fact_2792_sum__squares__le__zero__iff,axiom,
% 0.32/0.55      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.55        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 0.32/0.55        = ( ( X2 = zero_z3403309356797280102nteger )
% 0.32/0.55          & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_le_zero_iff
% 0.32/0.55  thf(fact_2793_sum__squares__le__zero__iff,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 0.32/0.55        = ( ( X2 = zero_zero_rat )
% 0.32/0.55          & ( Y = zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_le_zero_iff
% 0.32/0.55  thf(fact_2794_sum__squares__le__zero__iff,axiom,
% 0.32/0.55      ! [X2: int,Y: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 0.32/0.55        = ( ( X2 = zero_zero_int )
% 0.32/0.55          & ( Y = zero_zero_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_le_zero_iff
% 0.32/0.55  thf(fact_2795_mult__le__cancel__iff2,axiom,
% 0.32/0.55      ! [Z2: code_integer,X2: code_integer,Y: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z2 )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z2 @ X2 ) @ ( times_3573771949741848930nteger @ Z2 @ Y ) )
% 0.32/0.55          = ( ord_le3102999989581377725nteger @ X2 @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_iff2
% 0.32/0.55  thf(fact_2796_mult__le__cancel__iff2,axiom,
% 0.32/0.55      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 0.32/0.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X2 ) @ ( times_times_rat @ Z2 @ Y ) )
% 0.32/0.55          = ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_iff2
% 0.32/0.55  thf(fact_2797_mult__le__cancel__iff2,axiom,
% 0.32/0.55      ! [Z2: int,X2: int,Y: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.32/0.55       => ( ( ord_less_eq_int @ ( times_times_int @ Z2 @ X2 ) @ ( times_times_int @ Z2 @ Y ) )
% 0.32/0.55          = ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_iff2
% 0.32/0.55  thf(fact_2798_mult__le__cancel__iff1,axiom,
% 0.32/0.55      ! [Z2: code_integer,X2: code_integer,Y: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z2 )
% 0.32/0.55       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X2 @ Z2 ) @ ( times_3573771949741848930nteger @ Y @ Z2 ) )
% 0.32/0.55          = ( ord_le3102999989581377725nteger @ X2 @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_iff1
% 0.32/0.55  thf(fact_2799_mult__le__cancel__iff1,axiom,
% 0.32/0.55      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 0.32/0.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 0.32/0.55          = ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_iff1
% 0.32/0.55  thf(fact_2800_mult__le__cancel__iff1,axiom,
% 0.32/0.55      ! [Z2: int,X2: int,Y: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.32/0.55       => ( ( ord_less_eq_int @ ( times_times_int @ X2 @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 0.32/0.55          = ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_le_cancel_iff1
% 0.32/0.55  thf(fact_2801_nat__less__add__iff2,axiom,
% 0.32/0.55      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.55       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.55          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_less_add_iff2
% 0.32/0.55  thf(fact_2802_int__distrib_I3_J,axiom,
% 0.32/0.55      ! [Z1: int,Z22: int,W2: int] :
% 0.32/0.55        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W2 )
% 0.32/0.55        = ( minus_minus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % int_distrib(3)
% 0.32/0.55  thf(fact_2803_int__distrib_I4_J,axiom,
% 0.32/0.55      ! [W2: int,Z1: int,Z22: int] :
% 0.32/0.55        ( ( times_times_int @ W2 @ ( minus_minus_int @ Z1 @ Z22 ) )
% 0.32/0.55        = ( minus_minus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % int_distrib(4)
% 0.32/0.55  thf(fact_2804_diff__mult__distrib2,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.55        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_mult_distrib2
% 0.32/0.55  thf(fact_2805_diff__mult__distrib,axiom,
% 0.32/0.55      ! [M: nat,N: nat,K: nat] :
% 0.32/0.55        ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 0.32/0.55        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_mult_distrib
% 0.32/0.55  thf(fact_2806_diff__commute,axiom,
% 0.32/0.55      ! [I: nat,J: nat,K: nat] :
% 0.32/0.55        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.32/0.55        = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_commute
% 0.32/0.55  thf(fact_2807_nat__mult__eq__cancel__disj,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ( times_times_nat @ K @ M )
% 0.32/0.55          = ( times_times_nat @ K @ N ) )
% 0.32/0.55        = ( ( K = zero_zero_nat )
% 0.32/0.55          | ( M = N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_mult_eq_cancel_disj
% 0.32/0.55  thf(fact_2808_left__add__mult__distrib,axiom,
% 0.32/0.55      ! [I: nat,U: nat,J: nat,K: nat] :
% 0.32/0.55        ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.32/0.55        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 0.32/0.55  
% 0.32/0.55  % left_add_mult_distrib
% 0.32/0.55  thf(fact_2809_nat__mult__less__cancel1,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.55       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.55          = ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_mult_less_cancel1
% 0.32/0.55  thf(fact_2810_nat__mult__eq__cancel1,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.55       => ( ( ( times_times_nat @ K @ M )
% 0.32/0.55            = ( times_times_nat @ K @ N ) )
% 0.32/0.55          = ( M = N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_mult_eq_cancel1
% 0.32/0.55  thf(fact_2811_nat__diff__add__eq2,axiom,
% 0.32/0.55      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.55       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.55          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_diff_add_eq2
% 0.32/0.55  thf(fact_2812_nat__diff__add__eq1,axiom,
% 0.32/0.55      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ J @ I )
% 0.32/0.55       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.55          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_diff_add_eq1
% 0.32/0.55  thf(fact_2813_nat__le__add__iff2,axiom,
% 0.32/0.55      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.55       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.55          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_le_add_iff2
% 0.32/0.55  thf(fact_2814_nat__le__add__iff1,axiom,
% 0.32/0.55      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ J @ I )
% 0.32/0.55       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.55          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_le_add_iff1
% 0.32/0.55  thf(fact_2815_nat__eq__add__iff2,axiom,
% 0.32/0.55      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.55       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.32/0.55            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.55          = ( M
% 0.32/0.55            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_eq_add_iff2
% 0.32/0.55  thf(fact_2816_nat__eq__add__iff1,axiom,
% 0.32/0.55      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ J @ I )
% 0.32/0.55       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.32/0.55            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.55          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 0.32/0.55            = N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_eq_add_iff1
% 0.32/0.55  thf(fact_2817_mult__less__iff1,axiom,
% 0.32/0.55      ! [Z2: code_integer,X2: code_integer,Y: code_integer] :
% 0.32/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z2 )
% 0.32/0.55       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X2 @ Z2 ) @ ( times_3573771949741848930nteger @ Y @ Z2 ) )
% 0.32/0.55          = ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_iff1
% 0.32/0.55  thf(fact_2818_mult__less__iff1,axiom,
% 0.32/0.55      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 0.32/0.55       => ( ( ord_less_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 0.32/0.55          = ( ord_less_rat @ X2 @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_iff1
% 0.32/0.55  thf(fact_2819_mult__less__iff1,axiom,
% 0.32/0.55      ! [Z2: int,X2: int,Y: int] :
% 0.32/0.55        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.32/0.55       => ( ( ord_less_int @ ( times_times_int @ X2 @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 0.32/0.55          = ( ord_less_int @ X2 @ Y ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_less_iff1
% 0.32/0.55  thf(fact_2820_sum__squares__eq__zero__iff,axiom,
% 0.32/0.55      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.55        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 0.32/0.55          = zero_z3403309356797280102nteger )
% 0.32/0.55        = ( ( X2 = zero_z3403309356797280102nteger )
% 0.32/0.55          & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_eq_zero_iff
% 0.32/0.55  thf(fact_2821_sum__squares__eq__zero__iff,axiom,
% 0.32/0.55      ! [X2: rat,Y: rat] :
% 0.32/0.55        ( ( ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) )
% 0.32/0.55          = zero_zero_rat )
% 0.32/0.55        = ( ( X2 = zero_zero_rat )
% 0.32/0.55          & ( Y = zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_eq_zero_iff
% 0.32/0.55  thf(fact_2822_sum__squares__eq__zero__iff,axiom,
% 0.32/0.55      ! [X2: int,Y: int] :
% 0.32/0.55        ( ( ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) )
% 0.32/0.55          = zero_zero_int )
% 0.32/0.55        = ( ( X2 = zero_zero_int )
% 0.32/0.55          & ( Y = zero_zero_int ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % sum_squares_eq_zero_iff
% 0.32/0.55  thf(fact_2823_nat__mult__le__cancel1,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.55       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.55          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_mult_le_cancel1
% 0.32/0.55  thf(fact_2824_nat__less__add__iff1,axiom,
% 0.32/0.55      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ J @ I )
% 0.32/0.55       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.55          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_less_add_iff1
% 0.32/0.55  thf(fact_2825_nat0__intermed__int__val,axiom,
% 0.32/0.55      ! [N: nat,F: nat > int,K: int] :
% 0.32/0.55        ( ! [I3: nat] :
% 0.32/0.55            ( ( ord_less_nat @ I3 @ N )
% 0.32/0.55           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 0.32/0.55       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.32/0.55         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.32/0.55           => ? [I3: nat] :
% 0.32/0.55                ( ( ord_less_eq_nat @ I3 @ N )
% 0.32/0.55                & ( ( F @ I3 )
% 0.32/0.55                  = K ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat0_intermed_int_val
% 0.32/0.55  thf(fact_2826_slice__len,axiom,
% 0.32/0.55      ! [From: nat,To: nat,Xs: list_nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ From @ To )
% 0.32/0.55       => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 0.32/0.55         => ( ( size_size_list_nat @ ( slice_nat @ From @ To @ Xs ) )
% 0.32/0.55            = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % slice_len
% 0.32/0.55  thf(fact_2827_slice__len,axiom,
% 0.32/0.55      ! [From: nat,To: nat,Xs: list_int] :
% 0.32/0.55        ( ( ord_less_eq_nat @ From @ To )
% 0.32/0.55       => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 0.32/0.55         => ( ( size_size_list_int @ ( slice_int @ From @ To @ Xs ) )
% 0.32/0.55            = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % slice_len
% 0.32/0.55  thf(fact_2828_slice__len,axiom,
% 0.32/0.55      ! [From: nat,To: nat,Xs: list_o] :
% 0.32/0.55        ( ( ord_less_eq_nat @ From @ To )
% 0.32/0.55       => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 0.32/0.55         => ( ( size_size_list_o @ ( slice_o @ From @ To @ Xs ) )
% 0.32/0.55            = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % slice_len
% 0.32/0.55  thf(fact_2829_ceiling__divide__lower,axiom,
% 0.32/0.55      ! [Q2: rat,P3: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 0.32/0.55       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P3 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) @ P3 ) ) ).
% 0.32/0.55  
% 0.32/0.55  % ceiling_divide_lower
% 0.32/0.55  thf(fact_2830_floor__divide__upper,axiom,
% 0.32/0.55      ! [Q2: rat,P3: rat] :
% 0.32/0.55        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 0.32/0.55       => ( ord_less_rat @ P3 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P3 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % floor_divide_upper
% 0.32/0.55  thf(fact_2831_nat__ivt__aux,axiom,
% 0.32/0.55      ! [N: nat,F: nat > int,K: int] :
% 0.32/0.55        ( ! [I3: nat] :
% 0.32/0.55            ( ( ord_less_nat @ I3 @ N )
% 0.32/0.55           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 0.32/0.55       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.32/0.55         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.32/0.55           => ? [I3: nat] :
% 0.32/0.55                ( ( ord_less_eq_nat @ I3 @ N )
% 0.32/0.55                & ( ( F @ I3 )
% 0.32/0.55                  = K ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_ivt_aux
% 0.32/0.55  thf(fact_2832_mult__ceiling__le__Ints,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_18347121197199848620nteger @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_ceiling_le_Ints
% 0.32/0.55  thf(fact_2833_mult__ceiling__le__Ints,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.55         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_ceiling_le_Ints
% 0.32/0.55  thf(fact_2834_mult__ceiling__le__Ints,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.55         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_ceiling_le_Ints
% 0.32/0.55  thf(fact_2835_le__mult__floor__Ints,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.55         => ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_18347121197199848620nteger @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % le_mult_floor_Ints
% 0.32/0.55  thf(fact_2836_le__mult__floor__Ints,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.55         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % le_mult_floor_Ints
% 0.32/0.55  thf(fact_2837_le__mult__floor__Ints,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.55         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % le_mult_floor_Ints
% 0.32/0.55  thf(fact_2838_frac__unique__iff,axiom,
% 0.32/0.55      ! [X2: rat,A: rat] :
% 0.32/0.55        ( ( ( archimedean_frac_rat @ X2 )
% 0.32/0.55          = A )
% 0.32/0.55        = ( ( member_rat @ ( minus_minus_rat @ X2 @ A ) @ ring_1_Ints_rat )
% 0.32/0.55          & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55          & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % frac_unique_iff
% 0.32/0.55  thf(fact_2839_abs__idempotent,axiom,
% 0.32/0.55      ! [A: int] :
% 0.32/0.55        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.32/0.55        = ( abs_abs_int @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_idempotent
% 0.32/0.55  thf(fact_2840_abs__idempotent,axiom,
% 0.32/0.55      ! [A: code_integer] :
% 0.32/0.55        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.32/0.55        = ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_idempotent
% 0.32/0.55  thf(fact_2841_abs__idempotent,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.32/0.55        = ( abs_abs_rat @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_idempotent
% 0.32/0.55  thf(fact_2842_divide__eq__0__iff,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( ( divide_divide_rat @ A @ B )
% 0.32/0.55          = zero_zero_rat )
% 0.32/0.55        = ( ( A = zero_zero_rat )
% 0.32/0.55          | ( B = zero_zero_rat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % divide_eq_0_iff
% 0.32/0.55  thf(fact_2843_divide__cancel__left,axiom,
% 0.32/0.55      ! [C: rat,A: rat,B: rat] :
% 0.32/0.55        ( ( ( divide_divide_rat @ C @ A )
% 0.32/0.55          = ( divide_divide_rat @ C @ B ) )
% 0.32/0.55        = ( ( C = zero_zero_rat )
% 0.32/0.55          | ( A = B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % divide_cancel_left
% 0.32/0.55  thf(fact_2844_divide__cancel__right,axiom,
% 0.32/0.55      ! [A: rat,C: rat,B: rat] :
% 0.32/0.55        ( ( ( divide_divide_rat @ A @ C )
% 0.32/0.55          = ( divide_divide_rat @ B @ C ) )
% 0.32/0.55        = ( ( C = zero_zero_rat )
% 0.32/0.55          | ( A = B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % divide_cancel_right
% 0.32/0.55  thf(fact_2845_division__ring__divide__zero,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.32/0.55        = zero_zero_rat ) ).
% 0.32/0.55  
% 0.32/0.55  % division_ring_divide_zero
% 0.32/0.55  thf(fact_2846_div__0,axiom,
% 0.32/0.55      ! [A: nat] :
% 0.32/0.55        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.32/0.55        = zero_zero_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % div_0
% 0.32/0.55  thf(fact_2847_div__0,axiom,
% 0.32/0.55      ! [A: int] :
% 0.32/0.55        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.32/0.55        = zero_zero_int ) ).
% 0.32/0.55  
% 0.32/0.55  % div_0
% 0.32/0.55  thf(fact_2848_div__0,axiom,
% 0.32/0.55      ! [A: code_integer] :
% 0.32/0.55        ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.55        = zero_z3403309356797280102nteger ) ).
% 0.32/0.55  
% 0.32/0.55  % div_0
% 0.32/0.55  thf(fact_2849_div__0,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 0.32/0.55        = zero_zero_rat ) ).
% 0.32/0.55  
% 0.32/0.55  % div_0
% 0.32/0.55  thf(fact_2850_div__0,axiom,
% 0.32/0.55      ! [A: code_natural] :
% 0.32/0.55        ( ( divide5121882707175180666atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.55        = zero_z2226904508553997617atural ) ).
% 0.32/0.55  
% 0.32/0.55  % div_0
% 0.32/0.55  thf(fact_2851_div__by__0,axiom,
% 0.32/0.55      ! [A: nat] :
% 0.32/0.55        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.32/0.55        = zero_zero_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_0
% 0.32/0.55  thf(fact_2852_div__by__0,axiom,
% 0.32/0.55      ! [A: int] :
% 0.32/0.55        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.32/0.55        = zero_zero_int ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_0
% 0.32/0.55  thf(fact_2853_div__by__0,axiom,
% 0.32/0.55      ! [A: code_integer] :
% 0.32/0.55        ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.55        = zero_z3403309356797280102nteger ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_0
% 0.32/0.55  thf(fact_2854_div__by__0,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.32/0.55        = zero_zero_rat ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_0
% 0.32/0.55  thf(fact_2855_div__by__0,axiom,
% 0.32/0.55      ! [A: code_natural] :
% 0.32/0.55        ( ( divide5121882707175180666atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.55        = zero_z2226904508553997617atural ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_0
% 0.32/0.55  thf(fact_2856_div__by__1,axiom,
% 0.32/0.55      ! [A: nat] :
% 0.32/0.55        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.32/0.55        = A ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_1
% 0.32/0.55  thf(fact_2857_div__by__1,axiom,
% 0.32/0.55      ! [A: int] :
% 0.32/0.55        ( ( divide_divide_int @ A @ one_one_int )
% 0.32/0.55        = A ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_1
% 0.32/0.55  thf(fact_2858_div__by__1,axiom,
% 0.32/0.55      ! [A: code_integer] :
% 0.32/0.55        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 0.32/0.55        = A ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_1
% 0.32/0.55  thf(fact_2859_div__by__1,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ( ( divide_divide_rat @ A @ one_one_rat )
% 0.32/0.55        = A ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_1
% 0.32/0.55  thf(fact_2860_div__by__1,axiom,
% 0.32/0.55      ! [A: code_natural] :
% 0.32/0.55        ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 0.32/0.55        = A ) ).
% 0.32/0.55  
% 0.32/0.55  % div_by_1
% 0.32/0.55  thf(fact_2861_abs__0__eq,axiom,
% 0.32/0.55      ! [A: int] :
% 0.32/0.55        ( ( zero_zero_int
% 0.32/0.55          = ( abs_abs_int @ A ) )
% 0.32/0.55        = ( A = zero_zero_int ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_0_eq
% 0.32/0.55  thf(fact_2862_abs__0__eq,axiom,
% 0.32/0.55      ! [A: code_integer] :
% 0.32/0.55        ( ( zero_z3403309356797280102nteger
% 0.32/0.55          = ( abs_abs_Code_integer @ A ) )
% 0.32/0.55        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_0_eq
% 0.32/0.55  thf(fact_2863_abs__0__eq,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ( ( zero_zero_rat
% 0.32/0.55          = ( abs_abs_rat @ A ) )
% 0.32/0.55        = ( A = zero_zero_rat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_0_eq
% 0.32/0.55  thf(fact_2864_abs__eq__0,axiom,
% 0.32/0.55      ! [A: int] :
% 0.32/0.55        ( ( ( abs_abs_int @ A )
% 0.32/0.55          = zero_zero_int )
% 0.32/0.55        = ( A = zero_zero_int ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_eq_0
% 0.32/0.55  thf(fact_2865_abs__eq__0,axiom,
% 0.32/0.55      ! [A: code_integer] :
% 0.32/0.55        ( ( ( abs_abs_Code_integer @ A )
% 0.32/0.55          = zero_z3403309356797280102nteger )
% 0.32/0.55        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_eq_0
% 0.32/0.55  thf(fact_2866_abs__eq__0,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ( ( ( abs_abs_rat @ A )
% 0.32/0.55          = zero_zero_rat )
% 0.32/0.55        = ( A = zero_zero_rat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_eq_0
% 0.32/0.55  thf(fact_2867_abs__zero,axiom,
% 0.32/0.55      ( ( abs_abs_int @ zero_zero_int )
% 0.32/0.55      = zero_zero_int ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_zero
% 0.32/0.55  thf(fact_2868_abs__zero,axiom,
% 0.32/0.55      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.32/0.55      = zero_z3403309356797280102nteger ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_zero
% 0.32/0.55  thf(fact_2869_abs__zero,axiom,
% 0.32/0.55      ( ( abs_abs_rat @ zero_zero_rat )
% 0.32/0.55      = zero_zero_rat ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_zero
% 0.32/0.55  thf(fact_2870_abs__0,axiom,
% 0.32/0.55      ( ( abs_abs_int @ zero_zero_int )
% 0.32/0.55      = zero_zero_int ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_0
% 0.32/0.55  thf(fact_2871_abs__0,axiom,
% 0.32/0.55      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.32/0.55      = zero_z3403309356797280102nteger ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_0
% 0.32/0.55  thf(fact_2872_abs__0,axiom,
% 0.32/0.55      ( ( abs_abs_rat @ zero_zero_rat )
% 0.32/0.55      = zero_zero_rat ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_0
% 0.32/0.55  thf(fact_2873_abs__add__abs,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 0.32/0.55        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_add_abs
% 0.32/0.55  thf(fact_2874_abs__add__abs,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 0.32/0.55        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_add_abs
% 0.32/0.55  thf(fact_2875_abs__add__abs,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 0.32/0.55        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_add_abs
% 0.32/0.55  thf(fact_2876_abs__1,axiom,
% 0.32/0.55      ( ( abs_abs_int @ one_one_int )
% 0.32/0.55      = one_one_int ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_1
% 0.32/0.55  thf(fact_2877_abs__1,axiom,
% 0.32/0.55      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.32/0.55      = one_one_Code_integer ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_1
% 0.32/0.55  thf(fact_2878_abs__1,axiom,
% 0.32/0.55      ( ( abs_abs_rat @ one_one_rat )
% 0.32/0.55      = one_one_rat ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_1
% 0.32/0.55  thf(fact_2879_nat__mult__div__cancel__disj,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ( K = zero_zero_nat )
% 0.32/0.55         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.55            = zero_zero_nat ) )
% 0.32/0.55        & ( ( K != zero_zero_nat )
% 0.32/0.55         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.55            = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_mult_div_cancel_disj
% 0.32/0.55  thf(fact_2880_abs__minus__cancel,axiom,
% 0.32/0.55      ! [A: int] :
% 0.32/0.55        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.32/0.55        = ( abs_abs_int @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_minus_cancel
% 0.32/0.55  thf(fact_2881_abs__minus__cancel,axiom,
% 0.32/0.55      ! [A: code_integer] :
% 0.32/0.55        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.55        = ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_minus_cancel
% 0.32/0.55  thf(fact_2882_abs__minus__cancel,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.32/0.55        = ( abs_abs_rat @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_minus_cancel
% 0.32/0.55  thf(fact_2883_abs__of__nat,axiom,
% 0.32/0.55      ! [N: nat] :
% 0.32/0.55        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.55        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_of_nat
% 0.32/0.55  thf(fact_2884_abs__of__nat,axiom,
% 0.32/0.55      ! [N: nat] :
% 0.32/0.55        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.55        = ( semiri4939895301339042750nteger @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_of_nat
% 0.32/0.55  thf(fact_2885_abs__of__nat,axiom,
% 0.32/0.55      ! [N: nat] :
% 0.32/0.55        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.55        = ( semiri681578069525770553at_rat @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % abs_of_nat
% 0.32/0.55  thf(fact_2886_slice__eq__bounds__empty,axiom,
% 0.32/0.55      ! [I: nat,Xs: list_int] :
% 0.32/0.55        ( ( slice_int @ I @ I @ Xs )
% 0.32/0.55        = nil_int ) ).
% 0.32/0.55  
% 0.32/0.55  % slice_eq_bounds_empty
% 0.32/0.55  thf(fact_2887_slice__eq__bounds__empty,axiom,
% 0.32/0.55      ! [I: nat,Xs: list_nat] :
% 0.32/0.55        ( ( slice_nat @ I @ I @ Xs )
% 0.32/0.55        = nil_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % slice_eq_bounds_empty
% 0.32/0.55  thf(fact_2888_slice__eq__bounds__empty,axiom,
% 0.32/0.55      ! [I: nat,Xs: list_char] :
% 0.32/0.55        ( ( slice_char @ I @ I @ Xs )
% 0.32/0.55        = nil_char ) ).
% 0.32/0.55  
% 0.32/0.55  % slice_eq_bounds_empty
% 0.32/0.55  thf(fact_2889_slice__Nil,axiom,
% 0.32/0.55      ! [Begin: nat,End: nat] :
% 0.32/0.55        ( ( slice_int @ Begin @ End @ nil_int )
% 0.32/0.55        = nil_int ) ).
% 0.32/0.55  
% 0.32/0.55  % slice_Nil
% 0.32/0.55  thf(fact_2890_slice__Nil,axiom,
% 0.32/0.55      ! [Begin: nat,End: nat] :
% 0.32/0.55        ( ( slice_nat @ Begin @ End @ nil_nat )
% 0.32/0.55        = nil_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % slice_Nil
% 0.32/0.55  thf(fact_2891_slice__Nil,axiom,
% 0.32/0.55      ! [Begin: nat,End: nat] :
% 0.32/0.55        ( ( slice_char @ Begin @ End @ nil_char )
% 0.32/0.55        = nil_char ) ).
% 0.32/0.55  
% 0.32/0.55  % slice_Nil
% 0.32/0.55  thf(fact_2892_nonzero__mult__div__cancel__left,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( A != zero_zero_nat )
% 0.32/0.55       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 0.32/0.55          = B ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_left
% 0.32/0.55  thf(fact_2893_nonzero__mult__div__cancel__left,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( A != zero_zero_int )
% 0.32/0.55       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 0.32/0.55          = B ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_left
% 0.32/0.55  thf(fact_2894_nonzero__mult__div__cancel__left,axiom,
% 0.32/0.55      ! [A: code_integer,B: code_integer] :
% 0.32/0.55        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.55       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 0.32/0.55          = B ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_left
% 0.32/0.55  thf(fact_2895_nonzero__mult__div__cancel__left,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( A != zero_zero_rat )
% 0.32/0.55       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 0.32/0.55          = B ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_left
% 0.32/0.55  thf(fact_2896_nonzero__mult__div__cancel__left,axiom,
% 0.32/0.55      ! [A: code_natural,B: code_natural] :
% 0.32/0.55        ( ( A != zero_z2226904508553997617atural )
% 0.32/0.55       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ A )
% 0.32/0.55          = B ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_left
% 0.32/0.55  thf(fact_2897_nonzero__mult__div__cancel__right,axiom,
% 0.32/0.55      ! [B: nat,A: nat] :
% 0.32/0.55        ( ( B != zero_zero_nat )
% 0.32/0.55       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.32/0.55          = A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_right
% 0.32/0.55  thf(fact_2898_nonzero__mult__div__cancel__right,axiom,
% 0.32/0.55      ! [B: int,A: int] :
% 0.32/0.55        ( ( B != zero_zero_int )
% 0.32/0.55       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 0.32/0.55          = A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_right
% 0.32/0.55  thf(fact_2899_nonzero__mult__div__cancel__right,axiom,
% 0.32/0.55      ! [B: code_integer,A: code_integer] :
% 0.32/0.55        ( ( B != zero_z3403309356797280102nteger )
% 0.32/0.55       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 0.32/0.55          = A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_right
% 0.32/0.55  thf(fact_2900_nonzero__mult__div__cancel__right,axiom,
% 0.32/0.55      ! [B: rat,A: rat] :
% 0.32/0.55        ( ( B != zero_zero_rat )
% 0.32/0.55       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 0.32/0.55          = A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_right
% 0.32/0.55  thf(fact_2901_nonzero__mult__div__cancel__right,axiom,
% 0.32/0.55      ! [B: code_natural,A: code_natural] :
% 0.32/0.55        ( ( B != zero_z2226904508553997617atural )
% 0.32/0.55       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 0.32/0.55          = A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nonzero_mult_div_cancel_right
% 0.32/0.55  thf(fact_2902_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( C != zero_zero_rat )
% 0.32/0.56       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_mult_divide_mult_cancel_right2
% 0.32/0.56  thf(fact_2903_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( C != zero_zero_rat )
% 0.32/0.56       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.32/0.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_mult_divide_mult_cancel_right
% 0.32/0.56  thf(fact_2904_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( C != zero_zero_rat )
% 0.32/0.56       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 0.32/0.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_mult_divide_mult_cancel_left2
% 0.32/0.56  thf(fact_2905_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( C != zero_zero_rat )
% 0.32/0.56       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_mult_divide_mult_cancel_left
% 0.32/0.56  thf(fact_2906_mult__divide__mult__cancel__left__if,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ( C = zero_zero_rat )
% 0.32/0.56         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.56            = zero_zero_rat ) )
% 0.32/0.56        & ( ( C != zero_zero_rat )
% 0.32/0.56         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.56            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % mult_divide_mult_cancel_left_if
% 0.32/0.56  thf(fact_2907_zero__eq__1__divide__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( zero_zero_rat
% 0.32/0.56          = ( divide_divide_rat @ one_one_rat @ A ) )
% 0.32/0.56        = ( A = zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zero_eq_1_divide_iff
% 0.32/0.56  thf(fact_2908_one__divide__eq__0__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 0.32/0.56          = zero_zero_rat )
% 0.32/0.56        = ( A = zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % one_divide_eq_0_iff
% 0.32/0.56  thf(fact_2909_eq__divide__eq__1,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( one_one_rat
% 0.32/0.56          = ( divide_divide_rat @ B @ A ) )
% 0.32/0.56        = ( ( A != zero_zero_rat )
% 0.32/0.56          & ( A = B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % eq_divide_eq_1
% 0.32/0.56  thf(fact_2910_divide__eq__eq__1,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( ( divide_divide_rat @ B @ A )
% 0.32/0.56          = one_one_rat )
% 0.32/0.56        = ( ( A != zero_zero_rat )
% 0.32/0.56          & ( A = B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_eq_eq_1
% 0.32/0.56  thf(fact_2911_divide__self__if,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ( A = zero_zero_rat )
% 0.32/0.56         => ( ( divide_divide_rat @ A @ A )
% 0.32/0.56            = zero_zero_rat ) )
% 0.32/0.56        & ( ( A != zero_zero_rat )
% 0.32/0.56         => ( ( divide_divide_rat @ A @ A )
% 0.32/0.56            = one_one_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_self_if
% 0.32/0.56  thf(fact_2912_divide__self,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( A != zero_zero_rat )
% 0.32/0.56       => ( ( divide_divide_rat @ A @ A )
% 0.32/0.56          = one_one_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_self
% 0.32/0.56  thf(fact_2913_one__eq__divide__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( one_one_rat
% 0.32/0.56          = ( divide_divide_rat @ A @ B ) )
% 0.32/0.56        = ( ( B != zero_zero_rat )
% 0.32/0.56          & ( A = B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % one_eq_divide_iff
% 0.32/0.56  thf(fact_2914_divide__eq__1__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ( divide_divide_rat @ A @ B )
% 0.32/0.56          = one_one_rat )
% 0.32/0.56        = ( ( B != zero_zero_rat )
% 0.32/0.56          & ( A = B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_eq_1_iff
% 0.32/0.56  thf(fact_2915_div__self,axiom,
% 0.32/0.56      ! [A: nat] :
% 0.32/0.56        ( ( A != zero_zero_nat )
% 0.32/0.56       => ( ( divide_divide_nat @ A @ A )
% 0.32/0.56          = one_one_nat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_self
% 0.32/0.56  thf(fact_2916_div__self,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( A != zero_zero_int )
% 0.32/0.56       => ( ( divide_divide_int @ A @ A )
% 0.32/0.56          = one_one_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_self
% 0.32/0.56  thf(fact_2917_div__self,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ A @ A )
% 0.32/0.56          = one_one_Code_integer ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_self
% 0.32/0.56  thf(fact_2918_div__self,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( A != zero_zero_rat )
% 0.32/0.56       => ( ( divide_divide_rat @ A @ A )
% 0.32/0.56          = one_one_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_self
% 0.32/0.56  thf(fact_2919_div__self,axiom,
% 0.32/0.56      ! [A: code_natural] :
% 0.32/0.56        ( ( A != zero_z2226904508553997617atural )
% 0.32/0.56       => ( ( divide5121882707175180666atural @ A @ A )
% 0.32/0.56          = one_one_Code_natural ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_self
% 0.32/0.56  thf(fact_2920_abs__le__zero__iff,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.32/0.56        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_zero_iff
% 0.32/0.56  thf(fact_2921_abs__le__zero__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 0.32/0.56        = ( A = zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_zero_iff
% 0.32/0.56  thf(fact_2922_abs__le__zero__iff,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 0.32/0.56        = ( A = zero_zero_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_zero_iff
% 0.32/0.56  thf(fact_2923_abs__le__self__iff,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 0.32/0.56        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_self_iff
% 0.32/0.56  thf(fact_2924_abs__le__self__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 0.32/0.56        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_self_iff
% 0.32/0.56  thf(fact_2925_abs__le__self__iff,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 0.32/0.56        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_self_iff
% 0.32/0.56  thf(fact_2926_abs__of__nonneg,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.56       => ( ( abs_abs_Code_integer @ A )
% 0.32/0.56          = A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_nonneg
% 0.32/0.56  thf(fact_2927_abs__of__nonneg,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.56       => ( ( abs_abs_rat @ A )
% 0.32/0.56          = A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_nonneg
% 0.32/0.56  thf(fact_2928_abs__of__nonneg,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.56       => ( ( abs_abs_int @ A )
% 0.32/0.56          = A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_nonneg
% 0.32/0.56  thf(fact_2929_zero__less__abs__iff,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 0.32/0.56        = ( A != zero_z3403309356797280102nteger ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zero_less_abs_iff
% 0.32/0.56  thf(fact_2930_zero__less__abs__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 0.32/0.56        = ( A != zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zero_less_abs_iff
% 0.32/0.56  thf(fact_2931_zero__less__abs__iff,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 0.32/0.56        = ( A != zero_zero_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zero_less_abs_iff
% 0.32/0.56  thf(fact_2932_divide__minus1,axiom,
% 0.32/0.56      ! [X2: rat] :
% 0.32/0.56        ( ( divide_divide_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.56        = ( uminus_uminus_rat @ X2 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_minus1
% 0.32/0.56  thf(fact_2933_abs__neg__one,axiom,
% 0.32/0.56      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.56      = one_one_int ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_neg_one
% 0.32/0.56  thf(fact_2934_abs__neg__one,axiom,
% 0.32/0.56      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.56      = one_one_Code_integer ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_neg_one
% 0.32/0.56  thf(fact_2935_abs__neg__one,axiom,
% 0.32/0.56      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.56      = one_one_rat ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_neg_one
% 0.32/0.56  thf(fact_2936_abs__power__int__minus,axiom,
% 0.32/0.56      ! [A: rat,N: int] :
% 0.32/0.56        ( ( abs_abs_rat @ ( power_int_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.32/0.56        = ( abs_abs_rat @ ( power_int_rat @ A @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_power_int_minus
% 0.32/0.56  thf(fact_2937_of__int__abs,axiom,
% 0.32/0.56      ! [X2: int] :
% 0.32/0.56        ( ( ring_18347121197199848620nteger @ ( abs_abs_int @ X2 ) )
% 0.32/0.56        = ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % of_int_abs
% 0.32/0.56  thf(fact_2938_of__int__abs,axiom,
% 0.32/0.56      ! [X2: int] :
% 0.32/0.56        ( ( ring_1_of_int_rat @ ( abs_abs_int @ X2 ) )
% 0.32/0.56        = ( abs_abs_rat @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % of_int_abs
% 0.32/0.56  thf(fact_2939_of__int__abs,axiom,
% 0.32/0.56      ! [X2: int] :
% 0.32/0.56        ( ( ring_1_of_int_int @ ( abs_abs_int @ X2 ) )
% 0.32/0.56        = ( abs_abs_int @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % of_int_abs
% 0.32/0.56  thf(fact_2940_frac__eq__0__iff,axiom,
% 0.32/0.56      ! [X2: rat] :
% 0.32/0.56        ( ( ( archimedean_frac_rat @ X2 )
% 0.32/0.56          = zero_zero_rat )
% 0.32/0.56        = ( member_rat @ X2 @ ring_1_Ints_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % frac_eq_0_iff
% 0.32/0.56  thf(fact_2941_slice__complete,axiom,
% 0.32/0.56      ! [Xs: list_nat] :
% 0.32/0.56        ( ( slice_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) @ Xs )
% 0.32/0.56        = Xs ) ).
% 0.32/0.56  
% 0.32/0.56  % slice_complete
% 0.32/0.56  thf(fact_2942_slice__complete,axiom,
% 0.32/0.56      ! [Xs: list_int] :
% 0.32/0.56        ( ( slice_int @ zero_zero_nat @ ( size_size_list_int @ Xs ) @ Xs )
% 0.32/0.56        = Xs ) ).
% 0.32/0.56  
% 0.32/0.56  % slice_complete
% 0.32/0.56  thf(fact_2943_slice__complete,axiom,
% 0.32/0.56      ! [Xs: list_o] :
% 0.32/0.56        ( ( slice_o @ zero_zero_nat @ ( size_size_list_o @ Xs ) @ Xs )
% 0.32/0.56        = Xs ) ).
% 0.32/0.56  
% 0.32/0.56  % slice_complete
% 0.32/0.56  thf(fact_2944_zero__le__divide__1__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.32/0.56        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zero_le_divide_1_iff
% 0.32/0.56  thf(fact_2945_divide__le__0__1__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.32/0.56        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_le_0_1_iff
% 0.32/0.56  thf(fact_2946_zero__less__divide__1__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.32/0.56        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zero_less_divide_1_iff
% 0.32/0.56  thf(fact_2947_less__divide__eq__1__pos,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.32/0.56          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % less_divide_eq_1_pos
% 0.32/0.56  thf(fact_2948_less__divide__eq__1__neg,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.32/0.56          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % less_divide_eq_1_neg
% 0.32/0.56  thf(fact_2949_divide__less__eq__1__pos,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.32/0.56          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_less_eq_1_pos
% 0.32/0.56  thf(fact_2950_divide__less__eq__1__neg,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.32/0.56          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_less_eq_1_neg
% 0.32/0.56  thf(fact_2951_divide__less__0__1__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.32/0.56        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_less_0_1_iff
% 0.32/0.56  thf(fact_2952_nonzero__divide__mult__cancel__right,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( B != zero_zero_rat )
% 0.32/0.56       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 0.32/0.56          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_divide_mult_cancel_right
% 0.32/0.56  thf(fact_2953_nonzero__divide__mult__cancel__left,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( A != zero_zero_rat )
% 0.32/0.56       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 0.32/0.56          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_divide_mult_cancel_left
% 0.32/0.56  thf(fact_2954_abs__of__nonpos,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( abs_abs_Code_integer @ A )
% 0.32/0.56          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_nonpos
% 0.32/0.56  thf(fact_2955_abs__of__nonpos,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.56       => ( ( abs_abs_rat @ A )
% 0.32/0.56          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_nonpos
% 0.32/0.56  thf(fact_2956_abs__of__nonpos,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.56       => ( ( abs_abs_int @ A )
% 0.32/0.56          = ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_nonpos
% 0.32/0.56  thf(fact_2957_zero__le__divide__abs__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 0.32/0.56        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.56          | ( B = zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zero_le_divide_abs_iff
% 0.32/0.56  thf(fact_2958_divide__le__0__abs__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 0.32/0.56        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.56          | ( B = zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_le_0_abs_iff
% 0.32/0.56  thf(fact_2959_zabs__less__one__iff,axiom,
% 0.32/0.56      ! [Z2: int] :
% 0.32/0.56        ( ( ord_less_int @ ( abs_abs_int @ Z2 ) @ one_one_int )
% 0.32/0.56        = ( Z2 = zero_zero_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zabs_less_one_iff
% 0.32/0.56  thf(fact_2960_floor__add2,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 0.32/0.56          | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 0.32/0.56       => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 0.32/0.56          = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % floor_add2
% 0.32/0.56  thf(fact_2961_frac__gt__0__iff,axiom,
% 0.32/0.56      ! [X2: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) )
% 0.32/0.56        = ( ~ ( member_rat @ X2 @ ring_1_Ints_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % frac_gt_0_iff
% 0.32/0.56  thf(fact_2962_le__divide__eq__1__pos,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.32/0.56          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % le_divide_eq_1_pos
% 0.32/0.56  thf(fact_2963_le__divide__eq__1__neg,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.32/0.56          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % le_divide_eq_1_neg
% 0.32/0.56  thf(fact_2964_divide__le__eq__1__pos,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.32/0.56          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_le_eq_1_pos
% 0.32/0.56  thf(fact_2965_divide__le__eq__1__neg,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.32/0.56          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_le_eq_1_neg
% 0.32/0.56  thf(fact_2966_div__abs__eq__div__nat,axiom,
% 0.32/0.56      ! [K: int,L: int] :
% 0.32/0.56        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 0.32/0.56        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_abs_eq_div_nat
% 0.32/0.56  thf(fact_2967_zdiv__int,axiom,
% 0.32/0.56      ! [A: nat,B: nat] :
% 0.32/0.56        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 0.32/0.56        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zdiv_int
% 0.32/0.56  thf(fact_2968_Ints__abs,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( member_int @ A @ ring_1_Ints_int )
% 0.32/0.56       => ( member_int @ ( abs_abs_int @ A ) @ ring_1_Ints_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_abs
% 0.32/0.56  thf(fact_2969_Ints__abs,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( member_Code_integer @ ( abs_abs_Code_integer @ A ) @ ring_11222124179247155820nteger ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_abs
% 0.32/0.56  thf(fact_2970_Ints__abs,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.56       => ( member_rat @ ( abs_abs_rat @ A ) @ ring_1_Ints_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_abs
% 0.32/0.56  thf(fact_2971_nonzero__abs__divide,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( B != zero_zero_rat )
% 0.32/0.56       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.56          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_abs_divide
% 0.32/0.56  thf(fact_2972_abs__div__pos,axiom,
% 0.32/0.56      ! [Y: rat,X2: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.56       => ( ( divide_divide_rat @ ( abs_abs_rat @ X2 ) @ Y )
% 0.32/0.56          = ( abs_abs_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_div_pos
% 0.32/0.56  thf(fact_2973_abs__ge__self,axiom,
% 0.32/0.56      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_ge_self
% 0.32/0.56  thf(fact_2974_abs__ge__self,axiom,
% 0.32/0.56      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_ge_self
% 0.32/0.56  thf(fact_2975_abs__ge__self,axiom,
% 0.32/0.56      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_ge_self
% 0.32/0.56  thf(fact_2976_abs__le__D1,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.32/0.56       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_D1
% 0.32/0.56  thf(fact_2977_abs__le__D1,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.32/0.56       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_D1
% 0.32/0.56  thf(fact_2978_abs__le__D1,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.32/0.56       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_D1
% 0.32/0.56  thf(fact_2979_abs__eq__0__iff,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( ( abs_abs_int @ A )
% 0.32/0.56          = zero_zero_int )
% 0.32/0.56        = ( A = zero_zero_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_eq_0_iff
% 0.32/0.56  thf(fact_2980_abs__eq__0__iff,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( ( abs_abs_Code_integer @ A )
% 0.32/0.56          = zero_z3403309356797280102nteger )
% 0.32/0.56        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_eq_0_iff
% 0.32/0.56  thf(fact_2981_abs__eq__0__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ( abs_abs_rat @ A )
% 0.32/0.56          = zero_zero_rat )
% 0.32/0.56        = ( A = zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_eq_0_iff
% 0.32/0.56  thf(fact_2982_floor__divide__of__int__eq,axiom,
% 0.32/0.56      ! [K: int,L: int] :
% 0.32/0.56        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 0.32/0.56        = ( divide_divide_int @ K @ L ) ) ).
% 0.32/0.56  
% 0.32/0.56  % floor_divide_of_int_eq
% 0.32/0.56  thf(fact_2983_abs__one,axiom,
% 0.32/0.56      ( ( abs_abs_int @ one_one_int )
% 0.32/0.56      = one_one_int ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_one
% 0.32/0.56  thf(fact_2984_abs__one,axiom,
% 0.32/0.56      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.32/0.56      = one_one_Code_integer ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_one
% 0.32/0.56  thf(fact_2985_abs__one,axiom,
% 0.32/0.56      ( ( abs_abs_rat @ one_one_rat )
% 0.32/0.56      = one_one_rat ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_one
% 0.32/0.56  thf(fact_2986_abs__minus__commute,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.56        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_minus_commute
% 0.32/0.56  thf(fact_2987_abs__minus__commute,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.56        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_minus_commute
% 0.32/0.56  thf(fact_2988_abs__minus__commute,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 0.32/0.56        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_minus_commute
% 0.32/0.56  thf(fact_2989_add__divide__distrib,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.32/0.56        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_divide_distrib
% 0.32/0.56  thf(fact_2990_power__int__abs,axiom,
% 0.32/0.56      ! [A: rat,N: int] :
% 0.32/0.56        ( ( abs_abs_rat @ ( power_int_rat @ A @ N ) )
% 0.32/0.56        = ( power_int_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_int_abs
% 0.32/0.56  thf(fact_2991_nat__div__as__int,axiom,
% 0.32/0.56      ( divide_divide_nat
% 0.32/0.56      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_div_as_int
% 0.32/0.56  thf(fact_2992_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_2993_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: nat,Y: nat,C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.32/0.56          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_2994_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: nat,Y: nat,C: nat,A: nat,B: nat] :
% 0.32/0.56        ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.32/0.56          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_2995_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: nat,Y: nat,C: int,A: int,B: int] :
% 0.32/0.56        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.56          = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_2996_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_2997_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: int,Y: int,C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.32/0.56          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_2998_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: int,Y: int,C: nat,A: nat,B: nat] :
% 0.32/0.56        ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.32/0.56          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_2999_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: int,Y: int,C: int,A: int,B: int] :
% 0.32/0.56        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.56          = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_3000_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: code_integer,Y: code_integer,C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_3001_distrib__right__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X2 @ Y ) @ C )
% 0.32/0.56       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.32/0.56          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_right_NO_MATCH
% 0.32/0.56  thf(fact_3002_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.56        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3003_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: nat,Y: nat,A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.56          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3004_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: nat,Y: nat,A: nat,B: nat,C: nat] :
% 0.32/0.56        ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.56          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3005_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: nat,Y: nat,A: int,B: int,C: int] :
% 0.32/0.56        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.32/0.56          = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3006_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.56        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3007_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: int,Y: int,A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.56          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3008_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: int,Y: int,A: nat,B: nat,C: nat] :
% 0.32/0.56        ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.56          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3009_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: int,Y: int,A: int,B: int,C: int] :
% 0.32/0.56        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.32/0.56          = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3010_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: code_integer,Y: code_integer,A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.56        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3011_distrib__left__NO__MATCH,axiom,
% 0.32/0.56      ! [X2: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X2 @ Y ) @ A )
% 0.32/0.56       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.56          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % distrib_left_NO_MATCH
% 0.32/0.56  thf(fact_3012_power__int__divide__distrib,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat,M: int] :
% 0.32/0.56        ( ( power_int_rat @ ( divide_divide_rat @ X2 @ Y ) @ M )
% 0.32/0.56        = ( divide_divide_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ Y @ M ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_int_divide_distrib
% 0.32/0.56  thf(fact_3013_Ints__0,axiom,
% 0.32/0.56      member_int @ zero_zero_int @ ring_1_Ints_int ).
% 0.32/0.56  
% 0.32/0.56  % Ints_0
% 0.32/0.56  thf(fact_3014_Ints__0,axiom,
% 0.32/0.56      member_Code_integer @ zero_z3403309356797280102nteger @ ring_11222124179247155820nteger ).
% 0.32/0.56  
% 0.32/0.56  % Ints_0
% 0.32/0.56  thf(fact_3015_Ints__0,axiom,
% 0.32/0.56      member_rat @ zero_zero_rat @ ring_1_Ints_rat ).
% 0.32/0.56  
% 0.32/0.56  % Ints_0
% 0.32/0.56  thf(fact_3016_Ints__add,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ( member_Code_integer @ B @ ring_11222124179247155820nteger )
% 0.32/0.56         => ( member_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) @ ring_11222124179247155820nteger ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_add
% 0.32/0.56  thf(fact_3017_Ints__add,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.56       => ( ( member_rat @ B @ ring_1_Ints_rat )
% 0.32/0.56         => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_add
% 0.32/0.56  thf(fact_3018_Ints__add,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( member_int @ A @ ring_1_Ints_int )
% 0.32/0.56       => ( ( member_int @ B @ ring_1_Ints_int )
% 0.32/0.56         => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_add
% 0.32/0.56  thf(fact_3019_Ints__mult,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ( member_Code_integer @ B @ ring_11222124179247155820nteger )
% 0.32/0.56         => ( member_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ring_11222124179247155820nteger ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_mult
% 0.32/0.56  thf(fact_3020_Ints__mult,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.56       => ( ( member_rat @ B @ ring_1_Ints_rat )
% 0.32/0.56         => ( member_rat @ ( times_times_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_mult
% 0.32/0.56  thf(fact_3021_Ints__mult,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( member_int @ A @ ring_1_Ints_int )
% 0.32/0.56       => ( ( member_int @ B @ ring_1_Ints_int )
% 0.32/0.56         => ( member_int @ ( times_times_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_mult
% 0.32/0.56  thf(fact_3022_Ints__1,axiom,
% 0.32/0.56      member_int @ one_one_int @ ring_1_Ints_int ).
% 0.32/0.56  
% 0.32/0.56  % Ints_1
% 0.32/0.56  thf(fact_3023_Ints__1,axiom,
% 0.32/0.56      member_Code_integer @ one_one_Code_integer @ ring_11222124179247155820nteger ).
% 0.32/0.56  
% 0.32/0.56  % Ints_1
% 0.32/0.56  thf(fact_3024_Ints__1,axiom,
% 0.32/0.56      member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 0.32/0.56  
% 0.32/0.56  % Ints_1
% 0.32/0.56  thf(fact_3025_Ints__diff,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ( member_Code_integer @ B @ ring_11222124179247155820nteger )
% 0.32/0.56         => ( member_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) @ ring_11222124179247155820nteger ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_diff
% 0.32/0.56  thf(fact_3026_Ints__diff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.56       => ( ( member_rat @ B @ ring_1_Ints_rat )
% 0.32/0.56         => ( member_rat @ ( minus_minus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_diff
% 0.32/0.56  thf(fact_3027_Ints__diff,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( member_int @ A @ ring_1_Ints_int )
% 0.32/0.56       => ( ( member_int @ B @ ring_1_Ints_int )
% 0.32/0.56         => ( member_int @ ( minus_minus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_diff
% 0.32/0.56  thf(fact_3028_minus__in__Ints__iff,axiom,
% 0.32/0.56      ! [X2: int] :
% 0.32/0.56        ( ( member_int @ ( uminus_uminus_int @ X2 ) @ ring_1_Ints_int )
% 0.32/0.56        = ( member_int @ X2 @ ring_1_Ints_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minus_in_Ints_iff
% 0.32/0.56  thf(fact_3029_minus__in__Ints__iff,axiom,
% 0.32/0.56      ! [X2: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ ( uminus1351360451143612070nteger @ X2 ) @ ring_11222124179247155820nteger )
% 0.32/0.56        = ( member_Code_integer @ X2 @ ring_11222124179247155820nteger ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minus_in_Ints_iff
% 0.32/0.56  thf(fact_3030_minus__in__Ints__iff,axiom,
% 0.32/0.56      ! [X2: rat] :
% 0.32/0.56        ( ( member_rat @ ( uminus_uminus_rat @ X2 ) @ ring_1_Ints_rat )
% 0.32/0.56        = ( member_rat @ X2 @ ring_1_Ints_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minus_in_Ints_iff
% 0.32/0.56  thf(fact_3031_Ints__minus,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( member_int @ A @ ring_1_Ints_int )
% 0.32/0.56       => ( member_int @ ( uminus_uminus_int @ A ) @ ring_1_Ints_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_minus
% 0.32/0.56  thf(fact_3032_Ints__minus,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( member_Code_integer @ ( uminus1351360451143612070nteger @ A ) @ ring_11222124179247155820nteger ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_minus
% 0.32/0.56  thf(fact_3033_Ints__minus,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.56       => ( member_rat @ ( uminus_uminus_rat @ A ) @ ring_1_Ints_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_minus
% 0.32/0.56  thf(fact_3034_Ints__of__nat,axiom,
% 0.32/0.56      ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ring_1_Ints_int ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_of_nat
% 0.32/0.56  thf(fact_3035_Ints__of__nat,axiom,
% 0.32/0.56      ! [N: nat] : ( member_Code_integer @ ( semiri4939895301339042750nteger @ N ) @ ring_11222124179247155820nteger ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_of_nat
% 0.32/0.56  thf(fact_3036_Ints__of__nat,axiom,
% 0.32/0.56      ! [N: nat] : ( member_rat @ ( semiri681578069525770553at_rat @ N ) @ ring_1_Ints_rat ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_of_nat
% 0.32/0.56  thf(fact_3037_Ints__of__int,axiom,
% 0.32/0.56      ! [Z2: int] : ( member_Code_integer @ ( ring_18347121197199848620nteger @ Z2 ) @ ring_11222124179247155820nteger ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_of_int
% 0.32/0.56  thf(fact_3038_Ints__of__int,axiom,
% 0.32/0.56      ! [Z2: int] : ( member_rat @ ( ring_1_of_int_rat @ Z2 ) @ ring_1_Ints_rat ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_of_int
% 0.32/0.56  thf(fact_3039_Ints__of__int,axiom,
% 0.32/0.56      ! [Z2: int] : ( member_int @ ( ring_1_of_int_int @ Z2 ) @ ring_1_Ints_int ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_of_int
% 0.32/0.56  thf(fact_3040_Ints__induct,axiom,
% 0.32/0.56      ! [Q2: code_integer,P: code_integer > $o] :
% 0.32/0.56        ( ( member_Code_integer @ Q2 @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ! [Z4: int] : ( P @ ( ring_18347121197199848620nteger @ Z4 ) )
% 0.32/0.56         => ( P @ Q2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_induct
% 0.32/0.56  thf(fact_3041_Ints__induct,axiom,
% 0.32/0.56      ! [Q2: rat,P: rat > $o] :
% 0.32/0.56        ( ( member_rat @ Q2 @ ring_1_Ints_rat )
% 0.32/0.56       => ( ! [Z4: int] : ( P @ ( ring_1_of_int_rat @ Z4 ) )
% 0.32/0.56         => ( P @ Q2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_induct
% 0.32/0.56  thf(fact_3042_Ints__induct,axiom,
% 0.32/0.56      ! [Q2: int,P: int > $o] :
% 0.32/0.56        ( ( member_int @ Q2 @ ring_1_Ints_int )
% 0.32/0.56       => ( ! [Z4: int] : ( P @ ( ring_1_of_int_int @ Z4 ) )
% 0.32/0.56         => ( P @ Q2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_induct
% 0.32/0.56  thf(fact_3043_Ints__cases,axiom,
% 0.32/0.56      ! [Q2: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ Q2 @ ring_11222124179247155820nteger )
% 0.32/0.56       => ~ ! [Z4: int] :
% 0.32/0.56              ( Q2
% 0.32/0.56             != ( ring_18347121197199848620nteger @ Z4 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_cases
% 0.32/0.56  thf(fact_3044_Ints__cases,axiom,
% 0.32/0.56      ! [Q2: rat] :
% 0.32/0.56        ( ( member_rat @ Q2 @ ring_1_Ints_rat )
% 0.32/0.56       => ~ ! [Z4: int] :
% 0.32/0.56              ( Q2
% 0.32/0.56             != ( ring_1_of_int_rat @ Z4 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_cases
% 0.32/0.56  thf(fact_3045_Ints__cases,axiom,
% 0.32/0.56      ! [Q2: int] :
% 0.32/0.56        ( ( member_int @ Q2 @ ring_1_Ints_int )
% 0.32/0.56       => ~ ! [Z4: int] :
% 0.32/0.56              ( Q2
% 0.32/0.56             != ( ring_1_of_int_int @ Z4 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_cases
% 0.32/0.56  thf(fact_3046_Ints__nonzero__abs__ge1,axiom,
% 0.32/0.56      ! [X2: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ( X2 != zero_z3403309356797280102nteger )
% 0.32/0.56         => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_nonzero_abs_ge1
% 0.32/0.56  thf(fact_3047_Ints__nonzero__abs__ge1,axiom,
% 0.32/0.56      ! [X2: rat] :
% 0.32/0.56        ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 0.32/0.56       => ( ( X2 != zero_zero_rat )
% 0.32/0.56         => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_nonzero_abs_ge1
% 0.32/0.56  thf(fact_3048_Ints__nonzero__abs__ge1,axiom,
% 0.32/0.56      ! [X2: int] :
% 0.32/0.56        ( ( member_int @ X2 @ ring_1_Ints_int )
% 0.32/0.56       => ( ( X2 != zero_zero_int )
% 0.32/0.56         => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_nonzero_abs_ge1
% 0.32/0.56  thf(fact_3049_Ints__nonzero__abs__less1,axiom,
% 0.32/0.56      ! [X2: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer )
% 0.32/0.56         => ( X2 = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_nonzero_abs_less1
% 0.32/0.56  thf(fact_3050_Ints__nonzero__abs__less1,axiom,
% 0.32/0.56      ! [X2: rat] :
% 0.32/0.56        ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 0.32/0.56       => ( ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat )
% 0.32/0.56         => ( X2 = zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_nonzero_abs_less1
% 0.32/0.56  thf(fact_3051_Ints__nonzero__abs__less1,axiom,
% 0.32/0.56      ! [X2: int] :
% 0.32/0.56        ( ( member_int @ X2 @ ring_1_Ints_int )
% 0.32/0.56       => ( ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int )
% 0.32/0.56         => ( X2 = zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_nonzero_abs_less1
% 0.32/0.56  thf(fact_3052_Ints__eq__abs__less1,axiom,
% 0.32/0.56      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 0.32/0.56         => ( ( X2 = Y )
% 0.32/0.56            = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_eq_abs_less1
% 0.32/0.56  thf(fact_3053_Ints__eq__abs__less1,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 0.32/0.56       => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 0.32/0.56         => ( ( X2 = Y )
% 0.32/0.56            = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ Y ) ) @ one_one_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_eq_abs_less1
% 0.32/0.56  thf(fact_3054_Ints__eq__abs__less1,axiom,
% 0.32/0.56      ! [X2: int,Y: int] :
% 0.32/0.56        ( ( member_int @ X2 @ ring_1_Ints_int )
% 0.32/0.56       => ( ( member_int @ Y @ ring_1_Ints_int )
% 0.32/0.56         => ( ( X2 = Y )
% 0.32/0.56            = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Y ) ) @ one_one_int ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_eq_abs_less1
% 0.32/0.56  thf(fact_3055_floor__divide__of__nat__eq,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 0.32/0.56        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % floor_divide_of_nat_eq
% 0.32/0.56  thf(fact_3056_abs__ge__zero,axiom,
% 0.32/0.56      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_ge_zero
% 0.32/0.56  thf(fact_3057_abs__ge__zero,axiom,
% 0.32/0.56      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_ge_zero
% 0.32/0.56  thf(fact_3058_abs__ge__zero,axiom,
% 0.32/0.56      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_ge_zero
% 0.32/0.56  thf(fact_3059_abs__not__less__zero,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_not_less_zero
% 0.32/0.56  thf(fact_3060_abs__not__less__zero,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_not_less_zero
% 0.32/0.56  thf(fact_3061_abs__not__less__zero,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_not_less_zero
% 0.32/0.56  thf(fact_3062_abs__of__pos,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.56       => ( ( abs_abs_Code_integer @ A )
% 0.32/0.56          = A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_pos
% 0.32/0.56  thf(fact_3063_abs__of__pos,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56       => ( ( abs_abs_rat @ A )
% 0.32/0.56          = A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_pos
% 0.32/0.56  thf(fact_3064_abs__of__pos,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.56       => ( ( abs_abs_int @ A )
% 0.32/0.56          = A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_pos
% 0.32/0.56  thf(fact_3065_abs__triangle__ineq,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq
% 0.32/0.56  thf(fact_3066_abs__triangle__ineq,axiom,
% 0.32/0.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq
% 0.32/0.56  thf(fact_3067_abs__triangle__ineq,axiom,
% 0.32/0.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq
% 0.32/0.56  thf(fact_3068_abs__triangle__ineq2__sym,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq2_sym
% 0.32/0.56  thf(fact_3069_abs__triangle__ineq2__sym,axiom,
% 0.32/0.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq2_sym
% 0.32/0.56  thf(fact_3070_abs__triangle__ineq2__sym,axiom,
% 0.32/0.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq2_sym
% 0.32/0.56  thf(fact_3071_abs__triangle__ineq3,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq3
% 0.32/0.56  thf(fact_3072_abs__triangle__ineq3,axiom,
% 0.32/0.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq3
% 0.32/0.56  thf(fact_3073_abs__triangle__ineq3,axiom,
% 0.32/0.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq3
% 0.32/0.56  thf(fact_3074_abs__triangle__ineq2,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq2
% 0.32/0.56  thf(fact_3075_abs__triangle__ineq2,axiom,
% 0.32/0.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq2
% 0.32/0.56  thf(fact_3076_abs__triangle__ineq2,axiom,
% 0.32/0.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq2
% 0.32/0.56  thf(fact_3077_abs__leI,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.56       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.56         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_leI
% 0.32/0.56  thf(fact_3078_abs__leI,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.56         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_leI
% 0.32/0.56  thf(fact_3079_abs__leI,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.56       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.56         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_leI
% 0.32/0.56  thf(fact_3080_abs__le__D2,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.32/0.56       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_D2
% 0.32/0.56  thf(fact_3081_abs__le__D2,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.32/0.56       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_D2
% 0.32/0.56  thf(fact_3082_abs__le__D2,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.32/0.56       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_D2
% 0.32/0.56  thf(fact_3083_abs__le__iff,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.32/0.56        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.56          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_iff
% 0.32/0.56  thf(fact_3084_abs__le__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.32/0.56        = ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.56          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_iff
% 0.32/0.56  thf(fact_3085_abs__le__iff,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.32/0.56        = ( ( ord_less_eq_int @ A @ B )
% 0.32/0.56          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_le_iff
% 0.32/0.56  thf(fact_3086_abs__ge__minus__self,axiom,
% 0.32/0.56      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_ge_minus_self
% 0.32/0.56  thf(fact_3087_abs__ge__minus__self,axiom,
% 0.32/0.56      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_ge_minus_self
% 0.32/0.56  thf(fact_3088_abs__ge__minus__self,axiom,
% 0.32/0.56      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_ge_minus_self
% 0.32/0.56  thf(fact_3089_divide__right__mono__neg,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.56       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_right_mono_neg
% 0.32/0.56  thf(fact_3090_divide__nonpos__nonpos,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.32/0.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_nonpos_nonpos
% 0.32/0.56  thf(fact_3091_divide__nonpos__nonneg,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.32/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_nonpos_nonneg
% 0.32/0.56  thf(fact_3092_divide__nonneg__nonpos,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.56       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.32/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_nonneg_nonpos
% 0.32/0.56  thf(fact_3093_divide__nonneg__nonneg,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.32/0.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_nonneg_nonneg
% 0.32/0.56  thf(fact_3094_zero__le__divide__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.56            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.32/0.56          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.56            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zero_le_divide_iff
% 0.32/0.56  thf(fact_3095_divide__right__mono,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_right_mono
% 0.32/0.56  thf(fact_3096_divide__le__0__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.32/0.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.56            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.32/0.56          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.56            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_le_0_iff
% 0.32/0.56  thf(fact_3097_divide__neg__neg,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.32/0.56         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_neg_neg
% 0.32/0.56  thf(fact_3098_divide__neg__pos,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.56         => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_neg_pos
% 0.32/0.56  thf(fact_3099_divide__pos__neg,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 0.32/0.56       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.32/0.56         => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_pos_neg
% 0.32/0.56  thf(fact_3100_divide__pos__pos,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 0.32/0.56       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.56         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_pos_pos
% 0.32/0.56  thf(fact_3101_divide__less__0__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.32/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_less_0_iff
% 0.32/0.56  thf(fact_3102_divide__less__cancel,axiom,
% 0.32/0.56      ! [A: rat,C: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_rat @ A @ B ) )
% 0.32/0.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56           => ( ord_less_rat @ B @ A ) )
% 0.32/0.56          & ( C != zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_less_cancel
% 0.32/0.56  thf(fact_3103_zero__less__divide__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.32/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zero_less_divide_iff
% 0.32/0.56  thf(fact_3104_divide__strict__right__mono,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ B )
% 0.32/0.56       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_strict_right_mono
% 0.32/0.56  thf(fact_3105_divide__strict__right__mono__neg,axiom,
% 0.32/0.56      ! [B: rat,A: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_rat @ B @ A )
% 0.32/0.56       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_strict_right_mono_neg
% 0.32/0.56  thf(fact_3106_nonzero__eq__divide__eq,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( C != zero_zero_rat )
% 0.32/0.56       => ( ( A
% 0.32/0.56            = ( divide_divide_rat @ B @ C ) )
% 0.32/0.56          = ( ( times_times_rat @ A @ C )
% 0.32/0.56            = B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_eq_divide_eq
% 0.32/0.56  thf(fact_3107_nonzero__divide__eq__eq,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( C != zero_zero_rat )
% 0.32/0.56       => ( ( ( divide_divide_rat @ B @ C )
% 0.32/0.56            = A )
% 0.32/0.56          = ( B
% 0.32/0.56            = ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_divide_eq_eq
% 0.32/0.56  thf(fact_3108_eq__divide__imp,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( C != zero_zero_rat )
% 0.32/0.56       => ( ( ( times_times_rat @ A @ C )
% 0.32/0.56            = B )
% 0.32/0.56         => ( A
% 0.32/0.56            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % eq_divide_imp
% 0.32/0.56  thf(fact_3109_divide__eq__imp,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( C != zero_zero_rat )
% 0.32/0.56       => ( ( B
% 0.32/0.56            = ( times_times_rat @ A @ C ) )
% 0.32/0.56         => ( ( divide_divide_rat @ B @ C )
% 0.32/0.56            = A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_eq_imp
% 0.32/0.56  thf(fact_3110_eq__divide__eq,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( A
% 0.32/0.56          = ( divide_divide_rat @ B @ C ) )
% 0.32/0.56        = ( ( ( C != zero_zero_rat )
% 0.32/0.56           => ( ( times_times_rat @ A @ C )
% 0.32/0.56              = B ) )
% 0.32/0.56          & ( ( C = zero_zero_rat )
% 0.32/0.56           => ( A = zero_zero_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % eq_divide_eq
% 0.32/0.56  thf(fact_3111_divide__eq__eq,axiom,
% 0.32/0.56      ! [B: rat,C: rat,A: rat] :
% 0.32/0.56        ( ( ( divide_divide_rat @ B @ C )
% 0.32/0.56          = A )
% 0.32/0.56        = ( ( ( C != zero_zero_rat )
% 0.32/0.56           => ( B
% 0.32/0.56              = ( times_times_rat @ A @ C ) ) )
% 0.32/0.56          & ( ( C = zero_zero_rat )
% 0.32/0.56           => ( A = zero_zero_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_eq_eq
% 0.32/0.56  thf(fact_3112_frac__eq__eq,axiom,
% 0.32/0.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 0.32/0.56        ( ( Y != zero_zero_rat )
% 0.32/0.56       => ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( ( divide_divide_rat @ X2 @ Y )
% 0.32/0.56              = ( divide_divide_rat @ W2 @ Z2 ) )
% 0.32/0.56            = ( ( times_times_rat @ X2 @ Z2 )
% 0.32/0.56              = ( times_times_rat @ W2 @ Y ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % frac_eq_eq
% 0.32/0.56  thf(fact_3113_right__inverse__eq,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( B != zero_zero_rat )
% 0.32/0.56       => ( ( ( divide_divide_rat @ A @ B )
% 0.32/0.56            = one_one_rat )
% 0.32/0.56          = ( A = B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % right_inverse_eq
% 0.32/0.56  thf(fact_3114_nonzero__minus__divide__right,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( B != zero_zero_rat )
% 0.32/0.56       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.56          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_minus_divide_right
% 0.32/0.56  thf(fact_3115_nonzero__minus__divide__divide,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( B != zero_zero_rat )
% 0.32/0.56       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.32/0.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_minus_divide_divide
% 0.32/0.56  thf(fact_3116_abs__zmult__eq__1,axiom,
% 0.32/0.56      ! [M: int,N: int] :
% 0.32/0.56        ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 0.32/0.56          = one_one_int )
% 0.32/0.56       => ( ( abs_abs_int @ M )
% 0.32/0.56          = one_one_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_zmult_eq_1
% 0.32/0.56  thf(fact_3117_div__neg__pos__less0,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.56         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_neg_pos_less0
% 0.32/0.56  thf(fact_3118_neg__imp__zdiv__neg__iff,axiom,
% 0.32/0.56      ! [B: int,A: int] :
% 0.32/0.56        ( ( ord_less_int @ B @ zero_zero_int )
% 0.32/0.56       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.32/0.56          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_imp_zdiv_neg_iff
% 0.32/0.56  thf(fact_3119_pos__imp__zdiv__neg__iff,axiom,
% 0.32/0.56      ! [B: int,A: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.56       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.32/0.56          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_imp_zdiv_neg_iff
% 0.32/0.56  thf(fact_3120_power__int__one__over,axiom,
% 0.32/0.56      ! [X2: rat,N: int] :
% 0.32/0.56        ( ( power_int_rat @ ( divide_divide_rat @ one_one_rat @ X2 ) @ N )
% 0.32/0.56        = ( divide_divide_rat @ one_one_rat @ ( power_int_rat @ X2 @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_int_one_over
% 0.32/0.56  thf(fact_3121_Ints__double__eq__0__iff,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( member_int @ A @ ring_1_Ints_int )
% 0.32/0.56       => ( ( ( plus_plus_int @ A @ A )
% 0.32/0.56            = zero_zero_int )
% 0.32/0.56          = ( A = zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_double_eq_0_iff
% 0.32/0.56  thf(fact_3122_Ints__double__eq__0__iff,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 0.32/0.56            = zero_z3403309356797280102nteger )
% 0.32/0.56          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_double_eq_0_iff
% 0.32/0.56  thf(fact_3123_Ints__double__eq__0__iff,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.56       => ( ( ( plus_plus_rat @ A @ A )
% 0.32/0.56            = zero_zero_rat )
% 0.32/0.56          = ( A = zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_double_eq_0_iff
% 0.32/0.56  thf(fact_3124_dense__eq0__I,axiom,
% 0.32/0.56      ! [X2: rat] :
% 0.32/0.56        ( ! [E3: rat] :
% 0.32/0.56            ( ( ord_less_rat @ zero_zero_rat @ E3 )
% 0.32/0.56           => ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ E3 ) )
% 0.32/0.56       => ( X2 = zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % dense_eq0_I
% 0.32/0.56  thf(fact_3125_abs__eq__mult,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.56            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 0.32/0.56          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.56            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.32/0.56       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.32/0.56          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_eq_mult
% 0.32/0.56  thf(fact_3126_abs__eq__mult,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.56            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.32/0.56          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.56            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.32/0.56       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.56          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_eq_mult
% 0.32/0.56  thf(fact_3127_abs__eq__mult,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.56            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.32/0.56          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.56            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.32/0.56       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.32/0.56          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_eq_mult
% 0.32/0.56  thf(fact_3128_abs__mult__pos,axiom,
% 0.32/0.56      ! [X2: code_integer,Y: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 0.32/0.56       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X2 )
% 0.32/0.56          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_mult_pos
% 0.32/0.56  thf(fact_3129_abs__mult__pos,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.56       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X2 )
% 0.32/0.56          = ( abs_abs_rat @ ( times_times_rat @ Y @ X2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_mult_pos
% 0.32/0.56  thf(fact_3130_abs__mult__pos,axiom,
% 0.32/0.56      ! [X2: int,Y: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.32/0.56       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X2 )
% 0.32/0.56          = ( abs_abs_int @ ( times_times_int @ Y @ X2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_mult_pos
% 0.32/0.56  thf(fact_3131_abs__minus__le__zero,axiom,
% 0.32/0.56      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_minus_le_zero
% 0.32/0.56  thf(fact_3132_abs__minus__le__zero,axiom,
% 0.32/0.56      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_minus_le_zero
% 0.32/0.56  thf(fact_3133_abs__minus__le__zero,axiom,
% 0.32/0.56      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_minus_le_zero
% 0.32/0.56  thf(fact_3134_eq__abs__iff_H,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( A
% 0.32/0.56          = ( abs_abs_Code_integer @ B ) )
% 0.32/0.56        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.56          & ( ( B = A )
% 0.32/0.56            | ( B
% 0.32/0.56              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % eq_abs_iff'
% 0.32/0.56  thf(fact_3135_eq__abs__iff_H,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( A
% 0.32/0.56          = ( abs_abs_rat @ B ) )
% 0.32/0.56        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.56          & ( ( B = A )
% 0.32/0.56            | ( B
% 0.32/0.56              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % eq_abs_iff'
% 0.32/0.56  thf(fact_3136_eq__abs__iff_H,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( A
% 0.32/0.56          = ( abs_abs_int @ B ) )
% 0.32/0.56        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.56          & ( ( B = A )
% 0.32/0.56            | ( B
% 0.32/0.56              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % eq_abs_iff'
% 0.32/0.56  thf(fact_3137_abs__eq__iff_H,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( ( abs_abs_Code_integer @ A )
% 0.32/0.56          = B )
% 0.32/0.56        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.56          & ( ( A = B )
% 0.32/0.56            | ( A
% 0.32/0.56              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_eq_iff'
% 0.32/0.56  thf(fact_3138_abs__eq__iff_H,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ( abs_abs_rat @ A )
% 0.32/0.56          = B )
% 0.32/0.56        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.56          & ( ( A = B )
% 0.32/0.56            | ( A
% 0.32/0.56              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_eq_iff'
% 0.32/0.56  thf(fact_3139_abs__eq__iff_H,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ( abs_abs_int @ A )
% 0.32/0.56          = B )
% 0.32/0.56        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.56          & ( ( A = B )
% 0.32/0.56            | ( A
% 0.32/0.56              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_eq_iff'
% 0.32/0.56  thf(fact_3140_abs__diff__triangle__ineq,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_diff_triangle_ineq
% 0.32/0.56  thf(fact_3141_abs__diff__triangle__ineq,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_diff_triangle_ineq
% 0.32/0.56  thf(fact_3142_abs__diff__triangle__ineq,axiom,
% 0.32/0.56      ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_diff_triangle_ineq
% 0.32/0.56  thf(fact_3143_abs__triangle__ineq4,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq4
% 0.32/0.56  thf(fact_3144_abs__triangle__ineq4,axiom,
% 0.32/0.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq4
% 0.32/0.56  thf(fact_3145_abs__triangle__ineq4,axiom,
% 0.32/0.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_triangle_ineq4
% 0.32/0.56  thf(fact_3146_abs__diff__le__iff,axiom,
% 0.32/0.56      ! [X2: code_integer,A: code_integer,R: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 0.32/0.56        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 0.32/0.56          & ( ord_le3102999989581377725nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_diff_le_iff
% 0.32/0.56  thf(fact_3147_abs__diff__le__iff,axiom,
% 0.32/0.56      ! [X2: rat,A: rat,R: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 0.32/0.56        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 0.32/0.56          & ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_diff_le_iff
% 0.32/0.56  thf(fact_3148_abs__diff__le__iff,axiom,
% 0.32/0.56      ! [X2: int,A: int,R: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 0.32/0.56        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 0.32/0.56          & ( ord_less_eq_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_diff_le_iff
% 0.32/0.56  thf(fact_3149_abs__if,axiom,
% 0.32/0.56      ( abs_abs_int
% 0.32/0.56      = ( ^ [A2: int] : ( if_int @ ( ord_less_int @ A2 @ zero_zero_int ) @ ( uminus_uminus_int @ A2 ) @ A2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_if
% 0.32/0.56  thf(fact_3150_abs__if,axiom,
% 0.32/0.56      ( abs_abs_Code_integer
% 0.32/0.56      = ( ^ [A2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A2 ) @ A2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_if
% 0.32/0.56  thf(fact_3151_abs__if,axiom,
% 0.32/0.56      ( abs_abs_rat
% 0.32/0.56      = ( ^ [A2: rat] : ( if_rat @ ( ord_less_rat @ A2 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A2 ) @ A2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_if
% 0.32/0.56  thf(fact_3152_abs__of__neg,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.56       => ( ( abs_abs_int @ A )
% 0.32/0.56          = ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_neg
% 0.32/0.56  thf(fact_3153_abs__of__neg,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( abs_abs_Code_integer @ A )
% 0.32/0.56          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_neg
% 0.32/0.56  thf(fact_3154_abs__of__neg,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56       => ( ( abs_abs_rat @ A )
% 0.32/0.56          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_of_neg
% 0.32/0.56  thf(fact_3155_abs__if__raw,axiom,
% 0.32/0.56      ( abs_abs_int
% 0.32/0.56      = ( ^ [A2: int] : ( if_int @ ( ord_less_int @ A2 @ zero_zero_int ) @ ( uminus_uminus_int @ A2 ) @ A2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_if_raw
% 0.32/0.56  thf(fact_3156_abs__if__raw,axiom,
% 0.32/0.56      ( abs_abs_Code_integer
% 0.32/0.56      = ( ^ [A2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A2 ) @ A2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_if_raw
% 0.32/0.56  thf(fact_3157_abs__if__raw,axiom,
% 0.32/0.56      ( abs_abs_rat
% 0.32/0.56      = ( ^ [A2: rat] : ( if_rat @ ( ord_less_rat @ A2 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A2 ) @ A2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_if_raw
% 0.32/0.56  thf(fact_3158_abs__diff__less__iff,axiom,
% 0.32/0.56      ! [X2: code_integer,A: code_integer,R: code_integer] :
% 0.32/0.56        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 0.32/0.56        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 0.32/0.56          & ( ord_le6747313008572928689nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_diff_less_iff
% 0.32/0.56  thf(fact_3159_abs__diff__less__iff,axiom,
% 0.32/0.56      ! [X2: rat,A: rat,R: rat] :
% 0.32/0.56        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 0.32/0.56        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 0.32/0.56          & ( ord_less_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_diff_less_iff
% 0.32/0.56  thf(fact_3160_abs__diff__less__iff,axiom,
% 0.32/0.56      ! [X2: int,A: int,R: int] :
% 0.32/0.56        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 0.32/0.56        = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 0.32/0.56          & ( ord_less_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_diff_less_iff
% 0.32/0.56  thf(fact_3161_div__positive,axiom,
% 0.32/0.56      ! [B: code_integer,A: code_integer] :
% 0.32/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.56       => ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.56         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_positive
% 0.32/0.56  thf(fact_3162_div__positive,axiom,
% 0.32/0.56      ! [B: nat,A: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.32/0.56       => ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.56         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_positive
% 0.32/0.56  thf(fact_3163_div__positive,axiom,
% 0.32/0.56      ! [B: int,A: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.56       => ( ( ord_less_eq_int @ B @ A )
% 0.32/0.56         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_positive
% 0.32/0.56  thf(fact_3164_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.32/0.56      ! [A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.56       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.56         => ( ( divide6298287555418463151nteger @ A @ B )
% 0.32/0.56            = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_numeral_class.div_less
% 0.32/0.56  thf(fact_3165_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.32/0.56      ! [A: nat,B: nat] :
% 0.32/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.56       => ( ( ord_less_nat @ A @ B )
% 0.32/0.56         => ( ( divide_divide_nat @ A @ B )
% 0.32/0.56            = zero_zero_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_numeral_class.div_less
% 0.32/0.56  thf(fact_3166_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.56       => ( ( ord_less_int @ A @ B )
% 0.32/0.56         => ( ( divide_divide_int @ A @ B )
% 0.32/0.56            = zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_numeral_class.div_less
% 0.32/0.56  thf(fact_3167_divide__nonpos__pos,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_nonpos_pos
% 0.32/0.56  thf(fact_3168_divide__nonpos__neg,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.32/0.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_nonpos_neg
% 0.32/0.56  thf(fact_3169_divide__nonneg__pos,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.56       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_nonneg_pos
% 0.32/0.56  thf(fact_3170_divide__nonneg__neg,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.56       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.32/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_nonneg_neg
% 0.32/0.56  thf(fact_3171_divide__le__cancel,axiom,
% 0.32/0.56      ! [A: rat,C: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_eq_rat @ A @ B ) )
% 0.32/0.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_le_cancel
% 0.32/0.56  thf(fact_3172_frac__less2,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat,W2: rat,Z2: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 0.32/0.56       => ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.56         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 0.32/0.56           => ( ( ord_less_rat @ W2 @ Z2 )
% 0.32/0.56             => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % frac_less2
% 0.32/0.56  thf(fact_3173_frac__less,axiom,
% 0.32/0.56      ! [X2: rat,Y: rat,W2: rat,Z2: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 0.32/0.56       => ( ( ord_less_rat @ X2 @ Y )
% 0.32/0.56         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 0.32/0.56           => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 0.32/0.56             => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % frac_less
% 0.32/0.56  thf(fact_3174_frac__le,axiom,
% 0.32/0.56      ! [Y: rat,X2: rat,W2: rat,Z2: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.32/0.56       => ( ( ord_less_eq_rat @ X2 @ Y )
% 0.32/0.56         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 0.32/0.56           => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 0.32/0.56             => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % frac_le
% 0.32/0.56  thf(fact_3175_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.32/0.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.56          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.32/0.56  thf(fact_3176_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.32/0.56      ! [C: nat,A: nat,B: nat] :
% 0.32/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.32/0.56       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.32/0.56          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.32/0.56  thf(fact_3177_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.32/0.56      ! [C: int,A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.56       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.32/0.56          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.32/0.56  thf(fact_3178_divide__less__eq,axiom,
% 0.32/0.56      ! [B: rat,C: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.32/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_less_eq
% 0.32/0.56  thf(fact_3179_less__divide__eq,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.32/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % less_divide_eq
% 0.32/0.56  thf(fact_3180_neg__divide__less__eq,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.32/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_divide_less_eq
% 0.32/0.56  thf(fact_3181_neg__less__divide__eq,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.56          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_less_divide_eq
% 0.32/0.56  thf(fact_3182_pos__divide__less__eq,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.32/0.56          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_divide_less_eq
% 0.32/0.56  thf(fact_3183_pos__less__divide__eq,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_less_divide_eq
% 0.32/0.56  thf(fact_3184_mult__imp__div__pos__less,axiom,
% 0.32/0.56      ! [Y: rat,X2: rat,Z2: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.56       => ( ( ord_less_rat @ X2 @ ( times_times_rat @ Z2 @ Y ) )
% 0.32/0.56         => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % mult_imp_div_pos_less
% 0.32/0.56  thf(fact_3185_mult__imp__less__div__pos,axiom,
% 0.32/0.56      ! [Y: rat,Z2: rat,X2: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.56       => ( ( ord_less_rat @ ( times_times_rat @ Z2 @ Y ) @ X2 )
% 0.32/0.56         => ( ord_less_rat @ Z2 @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % mult_imp_less_div_pos
% 0.32/0.56  thf(fact_3186_divide__strict__left__mono,axiom,
% 0.32/0.56      ! [B: rat,A: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_rat @ B @ A )
% 0.32/0.56       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.56           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_strict_left_mono
% 0.32/0.56  thf(fact_3187_divide__strict__left__mono__neg,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ B )
% 0.32/0.56       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.56           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_strict_left_mono_neg
% 0.32/0.56  thf(fact_3188_less__divide__eq__1,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56            & ( ord_less_rat @ A @ B ) )
% 0.32/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % less_divide_eq_1
% 0.32/0.56  thf(fact_3189_divide__less__eq__1,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56            & ( ord_less_rat @ B @ A ) )
% 0.32/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56            & ( ord_less_rat @ A @ B ) )
% 0.32/0.56          | ( A = zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_less_eq_1
% 0.32/0.56  thf(fact_3190_add__divide__eq__if__simps_I2_J,axiom,
% 0.32/0.56      ! [Z2: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ( Z2 = zero_zero_rat )
% 0.32/0.56         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 0.32/0.56            = B ) )
% 0.32/0.56        & ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 0.32/0.56            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_divide_eq_if_simps(2)
% 0.32/0.56  thf(fact_3191_add__divide__eq__if__simps_I1_J,axiom,
% 0.32/0.56      ! [Z2: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ( Z2 = zero_zero_rat )
% 0.32/0.56         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 0.32/0.56            = A ) )
% 0.32/0.56        & ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 0.32/0.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_divide_eq_if_simps(1)
% 0.32/0.56  thf(fact_3192_add__frac__eq,axiom,
% 0.32/0.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 0.32/0.56        ( ( Y != zero_zero_rat )
% 0.32/0.56       => ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 0.32/0.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_frac_eq
% 0.32/0.56  thf(fact_3193_add__frac__num,axiom,
% 0.32/0.56      ! [Y: rat,X2: rat,Z2: rat] :
% 0.32/0.56        ( ( Y != zero_zero_rat )
% 0.32/0.56       => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z2 )
% 0.32/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_frac_num
% 0.32/0.56  thf(fact_3194_add__num__frac,axiom,
% 0.32/0.56      ! [Y: rat,Z2: rat,X2: rat] :
% 0.32/0.56        ( ( Y != zero_zero_rat )
% 0.32/0.56       => ( ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ X2 @ Y ) )
% 0.32/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_num_frac
% 0.32/0.56  thf(fact_3195_add__divide__eq__iff,axiom,
% 0.32/0.56      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.56        ( ( Z2 != zero_zero_rat )
% 0.32/0.56       => ( ( plus_plus_rat @ X2 @ ( divide_divide_rat @ Y @ Z2 ) )
% 0.32/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_divide_eq_iff
% 0.32/0.56  thf(fact_3196_divide__add__eq__iff,axiom,
% 0.32/0.56      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.56        ( ( Z2 != zero_zero_rat )
% 0.32/0.56       => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ Y )
% 0.32/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_add_eq_iff
% 0.32/0.56  thf(fact_3197_divide__diff__eq__iff,axiom,
% 0.32/0.56      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.56        ( ( Z2 != zero_zero_rat )
% 0.32/0.56       => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ Y )
% 0.32/0.56          = ( divide_divide_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_diff_eq_iff
% 0.32/0.56  thf(fact_3198_diff__divide__eq__iff,axiom,
% 0.32/0.56      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.56        ( ( Z2 != zero_zero_rat )
% 0.32/0.56       => ( ( minus_minus_rat @ X2 @ ( divide_divide_rat @ Y @ Z2 ) )
% 0.32/0.56          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % diff_divide_eq_iff
% 0.32/0.56  thf(fact_3199_diff__frac__eq,axiom,
% 0.32/0.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 0.32/0.56        ( ( Y != zero_zero_rat )
% 0.32/0.56       => ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 0.32/0.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % diff_frac_eq
% 0.32/0.56  thf(fact_3200_add__divide__eq__if__simps_I4_J,axiom,
% 0.32/0.56      ! [Z2: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ( Z2 = zero_zero_rat )
% 0.32/0.56         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 0.32/0.56            = A ) )
% 0.32/0.56        & ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 0.32/0.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_divide_eq_if_simps(4)
% 0.32/0.56  thf(fact_3201_less__half__sum,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ B )
% 0.32/0.56       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % less_half_sum
% 0.32/0.56  thf(fact_3202_gt__half__sum,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ B )
% 0.32/0.56       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 0.32/0.56  
% 0.32/0.56  % gt_half_sum
% 0.32/0.56  thf(fact_3203_eq__minus__divide__eq,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( A
% 0.32/0.56          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.56        = ( ( ( C != zero_zero_rat )
% 0.32/0.56           => ( ( times_times_rat @ A @ C )
% 0.32/0.56              = ( uminus_uminus_rat @ B ) ) )
% 0.32/0.56          & ( ( C = zero_zero_rat )
% 0.32/0.56           => ( A = zero_zero_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % eq_minus_divide_eq
% 0.32/0.56  thf(fact_3204_minus__divide__eq__eq,axiom,
% 0.32/0.56      ! [B: rat,C: rat,A: rat] :
% 0.32/0.56        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.56          = A )
% 0.32/0.56        = ( ( ( C != zero_zero_rat )
% 0.32/0.56           => ( ( uminus_uminus_rat @ B )
% 0.32/0.56              = ( times_times_rat @ A @ C ) ) )
% 0.32/0.56          & ( ( C = zero_zero_rat )
% 0.32/0.56           => ( A = zero_zero_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minus_divide_eq_eq
% 0.32/0.56  thf(fact_3205_nonzero__neg__divide__eq__eq,axiom,
% 0.32/0.56      ! [B: rat,A: rat,C: rat] :
% 0.32/0.56        ( ( B != zero_zero_rat )
% 0.32/0.56       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.56            = C )
% 0.32/0.56          = ( ( uminus_uminus_rat @ A )
% 0.32/0.56            = ( times_times_rat @ C @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_neg_divide_eq_eq
% 0.32/0.56  thf(fact_3206_nonzero__neg__divide__eq__eq2,axiom,
% 0.32/0.56      ! [B: rat,C: rat,A: rat] :
% 0.32/0.56        ( ( B != zero_zero_rat )
% 0.32/0.56       => ( ( C
% 0.32/0.56            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 0.32/0.56          = ( ( times_times_rat @ C @ B )
% 0.32/0.56            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonzero_neg_divide_eq_eq2
% 0.32/0.56  thf(fact_3207_divide__eq__minus__1__iff,axiom,
% 0.32/0.56      ! [A: rat,B: rat] :
% 0.32/0.56        ( ( ( divide_divide_rat @ A @ B )
% 0.32/0.56          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.56        = ( ( B != zero_zero_rat )
% 0.32/0.56          & ( A
% 0.32/0.56            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_eq_minus_1_iff
% 0.32/0.56  thf(fact_3208_zabs__def,axiom,
% 0.32/0.56      ( abs_abs_int
% 0.32/0.56      = ( ^ [I2: int] : ( if_int @ ( ord_less_int @ I2 @ zero_zero_int ) @ ( uminus_uminus_int @ I2 ) @ I2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zabs_def
% 0.32/0.56  thf(fact_3209_nat__mult__div__cancel1,axiom,
% 0.32/0.56      ! [K: nat,M: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.56       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.56          = ( divide_divide_nat @ M @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_mult_div_cancel1
% 0.32/0.56  thf(fact_3210_nat__abs__mult__distrib,axiom,
% 0.32/0.56      ! [W2: int,Z2: int] :
% 0.32/0.56        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W2 @ Z2 ) ) )
% 0.32/0.56        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W2 ) ) @ ( nat2 @ ( abs_abs_int @ Z2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_abs_mult_distrib
% 0.32/0.56  thf(fact_3211_nonneg1__imp__zdiv__pos__iff,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.32/0.56          = ( ( ord_less_eq_int @ B @ A )
% 0.32/0.56            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nonneg1_imp_zdiv_pos_iff
% 0.32/0.56  thf(fact_3212_pos__imp__zdiv__nonneg__iff,axiom,
% 0.32/0.56      ! [B: int,A: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.32/0.56          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_imp_zdiv_nonneg_iff
% 0.32/0.56  thf(fact_3213_neg__imp__zdiv__nonneg__iff,axiom,
% 0.32/0.56      ! [B: int,A: int] :
% 0.32/0.56        ( ( ord_less_int @ B @ zero_zero_int )
% 0.32/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.32/0.56          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_imp_zdiv_nonneg_iff
% 0.32/0.56  thf(fact_3214_pos__imp__zdiv__pos__iff,axiom,
% 0.32/0.56      ! [K: int,I: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 0.32/0.56          = ( ord_less_eq_int @ K @ I ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_imp_zdiv_pos_iff
% 0.32/0.56  thf(fact_3215_div__nonpos__pos__le0,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.56         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_nonpos_pos_le0
% 0.32/0.56  thf(fact_3216_div__nonneg__neg__le0,axiom,
% 0.32/0.56      ! [A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.56       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.32/0.56         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_nonneg_neg_le0
% 0.32/0.56  thf(fact_3217_div__positive__int,axiom,
% 0.32/0.56      ! [L: int,K: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ L @ K )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ L )
% 0.32/0.56         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_positive_int
% 0.32/0.56  thf(fact_3218_div__int__pos__iff,axiom,
% 0.32/0.56      ! [K: int,L: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 0.32/0.56        = ( ( K = zero_zero_int )
% 0.32/0.56          | ( L = zero_zero_int )
% 0.32/0.56          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.56            & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 0.32/0.56          | ( ( ord_less_int @ K @ zero_zero_int )
% 0.32/0.56            & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_int_pos_iff
% 0.32/0.56  thf(fact_3219_zdiv__mono2__neg,axiom,
% 0.32/0.56      ! [A: int,B5: int,B: int] :
% 0.32/0.56        ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.32/0.56         => ( ( ord_less_eq_int @ B5 @ B )
% 0.32/0.56           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B5 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zdiv_mono2_neg
% 0.32/0.56  thf(fact_3220_zdiv__mono1__neg,axiom,
% 0.32/0.56      ! [A: int,A5: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ A @ A5 )
% 0.32/0.56       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.32/0.56         => ( ord_less_eq_int @ ( divide_divide_int @ A5 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zdiv_mono1_neg
% 0.32/0.56  thf(fact_3221_zdiv__eq__0__iff,axiom,
% 0.32/0.56      ! [I: int,K: int] :
% 0.32/0.56        ( ( ( divide_divide_int @ I @ K )
% 0.32/0.56          = zero_zero_int )
% 0.32/0.56        = ( ( K = zero_zero_int )
% 0.32/0.56          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.32/0.56            & ( ord_less_int @ I @ K ) )
% 0.32/0.56          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.32/0.56            & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zdiv_eq_0_iff
% 0.32/0.56  thf(fact_3222_zdiv__mono2,axiom,
% 0.32/0.56      ! [A: int,B5: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.32/0.56         => ( ( ord_less_eq_int @ B5 @ B )
% 0.32/0.56           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B5 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zdiv_mono2
% 0.32/0.56  thf(fact_3223_zdiv__mono1,axiom,
% 0.32/0.56      ! [A: int,A5: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ A @ A5 )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.56         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A5 @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zdiv_mono1
% 0.32/0.56  thf(fact_3224_int__div__less__self,axiom,
% 0.32/0.56      ! [X2: int,K: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ X2 )
% 0.32/0.56       => ( ( ord_less_int @ one_one_int @ K )
% 0.32/0.56         => ( ord_less_int @ ( divide_divide_int @ X2 @ K ) @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % int_div_less_self
% 0.32/0.56  thf(fact_3225_power__int__diff,axiom,
% 0.32/0.56      ! [X2: rat,M: int,N: int] :
% 0.32/0.56        ( ( ( X2 != zero_zero_rat )
% 0.32/0.56          | ( M != N ) )
% 0.32/0.56       => ( ( power_int_rat @ X2 @ ( minus_minus_int @ M @ N ) )
% 0.32/0.56          = ( divide_divide_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ X2 @ N ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_int_diff
% 0.32/0.56  thf(fact_3226_Ints__odd__nonzero,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( member_int @ A @ ring_1_Ints_int )
% 0.32/0.56       => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 0.32/0.56         != zero_zero_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_odd_nonzero
% 0.32/0.56  thf(fact_3227_Ints__odd__nonzero,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A )
% 0.32/0.56         != zero_z3403309356797280102nteger ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_odd_nonzero
% 0.32/0.56  thf(fact_3228_Ints__odd__nonzero,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.56       => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 0.32/0.56         != zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_odd_nonzero
% 0.32/0.56  thf(fact_3229_abs__add__one__gt__zero,axiom,
% 0.32/0.56      ! [X2: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_add_one_gt_zero
% 0.32/0.56  thf(fact_3230_abs__add__one__gt__zero,axiom,
% 0.32/0.56      ! [X2: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_add_one_gt_zero
% 0.32/0.56  thf(fact_3231_abs__add__one__gt__zero,axiom,
% 0.32/0.56      ! [X2: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % abs_add_one_gt_zero
% 0.32/0.56  thf(fact_3232_of__int__leD,axiom,
% 0.32/0.56      ! [N: int,X2: code_integer] :
% 0.32/0.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 0.32/0.56       => ( ( N = zero_zero_int )
% 0.32/0.56          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % of_int_leD
% 0.32/0.56  thf(fact_3233_of__int__leD,axiom,
% 0.32/0.56      ! [N: int,X2: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 0.32/0.56       => ( ( N = zero_zero_int )
% 0.32/0.56          | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % of_int_leD
% 0.32/0.56  thf(fact_3234_of__int__leD,axiom,
% 0.32/0.56      ! [N: int,X2: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 0.32/0.56       => ( ( N = zero_zero_int )
% 0.32/0.56          | ( ord_less_eq_int @ one_one_int @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % of_int_leD
% 0.32/0.56  thf(fact_3235_of__int__lessD,axiom,
% 0.32/0.56      ! [N: int,X2: code_integer] :
% 0.32/0.56        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 0.32/0.56       => ( ( N = zero_zero_int )
% 0.32/0.56          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % of_int_lessD
% 0.32/0.56  thf(fact_3236_of__int__lessD,axiom,
% 0.32/0.56      ! [N: int,X2: rat] :
% 0.32/0.56        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 0.32/0.56       => ( ( N = zero_zero_int )
% 0.32/0.56          | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % of_int_lessD
% 0.32/0.56  thf(fact_3237_of__int__lessD,axiom,
% 0.32/0.56      ! [N: int,X2: int] :
% 0.32/0.56        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 0.32/0.56       => ( ( N = zero_zero_int )
% 0.32/0.56          | ( ord_less_int @ one_one_int @ X2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % of_int_lessD
% 0.32/0.56  thf(fact_3238_divide__le__eq,axiom,
% 0.32/0.56      ! [B: rat,C: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.32/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_le_eq
% 0.32/0.56  thf(fact_3239_le__divide__eq,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.32/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % le_divide_eq
% 0.32/0.56  thf(fact_3240_divide__left__mono,axiom,
% 0.32/0.56      ! [B: rat,A: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.32/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.56           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_left_mono
% 0.32/0.56  thf(fact_3241_neg__divide__le__eq,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.32/0.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_divide_le_eq
% 0.32/0.56  thf(fact_3242_neg__le__divide__eq,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.56          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_le_divide_eq
% 0.32/0.56  thf(fact_3243_pos__divide__le__eq,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.32/0.56          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_divide_le_eq
% 0.32/0.56  thf(fact_3244_pos__le__divide__eq,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_le_divide_eq
% 0.32/0.56  thf(fact_3245_mult__imp__div__pos__le,axiom,
% 0.32/0.56      ! [Y: rat,X2: rat,Z2: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.56       => ( ( ord_less_eq_rat @ X2 @ ( times_times_rat @ Z2 @ Y ) )
% 0.32/0.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % mult_imp_div_pos_le
% 0.32/0.56  thf(fact_3246_mult__imp__le__div__pos,axiom,
% 0.32/0.56      ! [Y: rat,Z2: rat,X2: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.56       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ Y ) @ X2 )
% 0.32/0.56         => ( ord_less_eq_rat @ Z2 @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % mult_imp_le_div_pos
% 0.32/0.56  thf(fact_3247_divide__left__mono__neg,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.56       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.32/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.56           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_left_mono_neg
% 0.32/0.56  thf(fact_3248_le__divide__eq__1,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56            & ( ord_less_eq_rat @ A @ B ) )
% 0.32/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % le_divide_eq_1
% 0.32/0.56  thf(fact_3249_divide__le__eq__1,axiom,
% 0.32/0.56      ! [B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56            & ( ord_less_eq_rat @ B @ A ) )
% 0.32/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56            & ( ord_less_eq_rat @ A @ B ) )
% 0.32/0.56          | ( A = zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % divide_le_eq_1
% 0.32/0.56  thf(fact_3250_frac__le__eq,axiom,
% 0.32/0.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 0.32/0.56        ( ( Y != zero_zero_rat )
% 0.32/0.56       => ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 0.32/0.56            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % frac_le_eq
% 0.32/0.56  thf(fact_3251_frac__less__eq,axiom,
% 0.32/0.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 0.32/0.56        ( ( Y != zero_zero_rat )
% 0.32/0.56       => ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 0.32/0.56            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % frac_less_eq
% 0.32/0.56  thf(fact_3252_pos__minus__divide__less__eq,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_minus_divide_less_eq
% 0.32/0.56  thf(fact_3253_pos__less__minus__divide__eq,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_less_minus_divide_eq
% 0.32/0.56  thf(fact_3254_neg__minus__divide__less__eq,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_minus_divide_less_eq
% 0.32/0.56  thf(fact_3255_neg__less__minus__divide__eq,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_less_minus_divide_eq
% 0.32/0.56  thf(fact_3256_minus__divide__less__eq,axiom,
% 0.32/0.56      ! [B: rat,C: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.32/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minus_divide_less_eq
% 0.32/0.56  thf(fact_3257_less__minus__divide__eq,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.32/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % less_minus_divide_eq
% 0.32/0.56  thf(fact_3258_minus__divide__add__eq__iff,axiom,
% 0.32/0.56      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.56        ( ( Z2 != zero_zero_rat )
% 0.32/0.56       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z2 ) ) @ Y )
% 0.32/0.56          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minus_divide_add_eq_iff
% 0.32/0.56  thf(fact_3259_add__divide__eq__if__simps_I3_J,axiom,
% 0.32/0.56      ! [Z2: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ( Z2 = zero_zero_rat )
% 0.32/0.56         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 0.32/0.56            = B ) )
% 0.32/0.56        & ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 0.32/0.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_divide_eq_if_simps(3)
% 0.32/0.56  thf(fact_3260_add__divide__eq__if__simps_I6_J,axiom,
% 0.32/0.56      ! [Z2: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ( Z2 = zero_zero_rat )
% 0.32/0.56         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 0.32/0.56            = ( uminus_uminus_rat @ B ) ) )
% 0.32/0.56        & ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 0.32/0.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_divide_eq_if_simps(6)
% 0.32/0.56  thf(fact_3261_add__divide__eq__if__simps_I5_J,axiom,
% 0.32/0.56      ! [Z2: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ( Z2 = zero_zero_rat )
% 0.32/0.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 0.32/0.56            = ( uminus_uminus_rat @ B ) ) )
% 0.32/0.56        & ( ( Z2 != zero_zero_rat )
% 0.32/0.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 0.32/0.56            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_divide_eq_if_simps(5)
% 0.32/0.56  thf(fact_3262_minus__divide__diff__eq__iff,axiom,
% 0.32/0.56      ! [Z2: rat,X2: rat,Y: rat] :
% 0.32/0.56        ( ( Z2 != zero_zero_rat )
% 0.32/0.56       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z2 ) ) @ Y )
% 0.32/0.56          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minus_divide_diff_eq_iff
% 0.32/0.56  thf(fact_3263_nat__abs__triangle__ineq,axiom,
% 0.32/0.56      ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_abs_triangle_ineq
% 0.32/0.56  thf(fact_3264_div__geq,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ~ ( ord_less_nat @ M @ N )
% 0.32/0.56         => ( ( divide_divide_nat @ M @ N )
% 0.32/0.56            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_geq
% 0.32/0.56  thf(fact_3265_verit__less__mono__div__int2,axiom,
% 0.32/0.56      ! [A4: int,B4: int,N: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ A4 @ B4 )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 0.32/0.56         => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A4 @ N ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_less_mono_div_int2
% 0.32/0.56  thf(fact_3266_div__eq__minus1,axiom,
% 0.32/0.56      ! [B: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.56       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.32/0.56          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_eq_minus1
% 0.32/0.56  thf(fact_3267_Ints__odd__less__0,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 0.32/0.56       => ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A ) @ zero_z3403309356797280102nteger )
% 0.32/0.56          = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_odd_less_0
% 0.32/0.56  thf(fact_3268_Ints__odd__less__0,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.32/0.56       => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 0.32/0.56          = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_odd_less_0
% 0.32/0.56  thf(fact_3269_Ints__odd__less__0,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( member_int @ A @ ring_1_Ints_int )
% 0.32/0.56       => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 0.32/0.56          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Ints_odd_less_0
% 0.32/0.56  thf(fact_3270_scaling__mono,axiom,
% 0.32/0.56      ! [U: rat,V: rat,R: rat,S: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ U @ V )
% 0.32/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 0.32/0.56         => ( ( ord_less_eq_rat @ R @ S )
% 0.32/0.56           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % scaling_mono
% 0.32/0.56  thf(fact_3271_pos__minus__divide__le__eq,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.56          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_minus_divide_le_eq
% 0.32/0.56  thf(fact_3272_pos__le__minus__divide__eq,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pos_le_minus_divide_eq
% 0.32/0.56  thf(fact_3273_neg__minus__divide__le__eq,axiom,
% 0.32/0.56      ! [C: rat,B: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_minus_divide_le_eq
% 0.32/0.56  thf(fact_3274_neg__le__minus__divide__eq,axiom,
% 0.32/0.56      ! [C: rat,A: rat,B: rat] :
% 0.32/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.56          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % neg_le_minus_divide_eq
% 0.32/0.56  thf(fact_3275_minus__divide__le__eq,axiom,
% 0.32/0.56      ! [B: rat,C: rat,A: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.32/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minus_divide_le_eq
% 0.32/0.56  thf(fact_3276_le__minus__divide__eq,axiom,
% 0.32/0.56      ! [A: rat,B: rat,C: rat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.32/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.56               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % le_minus_divide_eq
% 0.32/0.56  thf(fact_3277_nat__approx__posE,axiom,
% 0.32/0.56      ! [E: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.32/0.56       => ~ ! [N2: nat] :
% 0.32/0.56              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ E ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_approx_posE
% 0.32/0.56  thf(fact_3278_nat__abs__int__diff,axiom,
% 0.32/0.56      ! [A: nat,B: nat] :
% 0.32/0.56        ( ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.56         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.32/0.56            = ( minus_minus_nat @ B @ A ) ) )
% 0.32/0.56        & ( ~ ( ord_less_eq_nat @ A @ B )
% 0.32/0.56         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.32/0.56            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_abs_int_diff
% 0.32/0.56  thf(fact_3279_split__zdiv,axiom,
% 0.32/0.56      ! [P: int > $o,N: int,K: int] :
% 0.32/0.56        ( ( P @ ( divide_divide_int @ N @ K ) )
% 0.32/0.56        = ( ( ( K = zero_zero_int )
% 0.32/0.56           => ( P @ zero_zero_int ) )
% 0.32/0.56          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.56           => ! [I2: int,J3: int] :
% 0.32/0.56                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.32/0.56                  & ( ord_less_int @ J3 @ K )
% 0.32/0.56                  & ( N
% 0.32/0.56                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 0.32/0.56               => ( P @ I2 ) ) )
% 0.32/0.56          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.32/0.56           => ! [I2: int,J3: int] :
% 0.32/0.56                ( ( ( ord_less_int @ K @ J3 )
% 0.32/0.56                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.32/0.56                  & ( N
% 0.32/0.56                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 0.32/0.56               => ( P @ I2 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % split_zdiv
% 0.32/0.56  thf(fact_3280_int__div__neg__eq,axiom,
% 0.32/0.56      ! [A: int,B: int,Q2: int,R: int] :
% 0.32/0.56        ( ( A
% 0.32/0.56          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.32/0.56       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.32/0.56         => ( ( ord_less_int @ B @ R )
% 0.32/0.56           => ( ( divide_divide_int @ A @ B )
% 0.32/0.56              = Q2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % int_div_neg_eq
% 0.32/0.56  thf(fact_3281_int__div__pos__eq,axiom,
% 0.32/0.56      ! [A: int,B: int,Q2: int,R: int] :
% 0.32/0.56        ( ( A
% 0.32/0.56          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.32/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.32/0.56         => ( ( ord_less_int @ R @ B )
% 0.32/0.56           => ( ( divide_divide_int @ A @ B )
% 0.32/0.56              = Q2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % int_div_pos_eq
% 0.32/0.56  thf(fact_3282_frac__neg,axiom,
% 0.32/0.56      ! [X2: rat] :
% 0.32/0.56        ( ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 0.32/0.56         => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X2 ) )
% 0.32/0.56            = zero_zero_rat ) )
% 0.32/0.56        & ( ~ ( member_rat @ X2 @ ring_1_Ints_rat )
% 0.32/0.56         => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X2 ) )
% 0.32/0.56            = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X2 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % frac_neg
% 0.32/0.56  thf(fact_3283_nat__intermed__int__val,axiom,
% 0.32/0.56      ! [M: nat,N: nat,F: nat > int,K: int] :
% 0.32/0.56        ( ! [I3: nat] :
% 0.32/0.56            ( ( ( ord_less_eq_nat @ M @ I3 )
% 0.32/0.56              & ( ord_less_nat @ I3 @ N ) )
% 0.32/0.56           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 0.32/0.56       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.56         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 0.32/0.56           => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.32/0.56             => ? [I3: nat] :
% 0.32/0.56                  ( ( ord_less_eq_nat @ M @ I3 )
% 0.32/0.56                  & ( ord_less_eq_nat @ I3 @ N )
% 0.32/0.56                  & ( ( F @ I3 )
% 0.32/0.56                    = K ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_intermed_int_val
% 0.32/0.56  thf(fact_3284_floor__divide__lower,axiom,
% 0.32/0.56      ! [Q2: rat,P3: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 0.32/0.56       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P3 @ Q2 ) ) ) @ Q2 ) @ P3 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % floor_divide_lower
% 0.32/0.56  thf(fact_3285_ceiling__divide__upper,axiom,
% 0.32/0.56      ! [Q2: rat,P3: rat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 0.32/0.56       => ( ord_less_eq_rat @ P3 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P3 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % ceiling_divide_upper
% 0.32/0.56  thf(fact_3286_decr__lemma,axiom,
% 0.32/0.56      ! [D: int,X2: int,Z2: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.56       => ( ord_less_int @ ( minus_minus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z2 ) ) @ one_one_int ) @ D ) ) @ Z2 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % decr_lemma
% 0.32/0.56  thf(fact_3287_incr__lemma,axiom,
% 0.32/0.56      ! [D: int,Z2: int,X2: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.56       => ( ord_less_int @ Z2 @ ( plus_plus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z2 ) ) @ one_one_int ) @ D ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % incr_lemma
% 0.32/0.56  thf(fact_3288_div__pos__geq,axiom,
% 0.32/0.56      ! [L: int,K: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ L )
% 0.32/0.56       => ( ( ord_less_eq_int @ L @ K )
% 0.32/0.56         => ( ( divide_divide_int @ K @ L )
% 0.32/0.56            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_pos_geq
% 0.32/0.56  thf(fact_3289_div__mult__self1,axiom,
% 0.32/0.56      ! [B: nat,A: nat,C: nat] :
% 0.32/0.56        ( ( B != zero_zero_nat )
% 0.32/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.32/0.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self1
% 0.32/0.56  thf(fact_3290_div__mult__self1,axiom,
% 0.32/0.56      ! [B: int,A: int,C: int] :
% 0.32/0.56        ( ( B != zero_zero_int )
% 0.32/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.32/0.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self1
% 0.32/0.56  thf(fact_3291_div__mult__self1,axiom,
% 0.32/0.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self1
% 0.32/0.56  thf(fact_3292_div__mult__self1,axiom,
% 0.32/0.56      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.32/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.32/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 0.32/0.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self1
% 0.32/0.56  thf(fact_3293_div__mult__self2,axiom,
% 0.32/0.56      ! [B: nat,A: nat,C: nat] :
% 0.32/0.56        ( ( B != zero_zero_nat )
% 0.32/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.32/0.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self2
% 0.32/0.56  thf(fact_3294_div__mult__self2,axiom,
% 0.32/0.56      ! [B: int,A: int,C: int] :
% 0.32/0.56        ( ( B != zero_zero_int )
% 0.32/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.32/0.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self2
% 0.32/0.56  thf(fact_3295_div__mult__self2,axiom,
% 0.32/0.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self2
% 0.32/0.56  thf(fact_3296_div__mult__self2,axiom,
% 0.32/0.56      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.32/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.32/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 0.32/0.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self2
% 0.32/0.56  thf(fact_3297_div__mult__self3,axiom,
% 0.32/0.56      ! [B: nat,C: nat,A: nat] :
% 0.32/0.56        ( ( B != zero_zero_nat )
% 0.32/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.32/0.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self3
% 0.32/0.56  thf(fact_3298_div__mult__self3,axiom,
% 0.32/0.56      ! [B: int,C: int,A: int] :
% 0.32/0.56        ( ( B != zero_zero_int )
% 0.32/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.32/0.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self3
% 0.32/0.56  thf(fact_3299_div__mult__self3,axiom,
% 0.32/0.56      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.32/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self3
% 0.32/0.56  thf(fact_3300_div__mult__self3,axiom,
% 0.32/0.56      ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.32/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.32/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 0.32/0.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self3
% 0.32/0.56  thf(fact_3301_div__mult__self4,axiom,
% 0.32/0.56      ! [B: nat,C: nat,A: nat] :
% 0.32/0.56        ( ( B != zero_zero_nat )
% 0.32/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.32/0.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self4
% 0.32/0.56  thf(fact_3302_div__mult__self4,axiom,
% 0.32/0.56      ! [B: int,C: int,A: int] :
% 0.32/0.56        ( ( B != zero_zero_int )
% 0.32/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.32/0.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self4
% 0.32/0.56  thf(fact_3303_div__mult__self4,axiom,
% 0.32/0.56      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.32/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self4
% 0.32/0.56  thf(fact_3304_div__mult__self4,axiom,
% 0.32/0.56      ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.32/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.32/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 0.32/0.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self4
% 0.32/0.56  thf(fact_3305_div__pos__pos__trivial,axiom,
% 0.32/0.56      ! [K: int,L: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.56       => ( ( ord_less_int @ K @ L )
% 0.32/0.56         => ( ( divide_divide_int @ K @ L )
% 0.32/0.56            = zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_pos_pos_trivial
% 0.32/0.56  thf(fact_3306_div__neg__neg__trivial,axiom,
% 0.32/0.56      ! [K: int,L: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.32/0.56       => ( ( ord_less_int @ L @ K )
% 0.32/0.56         => ( ( divide_divide_int @ K @ L )
% 0.32/0.56            = zero_zero_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_neg_neg_trivial
% 0.32/0.56  thf(fact_3307_div__mult__mult1__if,axiom,
% 0.32/0.56      ! [C: nat,A: nat,B: nat] :
% 0.32/0.56        ( ( ( C = zero_zero_nat )
% 0.32/0.56         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.32/0.56            = zero_zero_nat ) )
% 0.32/0.56        & ( ( C != zero_zero_nat )
% 0.32/0.56         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.32/0.56            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult1_if
% 0.32/0.56  thf(fact_3308_div__mult__mult1__if,axiom,
% 0.32/0.56      ! [C: int,A: int,B: int] :
% 0.32/0.56        ( ( ( C = zero_zero_int )
% 0.32/0.56         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.56            = zero_zero_int ) )
% 0.32/0.56        & ( ( C != zero_zero_int )
% 0.32/0.56         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.56            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult1_if
% 0.32/0.56  thf(fact_3309_div__mult__mult1__if,axiom,
% 0.32/0.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( ( C = zero_z3403309356797280102nteger )
% 0.32/0.56         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.56            = zero_z3403309356797280102nteger ) )
% 0.32/0.56        & ( ( C != zero_z3403309356797280102nteger )
% 0.32/0.56         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.56            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult1_if
% 0.32/0.56  thf(fact_3310_div__mult__mult1__if,axiom,
% 0.32/0.56      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.32/0.56        ( ( ( C = zero_z2226904508553997617atural )
% 0.32/0.56         => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 0.32/0.56            = zero_z2226904508553997617atural ) )
% 0.32/0.56        & ( ( C != zero_z2226904508553997617atural )
% 0.32/0.56         => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 0.32/0.56            = ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult1_if
% 0.32/0.56  thf(fact_3311_div__mult__mult2,axiom,
% 0.32/0.56      ! [C: nat,A: nat,B: nat] :
% 0.32/0.56        ( ( C != zero_zero_nat )
% 0.32/0.56       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.32/0.56          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult2
% 0.32/0.56  thf(fact_3312_div__mult__mult2,axiom,
% 0.32/0.56      ! [C: int,A: int,B: int] :
% 0.32/0.56        ( ( C != zero_zero_int )
% 0.32/0.56       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.32/0.56          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult2
% 0.32/0.56  thf(fact_3313_div__mult__mult2,axiom,
% 0.32/0.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( C != zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.56          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult2
% 0.32/0.56  thf(fact_3314_div__mult__mult2,axiom,
% 0.32/0.56      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.32/0.56        ( ( C != zero_z2226904508553997617atural )
% 0.32/0.56       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 0.32/0.56          = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult2
% 0.32/0.56  thf(fact_3315_div__mult__mult1,axiom,
% 0.32/0.56      ! [C: nat,A: nat,B: nat] :
% 0.32/0.56        ( ( C != zero_zero_nat )
% 0.32/0.56       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.32/0.56          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult1
% 0.32/0.56  thf(fact_3316_div__mult__mult1,axiom,
% 0.32/0.56      ! [C: int,A: int,B: int] :
% 0.32/0.56        ( ( C != zero_zero_int )
% 0.32/0.56       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.56          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult1
% 0.32/0.56  thf(fact_3317_div__mult__mult1,axiom,
% 0.32/0.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.56        ( ( C != zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.56          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult1
% 0.32/0.56  thf(fact_3318_div__mult__mult1,axiom,
% 0.32/0.56      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.32/0.56        ( ( C != zero_z2226904508553997617atural )
% 0.32/0.56       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 0.32/0.56          = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_mult1
% 0.32/0.56  thf(fact_3319_div__minus1__right,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.56        = ( uminus_uminus_int @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_minus1_right
% 0.32/0.56  thf(fact_3320_div__minus1__right,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.56        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_minus1_right
% 0.32/0.56  thf(fact_3321_div__by__Suc__0,axiom,
% 0.32/0.56      ! [M: nat] :
% 0.32/0.56        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.32/0.56        = M ) ).
% 0.32/0.56  
% 0.32/0.56  % div_by_Suc_0
% 0.32/0.56  thf(fact_3322_div__less,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ M @ N )
% 0.32/0.56       => ( ( divide_divide_nat @ M @ N )
% 0.32/0.56          = zero_zero_nat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_less
% 0.32/0.56  thf(fact_3323_div__mult__self__is__m,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 0.32/0.56          = M ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self_is_m
% 0.32/0.56  thf(fact_3324_div__mult__self1__is__m,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 0.32/0.56          = M ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult_self1_is_m
% 0.32/0.56  thf(fact_3325_div__le__dividend,axiom,
% 0.32/0.56      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 0.32/0.56  
% 0.32/0.56  % div_le_dividend
% 0.32/0.56  thf(fact_3326_div__le__mono,axiom,
% 0.32/0.56      ! [M: nat,N: nat,K: nat] :
% 0.32/0.56        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.56       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_le_mono
% 0.32/0.56  thf(fact_3327_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( ( divide_divide_nat @ M @ N )
% 0.32/0.56          = zero_zero_nat )
% 0.32/0.56        = ( ( ord_less_nat @ M @ N )
% 0.32/0.56          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Euclidean_Division.div_eq_0_iff
% 0.32/0.56  thf(fact_3328_Suc__div__le__mono,axiom,
% 0.32/0.56      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Suc_div_le_mono
% 0.32/0.56  thf(fact_3329_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.56        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.32/0.56  thf(fact_3330_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.56        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.32/0.56  thf(fact_3331_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( semiri4939895301339042750nteger @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.56        = ( divide6298287555418463151nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.32/0.56  thf(fact_3332_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( semiri3763490453095760265atural @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.56        = ( divide5121882707175180666atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.32/0.56  thf(fact_3333_div__times__less__eq__dividend,axiom,
% 0.32/0.56      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 0.32/0.56  
% 0.32/0.56  % div_times_less_eq_dividend
% 0.32/0.56  thf(fact_3334_times__div__less__eq__dividend,axiom,
% 0.32/0.56      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 0.32/0.56  
% 0.32/0.56  % times_div_less_eq_dividend
% 0.32/0.56  thf(fact_3335_div__mult2__eq_H,axiom,
% 0.32/0.56      ! [A: int,M: nat,N: nat] :
% 0.32/0.56        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.56        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult2_eq'
% 0.32/0.56  thf(fact_3336_div__mult2__eq_H,axiom,
% 0.32/0.56      ! [A: nat,M: nat,N: nat] :
% 0.32/0.56        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.32/0.56        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult2_eq'
% 0.32/0.56  thf(fact_3337_div__mult2__eq_H,axiom,
% 0.32/0.56      ! [A: code_integer,M: nat,N: nat] :
% 0.32/0.56        ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 0.32/0.56        = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult2_eq'
% 0.32/0.56  thf(fact_3338_div__mult2__eq_H,axiom,
% 0.32/0.56      ! [A: code_natural,M: nat,N: nat] :
% 0.32/0.56        ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) )
% 0.32/0.56        = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mult2_eq'
% 0.32/0.56  thf(fact_3339_div__le__mono2,axiom,
% 0.32/0.56      ! [M: nat,N: nat,K: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.56       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.56         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_le_mono2
% 0.32/0.56  thf(fact_3340_div__greater__zero__iff,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.56        = ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.56          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_greater_zero_iff
% 0.32/0.56  thf(fact_3341_div__less__iff__less__mult,axiom,
% 0.32/0.56      ! [Q2: nat,M: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.32/0.56       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 0.32/0.56          = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_less_iff_less_mult
% 0.32/0.56  thf(fact_3342_div__eq__dividend__iff,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.56       => ( ( ( divide_divide_nat @ M @ N )
% 0.32/0.56            = M )
% 0.32/0.56          = ( N = one_one_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_eq_dividend_iff
% 0.32/0.56  thf(fact_3343_div__less__dividend,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ one_one_nat @ N )
% 0.32/0.56       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.56         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_less_dividend
% 0.32/0.56  thf(fact_3344_zdiv__zmult2__eq,axiom,
% 0.32/0.56      ! [C: int,A: int,B: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.32/0.56       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.32/0.56          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zdiv_zmult2_eq
% 0.32/0.56  thf(fact_3345_nat__div__distrib,axiom,
% 0.32/0.56      ! [X2: int,Y: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.32/0.56       => ( ( nat2 @ ( divide_divide_int @ X2 @ Y ) )
% 0.32/0.56          = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_div_distrib
% 0.32/0.56  thf(fact_3346_nat__div__distrib_H,axiom,
% 0.32/0.56      ! [Y: int,X2: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.56       => ( ( nat2 @ ( divide_divide_int @ X2 @ Y ) )
% 0.32/0.56          = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_div_distrib'
% 0.32/0.56  thf(fact_3347_div__add__self2,axiom,
% 0.32/0.56      ! [B: nat,A: nat] :
% 0.32/0.56        ( ( B != zero_zero_nat )
% 0.32/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.32/0.56          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_add_self2
% 0.32/0.56  thf(fact_3348_div__add__self2,axiom,
% 0.32/0.56      ! [B: int,A: int] :
% 0.32/0.56        ( ( B != zero_zero_int )
% 0.32/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.32/0.56          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_add_self2
% 0.32/0.56  thf(fact_3349_div__add__self2,axiom,
% 0.32/0.56      ! [B: code_integer,A: code_integer] :
% 0.32/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_add_self2
% 0.32/0.56  thf(fact_3350_div__add__self2,axiom,
% 0.32/0.56      ! [B: code_natural,A: code_natural] :
% 0.32/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.32/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 0.32/0.56          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_add_self2
% 0.32/0.56  thf(fact_3351_div__add__self1,axiom,
% 0.32/0.56      ! [B: nat,A: nat] :
% 0.32/0.56        ( ( B != zero_zero_nat )
% 0.32/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.32/0.56          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_add_self1
% 0.32/0.56  thf(fact_3352_div__add__self1,axiom,
% 0.32/0.56      ! [B: int,A: int] :
% 0.32/0.56        ( ( B != zero_zero_int )
% 0.32/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.32/0.56          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_add_self1
% 0.32/0.56  thf(fact_3353_div__add__self1,axiom,
% 0.32/0.56      ! [B: code_integer,A: code_integer] :
% 0.32/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.32/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.32/0.56          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_add_self1
% 0.32/0.56  thf(fact_3354_div__add__self1,axiom,
% 0.32/0.56      ! [B: code_natural,A: code_natural] :
% 0.32/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.32/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 0.32/0.56          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_add_self1
% 0.32/0.56  thf(fact_3355_div__if,axiom,
% 0.32/0.56      ( divide_divide_nat
% 0.32/0.56      = ( ^ [M2: nat,N3: nat] :
% 0.32/0.56            ( if_nat
% 0.32/0.56            @ ( ( ord_less_nat @ M2 @ N3 )
% 0.32/0.56              | ( N3 = zero_zero_nat ) )
% 0.32/0.56            @ zero_zero_nat
% 0.32/0.56            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N3 ) @ N3 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_if
% 0.32/0.56  thf(fact_3356_less__eq__div__iff__mult__less__eq,axiom,
% 0.32/0.56      ! [Q2: nat,M: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.32/0.56       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 0.32/0.56          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % less_eq_div_iff_mult_less_eq
% 0.32/0.56  thf(fact_3357_div__nat__eqI,axiom,
% 0.32/0.56      ! [N: nat,Q2: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 0.32/0.56       => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 0.32/0.56         => ( ( divide_divide_nat @ M @ N )
% 0.32/0.56            = Q2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_nat_eqI
% 0.32/0.56  thf(fact_3358_split__div,axiom,
% 0.32/0.56      ! [P: nat > $o,M: nat,N: nat] :
% 0.32/0.56        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.56        = ( ( ( N = zero_zero_nat )
% 0.32/0.56           => ( P @ zero_zero_nat ) )
% 0.32/0.56          & ( ( N != zero_zero_nat )
% 0.32/0.56           => ! [I2: nat,J3: nat] :
% 0.32/0.56                ( ( ord_less_nat @ J3 @ N )
% 0.32/0.56               => ( ( M
% 0.32/0.56                    = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 0.32/0.56                 => ( P @ I2 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % split_div
% 0.32/0.56  thf(fact_3359_dividend__less__div__times,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % dividend_less_div_times
% 0.32/0.56  thf(fact_3360_dividend__less__times__div,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % dividend_less_times_div
% 0.32/0.56  thf(fact_3361_le__div__geq,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.56         => ( ( divide_divide_nat @ M @ N )
% 0.32/0.56            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % le_div_geq
% 0.32/0.56  thf(fact_3362_split__div_H,axiom,
% 0.32/0.56      ! [P: nat > $o,M: nat,N: nat] :
% 0.32/0.56        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.56        = ( ( ( N = zero_zero_nat )
% 0.32/0.56            & ( P @ zero_zero_nat ) )
% 0.32/0.56          | ? [Q6: nat] :
% 0.32/0.56              ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q6 ) @ M )
% 0.32/0.56              & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q6 ) ) )
% 0.32/0.56              & ( P @ Q6 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % split_div'
% 0.32/0.56  thf(fact_3363_div__pos__neg__trivial,axiom,
% 0.32/0.56      ! [K: int,L: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.56       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.32/0.56         => ( ( divide_divide_int @ K @ L )
% 0.32/0.56            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_pos_neg_trivial
% 0.32/0.56  thf(fact_3364_bits__div__by__1,axiom,
% 0.32/0.56      ! [A: nat] :
% 0.32/0.56        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.32/0.56        = A ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_by_1
% 0.32/0.56  thf(fact_3365_bits__div__by__1,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( divide_divide_int @ A @ one_one_int )
% 0.32/0.56        = A ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_by_1
% 0.32/0.56  thf(fact_3366_bits__div__by__1,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 0.32/0.56        = A ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_by_1
% 0.32/0.56  thf(fact_3367_bits__div__by__1,axiom,
% 0.32/0.56      ! [A: code_natural] :
% 0.32/0.56        ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 0.32/0.56        = A ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_by_1
% 0.32/0.56  thf(fact_3368_bits__div__by__0,axiom,
% 0.32/0.56      ! [A: nat] :
% 0.32/0.56        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.32/0.56        = zero_zero_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_by_0
% 0.32/0.56  thf(fact_3369_bits__div__by__0,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.32/0.56        = zero_zero_int ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_by_0
% 0.32/0.56  thf(fact_3370_bits__div__by__0,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.56        = zero_z3403309356797280102nteger ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_by_0
% 0.32/0.56  thf(fact_3371_bits__div__by__0,axiom,
% 0.32/0.56      ! [A: code_natural] :
% 0.32/0.56        ( ( divide5121882707175180666atural @ A @ zero_z2226904508553997617atural )
% 0.32/0.56        = zero_z2226904508553997617atural ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_by_0
% 0.32/0.56  thf(fact_3372_bits__div__0,axiom,
% 0.32/0.56      ! [A: nat] :
% 0.32/0.56        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.32/0.56        = zero_zero_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_0
% 0.32/0.56  thf(fact_3373_bits__div__0,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.32/0.56        = zero_zero_int ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_0
% 0.32/0.56  thf(fact_3374_bits__div__0,axiom,
% 0.32/0.56      ! [A: code_integer] :
% 0.32/0.56        ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.56        = zero_z3403309356797280102nteger ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_0
% 0.32/0.56  thf(fact_3375_bits__div__0,axiom,
% 0.32/0.56      ! [A: code_natural] :
% 0.32/0.56        ( ( divide5121882707175180666atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.56        = zero_z2226904508553997617atural ) ).
% 0.32/0.56  
% 0.32/0.56  % bits_div_0
% 0.32/0.56  thf(fact_3376_int__power__div__base,axiom,
% 0.32/0.56      ! [M: nat,K: int] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.56         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 0.32/0.56            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % int_power_div_base
% 0.32/0.56  thf(fact_3377_gbinomial__absorption_H,axiom,
% 0.32/0.56      ! [K: nat,A: rat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.56       => ( ( gbinomial_rat @ A @ K )
% 0.32/0.56          = ( 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 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % gbinomial_absorption'
% 0.32/0.56  thf(fact_3378_pochhammer__absorb__comp,axiom,
% 0.32/0.56      ! [R: int,K: nat] :
% 0.32/0.56        ( ( times_times_int @ ( minus_minus_int @ R @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R ) @ K ) )
% 0.32/0.56        = ( times_times_int @ R @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R ) @ one_one_int ) @ K ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pochhammer_absorb_comp
% 0.32/0.56  thf(fact_3379_pochhammer__absorb__comp,axiom,
% 0.32/0.56      ! [R: code_integer,K: nat] :
% 0.32/0.56        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R ) @ K ) )
% 0.32/0.56        = ( times_3573771949741848930nteger @ R @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pochhammer_absorb_comp
% 0.32/0.56  thf(fact_3380_pochhammer__absorb__comp,axiom,
% 0.32/0.56      ! [R: rat,K: nat] :
% 0.32/0.56        ( ( times_times_rat @ ( minus_minus_rat @ R @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R ) @ K ) )
% 0.32/0.56        = ( times_times_rat @ R @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R ) @ one_one_rat ) @ K ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pochhammer_absorb_comp
% 0.32/0.56  thf(fact_3381_fact__reduce,axiom,
% 0.32/0.56      ! [N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ( semiri1406184849735516958ct_int @ N )
% 0.32/0.56          = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % fact_reduce
% 0.32/0.56  thf(fact_3382_fact__reduce,axiom,
% 0.32/0.56      ! [N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ( semiri3624122377584611663nteger @ N )
% 0.32/0.56          = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % fact_reduce
% 0.32/0.56  thf(fact_3383_fact__reduce,axiom,
% 0.32/0.56      ! [N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ( semiri773545260158071498ct_rat @ N )
% 0.32/0.56          = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_reduce
% 0.32/0.57  thf(fact_3384_fact__reduce,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.57       => ( ( semiri2447717529341329178atural @ N )
% 0.32/0.57          = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( semiri2447717529341329178atural @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_reduce
% 0.32/0.57  thf(fact_3385_fact__reduce,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.57       => ( ( semiri1408675320244567234ct_nat @ N )
% 0.32/0.57          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_reduce
% 0.32/0.57  thf(fact_3386_power__one,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N )
% 0.32/0.57        = one_one_Code_integer ) ).
% 0.32/0.57  
% 0.32/0.57  % power_one
% 0.32/0.57  thf(fact_3387_power__one,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_power_rat @ one_one_rat @ N )
% 0.32/0.57        = one_one_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % power_one
% 0.32/0.57  thf(fact_3388_power__one,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_7079662738309270450atural @ one_one_Code_natural @ N )
% 0.32/0.57        = one_one_Code_natural ) ).
% 0.32/0.57  
% 0.32/0.57  % power_one
% 0.32/0.57  thf(fact_3389_power__one,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_power_int @ one_one_int @ N )
% 0.32/0.57        = one_one_int ) ).
% 0.32/0.57  
% 0.32/0.57  % power_one
% 0.32/0.57  thf(fact_3390_power__one,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_power_nat @ one_one_nat @ N )
% 0.32/0.57        = one_one_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % power_one
% 0.32/0.57  thf(fact_3391_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ( semiri1314217659103216013at_int @ X2 )
% 0.32/0.57          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 0.32/0.57        = ( X2
% 0.32/0.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3392_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ( semiri1316708129612266289at_nat @ X2 )
% 0.32/0.57          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 0.32/0.57        = ( X2
% 0.32/0.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3393_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ( semiri4939895301339042750nteger @ X2 )
% 0.32/0.57          = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 0.32/0.57        = ( X2
% 0.32/0.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3394_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ( semiri681578069525770553at_rat @ X2 )
% 0.32/0.57          = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 0.32/0.57        = ( X2
% 0.32/0.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3395_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ( semiri3763490453095760265atural @ X2 )
% 0.32/0.57          = ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) )
% 0.32/0.57        = ( X2
% 0.32/0.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3396_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 )
% 0.32/0.57          = ( semiri1314217659103216013at_int @ X2 ) )
% 0.32/0.57        = ( ( power_power_nat @ B @ W2 )
% 0.32/0.57          = X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3397_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 )
% 0.32/0.57          = ( semiri1316708129612266289at_nat @ X2 ) )
% 0.32/0.57        = ( ( power_power_nat @ B @ W2 )
% 0.32/0.57          = X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3398_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 )
% 0.32/0.57          = ( semiri4939895301339042750nteger @ X2 ) )
% 0.32/0.57        = ( ( power_power_nat @ B @ W2 )
% 0.32/0.57          = X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3399_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 )
% 0.32/0.57          = ( semiri681578069525770553at_rat @ X2 ) )
% 0.32/0.57        = ( ( power_power_nat @ B @ W2 )
% 0.32/0.57          = X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3400_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 )
% 0.32/0.57          = ( semiri3763490453095760265atural @ X2 ) )
% 0.32/0.57        = ( ( power_power_nat @ B @ W2 )
% 0.32/0.57          = X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3401_of__nat__power,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 0.32/0.57        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power
% 0.32/0.57  thf(fact_3402_of__nat__power,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 0.32/0.57        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power
% 0.32/0.57  thf(fact_3403_of__nat__power,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( semiri4939895301339042750nteger @ ( power_power_nat @ M @ N ) )
% 0.32/0.57        = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ M ) @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power
% 0.32/0.57  thf(fact_3404_of__nat__power,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 0.32/0.57        = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power
% 0.32/0.57  thf(fact_3405_of__nat__power,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( semiri3763490453095760265atural @ ( power_power_nat @ M @ N ) )
% 0.32/0.57        = ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ M ) @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power
% 0.32/0.57  thf(fact_3406_power__one__right,axiom,
% 0.32/0.57      ! [A: int] :
% 0.32/0.57        ( ( power_power_int @ A @ one_one_nat )
% 0.32/0.57        = A ) ).
% 0.32/0.57  
% 0.32/0.57  % power_one_right
% 0.32/0.57  thf(fact_3407_power__one__right,axiom,
% 0.32/0.57      ! [A: nat] :
% 0.32/0.57        ( ( power_power_nat @ A @ one_one_nat )
% 0.32/0.57        = A ) ).
% 0.32/0.57  
% 0.32/0.57  % power_one_right
% 0.32/0.57  thf(fact_3408_of__nat__fact,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri1314217659103216013at_int @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.32/0.57        = ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_fact
% 0.32/0.57  thf(fact_3409_of__nat__fact,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri4939895301339042750nteger @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.32/0.57        = ( semiri3624122377584611663nteger @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_fact
% 0.32/0.57  thf(fact_3410_of__nat__fact,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri681578069525770553at_rat @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.32/0.57        = ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_fact
% 0.32/0.57  thf(fact_3411_of__nat__fact,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri3763490453095760265atural @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.32/0.57        = ( semiri2447717529341329178atural @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_fact
% 0.32/0.57  thf(fact_3412_of__nat__fact,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri1316708129612266289at_nat @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.32/0.57        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_fact
% 0.32/0.57  thf(fact_3413_power__inject__exp,axiom,
% 0.32/0.57      ! [A: code_natural,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 0.32/0.57       => ( ( ( power_7079662738309270450atural @ A @ M )
% 0.32/0.57            = ( power_7079662738309270450atural @ A @ N ) )
% 0.32/0.57          = ( M = N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_inject_exp
% 0.32/0.57  thf(fact_3414_power__inject__exp,axiom,
% 0.32/0.57      ! [A: code_integer,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.32/0.57       => ( ( ( power_8256067586552552935nteger @ A @ M )
% 0.32/0.57            = ( power_8256067586552552935nteger @ A @ N ) )
% 0.32/0.57          = ( M = N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_inject_exp
% 0.32/0.57  thf(fact_3415_power__inject__exp,axiom,
% 0.32/0.57      ! [A: rat,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_rat @ one_one_rat @ A )
% 0.32/0.57       => ( ( ( power_power_rat @ A @ M )
% 0.32/0.57            = ( power_power_rat @ A @ N ) )
% 0.32/0.57          = ( M = N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_inject_exp
% 0.32/0.57  thf(fact_3416_power__inject__exp,axiom,
% 0.32/0.57      ! [A: nat,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_nat @ one_one_nat @ A )
% 0.32/0.57       => ( ( ( power_power_nat @ A @ M )
% 0.32/0.57            = ( power_power_nat @ A @ N ) )
% 0.32/0.57          = ( M = N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_inject_exp
% 0.32/0.57  thf(fact_3417_power__inject__exp,axiom,
% 0.32/0.57      ! [A: int,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_int @ one_one_int @ A )
% 0.32/0.57       => ( ( ( power_power_int @ A @ M )
% 0.32/0.57            = ( power_power_int @ A @ N ) )
% 0.32/0.57          = ( M = N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_inject_exp
% 0.32/0.57  thf(fact_3418_power__0__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( suc @ N ) )
% 0.32/0.57        = zero_z3403309356797280102nteger ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0_Suc
% 0.32/0.57  thf(fact_3419_power__0__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 0.32/0.57        = zero_zero_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0_Suc
% 0.32/0.57  thf(fact_3420_power__0__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ ( suc @ N ) )
% 0.32/0.57        = zero_z2226904508553997617atural ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0_Suc
% 0.32/0.57  thf(fact_3421_power__0__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 0.32/0.57        = zero_zero_int ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0_Suc
% 0.32/0.57  thf(fact_3422_power__0__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.32/0.57        = zero_zero_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0_Suc
% 0.32/0.57  thf(fact_3423_power__Suc0__right,axiom,
% 0.32/0.57      ! [A: int] :
% 0.32/0.57        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 0.32/0.57        = A ) ).
% 0.32/0.57  
% 0.32/0.57  % power_Suc0_right
% 0.32/0.57  thf(fact_3424_power__Suc0__right,axiom,
% 0.32/0.57      ! [A: nat] :
% 0.32/0.57        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.32/0.57        = A ) ).
% 0.32/0.57  
% 0.32/0.57  % power_Suc0_right
% 0.32/0.57  thf(fact_3425_gbinomial__0_I2_J,axiom,
% 0.32/0.57      ! [K: nat] :
% 0.32/0.57        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 0.32/0.57        = zero_zero_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(2)
% 0.32/0.57  thf(fact_3426_gbinomial__0_I2_J,axiom,
% 0.32/0.57      ! [K: nat] :
% 0.32/0.57        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 0.32/0.57        = zero_zero_int ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(2)
% 0.32/0.57  thf(fact_3427_gbinomial__0_I2_J,axiom,
% 0.32/0.57      ! [K: nat] :
% 0.32/0.57        ( ( gbinom8545251970709558553nteger @ zero_z3403309356797280102nteger @ ( suc @ K ) )
% 0.32/0.57        = zero_z3403309356797280102nteger ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(2)
% 0.32/0.57  thf(fact_3428_gbinomial__0_I2_J,axiom,
% 0.32/0.57      ! [K: nat] :
% 0.32/0.57        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 0.32/0.57        = zero_zero_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(2)
% 0.32/0.57  thf(fact_3429_gbinomial__0_I2_J,axiom,
% 0.32/0.57      ! [K: nat] :
% 0.32/0.57        ( ( gbinom7368847122466276068atural @ zero_z2226904508553997617atural @ ( suc @ K ) )
% 0.32/0.57        = zero_z2226904508553997617atural ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(2)
% 0.32/0.57  thf(fact_3430_fact__0,axiom,
% 0.32/0.57      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 0.32/0.57      = one_one_int ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_0
% 0.32/0.57  thf(fact_3431_fact__0,axiom,
% 0.32/0.57      ( ( semiri3624122377584611663nteger @ zero_zero_nat )
% 0.32/0.57      = one_one_Code_integer ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_0
% 0.32/0.57  thf(fact_3432_fact__0,axiom,
% 0.32/0.57      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 0.32/0.57      = one_one_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_0
% 0.32/0.57  thf(fact_3433_fact__0,axiom,
% 0.32/0.57      ( ( semiri2447717529341329178atural @ zero_zero_nat )
% 0.32/0.57      = one_one_Code_natural ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_0
% 0.32/0.57  thf(fact_3434_fact__0,axiom,
% 0.32/0.57      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 0.32/0.57      = one_one_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_0
% 0.32/0.57  thf(fact_3435_gbinomial__0_I1_J,axiom,
% 0.32/0.57      ! [A: int] :
% 0.32/0.57        ( ( gbinomial_int @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_int ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(1)
% 0.32/0.57  thf(fact_3436_gbinomial__0_I1_J,axiom,
% 0.32/0.57      ! [A: nat] :
% 0.32/0.57        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(1)
% 0.32/0.57  thf(fact_3437_gbinomial__0_I1_J,axiom,
% 0.32/0.57      ! [A: code_integer] :
% 0.32/0.57        ( ( gbinom8545251970709558553nteger @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_Code_integer ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(1)
% 0.32/0.57  thf(fact_3438_gbinomial__0_I1_J,axiom,
% 0.32/0.57      ! [A: rat] :
% 0.32/0.57        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(1)
% 0.32/0.57  thf(fact_3439_gbinomial__0_I1_J,axiom,
% 0.32/0.57      ! [A: code_natural] :
% 0.32/0.57        ( ( gbinom7368847122466276068atural @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_Code_natural ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_0(1)
% 0.32/0.57  thf(fact_3440_pochhammer__0,axiom,
% 0.32/0.57      ! [A: int] :
% 0.32/0.57        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_int ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_0
% 0.32/0.57  thf(fact_3441_pochhammer__0,axiom,
% 0.32/0.57      ! [A: nat] :
% 0.32/0.57        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_0
% 0.32/0.57  thf(fact_3442_pochhammer__0,axiom,
% 0.32/0.57      ! [A: code_integer] :
% 0.32/0.57        ( ( comm_s8582702949713902594nteger @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_Code_integer ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_0
% 0.32/0.57  thf(fact_3443_pochhammer__0,axiom,
% 0.32/0.57      ! [A: rat] :
% 0.32/0.57        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_0
% 0.32/0.57  thf(fact_3444_pochhammer__0,axiom,
% 0.32/0.57      ! [A: code_natural] :
% 0.32/0.57        ( ( comm_s7406298101470620109atural @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_Code_natural ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_0
% 0.32/0.57  thf(fact_3445_fact__1,axiom,
% 0.32/0.57      ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 0.32/0.57      = one_one_int ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_1
% 0.32/0.57  thf(fact_3446_fact__1,axiom,
% 0.32/0.57      ( ( semiri3624122377584611663nteger @ one_one_nat )
% 0.32/0.57      = one_one_Code_integer ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_1
% 0.32/0.57  thf(fact_3447_fact__1,axiom,
% 0.32/0.57      ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 0.32/0.57      = one_one_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_1
% 0.32/0.57  thf(fact_3448_fact__1,axiom,
% 0.32/0.57      ( ( semiri2447717529341329178atural @ one_one_nat )
% 0.32/0.57      = one_one_Code_natural ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_1
% 0.32/0.57  thf(fact_3449_fact__1,axiom,
% 0.32/0.57      ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 0.32/0.57      = one_one_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_1
% 0.32/0.57  thf(fact_3450_of__int__power,axiom,
% 0.32/0.57      ! [Z2: int,N: nat] :
% 0.32/0.57        ( ( ring_18347121197199848620nteger @ ( power_power_int @ Z2 @ N ) )
% 0.32/0.57        = ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power
% 0.32/0.57  thf(fact_3451_of__int__power,axiom,
% 0.32/0.57      ! [Z2: int,N: nat] :
% 0.32/0.57        ( ( ring_1_of_int_rat @ ( power_power_int @ Z2 @ N ) )
% 0.32/0.57        = ( power_power_rat @ ( ring_1_of_int_rat @ Z2 ) @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power
% 0.32/0.57  thf(fact_3452_of__int__power,axiom,
% 0.32/0.57      ! [Z2: int,N: nat] :
% 0.32/0.57        ( ( ring_1_of_int_int @ ( power_power_int @ Z2 @ N ) )
% 0.32/0.57        = ( power_power_int @ ( ring_1_of_int_int @ Z2 ) @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power
% 0.32/0.57  thf(fact_3453_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: int,W2: nat,X2: int] :
% 0.32/0.57        ( ( ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 )
% 0.32/0.57          = ( ring_18347121197199848620nteger @ X2 ) )
% 0.32/0.57        = ( ( power_power_int @ B @ W2 )
% 0.32/0.57          = X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_eq_of_int_power_cancel_iff
% 0.32/0.57  thf(fact_3454_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: int,W2: nat,X2: int] :
% 0.32/0.57        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 )
% 0.32/0.57          = ( ring_1_of_int_rat @ X2 ) )
% 0.32/0.57        = ( ( power_power_int @ B @ W2 )
% 0.32/0.57          = X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_eq_of_int_power_cancel_iff
% 0.32/0.57  thf(fact_3455_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: int,W2: nat,X2: int] :
% 0.32/0.57        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 )
% 0.32/0.57          = ( ring_1_of_int_int @ X2 ) )
% 0.32/0.57        = ( ( power_power_int @ B @ W2 )
% 0.32/0.57          = X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_eq_of_int_power_cancel_iff
% 0.32/0.57  thf(fact_3456_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.57      ! [X2: int,B: int,W2: nat] :
% 0.32/0.57        ( ( ( ring_18347121197199848620nteger @ X2 )
% 0.32/0.57          = ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) )
% 0.32/0.57        = ( X2
% 0.32/0.57          = ( power_power_int @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power_eq_of_int_cancel_iff
% 0.32/0.57  thf(fact_3457_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.57      ! [X2: int,B: int,W2: nat] :
% 0.32/0.57        ( ( ( ring_1_of_int_rat @ X2 )
% 0.32/0.57          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 0.32/0.57        = ( X2
% 0.32/0.57          = ( power_power_int @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power_eq_of_int_cancel_iff
% 0.32/0.57  thf(fact_3458_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.57      ! [X2: int,B: int,W2: nat] :
% 0.32/0.57        ( ( ( ring_1_of_int_int @ X2 )
% 0.32/0.57          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 0.32/0.57        = ( X2
% 0.32/0.57          = ( power_power_int @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power_eq_of_int_cancel_iff
% 0.32/0.57  thf(fact_3459_power__strict__increasing__iff,axiom,
% 0.32/0.57      ! [B: code_natural,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ B )
% 0.32/0.57       => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ B @ X2 ) @ ( power_7079662738309270450atural @ B @ Y ) )
% 0.32/0.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_increasing_iff
% 0.32/0.57  thf(fact_3460_power__strict__increasing__iff,axiom,
% 0.32/0.57      ! [B: code_integer,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 0.32/0.57       => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X2 ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 0.32/0.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_increasing_iff
% 0.32/0.57  thf(fact_3461_power__strict__increasing__iff,axiom,
% 0.32/0.57      ! [B: rat,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_less_rat @ one_one_rat @ B )
% 0.32/0.57       => ( ( ord_less_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y ) )
% 0.32/0.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_increasing_iff
% 0.32/0.57  thf(fact_3462_power__strict__increasing__iff,axiom,
% 0.32/0.57      ! [B: nat,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_less_nat @ one_one_nat @ B )
% 0.32/0.57       => ( ( ord_less_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y ) )
% 0.32/0.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_increasing_iff
% 0.32/0.57  thf(fact_3463_power__strict__increasing__iff,axiom,
% 0.32/0.57      ! [B: int,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_less_int @ one_one_int @ B )
% 0.32/0.57       => ( ( ord_less_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y ) )
% 0.32/0.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_increasing_iff
% 0.32/0.57  thf(fact_3464_minus__one__mult__self,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 0.32/0.57        = one_one_int ) ).
% 0.32/0.57  
% 0.32/0.57  % minus_one_mult_self
% 0.32/0.57  thf(fact_3465_minus__one__mult__self,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 0.32/0.57        = one_one_Code_integer ) ).
% 0.32/0.57  
% 0.32/0.57  % minus_one_mult_self
% 0.32/0.57  thf(fact_3466_minus__one__mult__self,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 0.32/0.57        = one_one_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % minus_one_mult_self
% 0.32/0.57  thf(fact_3467_left__minus__one__mult__self,axiom,
% 0.32/0.57      ! [N: nat,A: int] :
% 0.32/0.57        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 0.32/0.57        = A ) ).
% 0.32/0.57  
% 0.32/0.57  % left_minus_one_mult_self
% 0.32/0.57  thf(fact_3468_left__minus__one__mult__self,axiom,
% 0.32/0.57      ! [N: nat,A: code_integer] :
% 0.32/0.57        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 0.32/0.57        = A ) ).
% 0.32/0.57  
% 0.32/0.57  % left_minus_one_mult_self
% 0.32/0.57  thf(fact_3469_left__minus__one__mult__self,axiom,
% 0.32/0.57      ! [N: nat,A: rat] :
% 0.32/0.57        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 0.32/0.57        = A ) ).
% 0.32/0.57  
% 0.32/0.57  % left_minus_one_mult_self
% 0.32/0.57  thf(fact_3470_power__eq__0__iff,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat] :
% 0.32/0.57        ( ( ( power_8256067586552552935nteger @ A @ N )
% 0.32/0.57          = zero_z3403309356797280102nteger )
% 0.32/0.57        = ( ( A = zero_z3403309356797280102nteger )
% 0.32/0.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_eq_0_iff
% 0.32/0.57  thf(fact_3471_power__eq__0__iff,axiom,
% 0.32/0.57      ! [A: rat,N: nat] :
% 0.32/0.57        ( ( ( power_power_rat @ A @ N )
% 0.32/0.57          = zero_zero_rat )
% 0.32/0.57        = ( ( A = zero_zero_rat )
% 0.32/0.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_eq_0_iff
% 0.32/0.57  thf(fact_3472_power__eq__0__iff,axiom,
% 0.32/0.57      ! [A: code_natural,N: nat] :
% 0.32/0.57        ( ( ( power_7079662738309270450atural @ A @ N )
% 0.32/0.57          = zero_z2226904508553997617atural )
% 0.32/0.57        = ( ( A = zero_z2226904508553997617atural )
% 0.32/0.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_eq_0_iff
% 0.32/0.57  thf(fact_3473_power__eq__0__iff,axiom,
% 0.32/0.57      ! [A: int,N: nat] :
% 0.32/0.57        ( ( ( power_power_int @ A @ N )
% 0.32/0.57          = zero_zero_int )
% 0.32/0.57        = ( ( A = zero_zero_int )
% 0.32/0.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_eq_0_iff
% 0.32/0.57  thf(fact_3474_power__eq__0__iff,axiom,
% 0.32/0.57      ! [A: nat,N: nat] :
% 0.32/0.57        ( ( ( power_power_nat @ A @ N )
% 0.32/0.57          = zero_zero_nat )
% 0.32/0.57        = ( ( A = zero_zero_nat )
% 0.32/0.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_eq_0_iff
% 0.32/0.57  thf(fact_3475_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 0.32/0.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_less_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3476_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 0.32/0.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_less_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3477_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 0.32/0.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_less_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3478_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 0.32/0.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_less_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3479_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) @ ( semiri3763490453095760265atural @ X2 ) )
% 0.32/0.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_less_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3480_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_less_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3481_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_less_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3482_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_less_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3483_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_less_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3484_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ X2 ) @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_less_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3485_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_le_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3486_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ X2 ) @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_le_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3487_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_le_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3488_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_le_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3489_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.57      ! [X2: nat,B: nat,W2: nat] :
% 0.32/0.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_power_le_of_nat_cancel_iff
% 0.32/0.57  thf(fact_3490_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_le_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3491_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) @ ( semiri3763490453095760265atural @ X2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_le_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3492_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_le_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3493_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_le_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3494_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: nat,W2: nat,X2: nat] :
% 0.32/0.57        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 0.32/0.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_le_of_nat_power_cancel_iff
% 0.32/0.57  thf(fact_3495_fact__Suc__0,axiom,
% 0.32/0.57      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 0.32/0.57      = one_one_int ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc_0
% 0.32/0.57  thf(fact_3496_fact__Suc__0,axiom,
% 0.32/0.57      ( ( semiri3624122377584611663nteger @ ( suc @ zero_zero_nat ) )
% 0.32/0.57      = one_one_Code_integer ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc_0
% 0.32/0.57  thf(fact_3497_fact__Suc__0,axiom,
% 0.32/0.57      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 0.32/0.57      = one_one_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc_0
% 0.32/0.57  thf(fact_3498_fact__Suc__0,axiom,
% 0.32/0.57      ( ( semiri2447717529341329178atural @ ( suc @ zero_zero_nat ) )
% 0.32/0.57      = one_one_Code_natural ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc_0
% 0.32/0.57  thf(fact_3499_fact__Suc__0,axiom,
% 0.32/0.57      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 0.32/0.57      = one_one_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc_0
% 0.32/0.57  thf(fact_3500_fact__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 0.32/0.57        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc
% 0.32/0.57  thf(fact_3501_fact__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri3624122377584611663nteger @ ( suc @ N ) )
% 0.32/0.57        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc
% 0.32/0.57  thf(fact_3502_fact__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 0.32/0.57        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc
% 0.32/0.57  thf(fact_3503_fact__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri2447717529341329178atural @ ( suc @ N ) )
% 0.32/0.57        = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ ( suc @ N ) ) @ ( semiri2447717529341329178atural @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc
% 0.32/0.57  thf(fact_3504_fact__Suc,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 0.32/0.57        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_Suc
% 0.32/0.57  thf(fact_3505_power__strict__decreasing__iff,axiom,
% 0.32/0.57      ! [B: code_natural,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.57       => ( ( ord_le5570908160329646204atural @ B @ one_one_Code_natural )
% 0.32/0.57         => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ B @ M ) @ ( power_7079662738309270450atural @ B @ N ) )
% 0.32/0.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_decreasing_iff
% 0.32/0.57  thf(fact_3506_power__strict__decreasing__iff,axiom,
% 0.32/0.57      ! [B: code_integer,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.57       => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 0.32/0.57         => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 0.32/0.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_decreasing_iff
% 0.32/0.57  thf(fact_3507_power__strict__decreasing__iff,axiom,
% 0.32/0.57      ! [B: rat,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.32/0.57       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.32/0.57         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.32/0.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_decreasing_iff
% 0.32/0.57  thf(fact_3508_power__strict__decreasing__iff,axiom,
% 0.32/0.57      ! [B: nat,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.32/0.57       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.32/0.57         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.32/0.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_decreasing_iff
% 0.32/0.57  thf(fact_3509_power__strict__decreasing__iff,axiom,
% 0.32/0.57      ! [B: int,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.57       => ( ( ord_less_int @ B @ one_one_int )
% 0.32/0.57         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.32/0.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_strict_decreasing_iff
% 0.32/0.57  thf(fact_3510_power__mono__iff,axiom,
% 0.32/0.57      ! [A: code_integer,B: code_integer,N: nat] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.57           => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 0.32/0.57              = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono_iff
% 0.32/0.57  thf(fact_3511_power__mono__iff,axiom,
% 0.32/0.57      ! [A: code_natural,B: code_natural,N: nat] :
% 0.32/0.57        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.57           => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ B @ N ) )
% 0.32/0.57              = ( ord_le1926595141338095240atural @ A @ B ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono_iff
% 0.32/0.57  thf(fact_3512_power__mono__iff,axiom,
% 0.32/0.57      ! [A: rat,B: rat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.57           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.32/0.57              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono_iff
% 0.32/0.57  thf(fact_3513_power__mono__iff,axiom,
% 0.32/0.57      ! [A: nat,B: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.57           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.32/0.57              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono_iff
% 0.32/0.57  thf(fact_3514_power__mono__iff,axiom,
% 0.32/0.57      ! [A: int,B: int,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.57           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.32/0.57              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono_iff
% 0.32/0.57  thf(fact_3515_power__increasing__iff,axiom,
% 0.32/0.57      ! [B: code_natural,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ B )
% 0.32/0.57       => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ B @ X2 ) @ ( power_7079662738309270450atural @ B @ Y ) )
% 0.32/0.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_increasing_iff
% 0.32/0.57  thf(fact_3516_power__increasing__iff,axiom,
% 0.32/0.57      ! [B: code_integer,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 0.32/0.57       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X2 ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 0.32/0.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_increasing_iff
% 0.32/0.57  thf(fact_3517_power__increasing__iff,axiom,
% 0.32/0.57      ! [B: rat,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_less_rat @ one_one_rat @ B )
% 0.32/0.57       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y ) )
% 0.32/0.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_increasing_iff
% 0.32/0.57  thf(fact_3518_power__increasing__iff,axiom,
% 0.32/0.57      ! [B: nat,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_less_nat @ one_one_nat @ B )
% 0.32/0.57       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y ) )
% 0.32/0.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_increasing_iff
% 0.32/0.57  thf(fact_3519_power__increasing__iff,axiom,
% 0.32/0.57      ! [B: int,X2: nat,Y: nat] :
% 0.32/0.57        ( ( ord_less_int @ one_one_int @ B )
% 0.32/0.57       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y ) )
% 0.32/0.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_increasing_iff
% 0.32/0.57  thf(fact_3520_zero__less__power__abs__iff,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 0.32/0.57        = ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.57          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_less_power_abs_iff
% 0.32/0.57  thf(fact_3521_zero__less__power__abs__iff,axiom,
% 0.32/0.57      ! [A: rat,N: nat] :
% 0.32/0.57        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 0.32/0.57        = ( ( A != zero_zero_rat )
% 0.32/0.57          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_less_power_abs_iff
% 0.32/0.57  thf(fact_3522_zero__less__power__abs__iff,axiom,
% 0.32/0.57      ! [A: int,N: nat] :
% 0.32/0.57        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 0.32/0.57        = ( ( A != zero_zero_int )
% 0.32/0.57          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_less_power_abs_iff
% 0.32/0.57  thf(fact_3523_of__int__le__of__int__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: int,W2: nat,X2: int] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) @ ( ring_18347121197199848620nteger @ X2 ) )
% 0.32/0.57        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_le_of_int_power_cancel_iff
% 0.32/0.57  thf(fact_3524_of__int__le__of__int__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: int,W2: nat,X2: int] :
% 0.32/0.57        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X2 ) )
% 0.32/0.57        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_le_of_int_power_cancel_iff
% 0.32/0.57  thf(fact_3525_of__int__le__of__int__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: int,W2: nat,X2: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X2 ) )
% 0.32/0.57        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_le_of_int_power_cancel_iff
% 0.32/0.57  thf(fact_3526_of__int__power__le__of__int__cancel__iff,axiom,
% 0.32/0.57      ! [X2: int,B: int,W2: nat] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power_le_of_int_cancel_iff
% 0.32/0.57  thf(fact_3527_of__int__power__le__of__int__cancel__iff,axiom,
% 0.32/0.57      ! [X2: int,B: int,W2: nat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power_le_of_int_cancel_iff
% 0.32/0.57  thf(fact_3528_of__int__power__le__of__int__cancel__iff,axiom,
% 0.32/0.57      ! [X2: int,B: int,W2: nat] :
% 0.32/0.57        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power_le_of_int_cancel_iff
% 0.32/0.57  thf(fact_3529_of__int__less__of__int__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: int,W2: nat,X2: int] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) @ ( ring_18347121197199848620nteger @ X2 ) )
% 0.32/0.57        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_less_of_int_power_cancel_iff
% 0.32/0.57  thf(fact_3530_of__int__less__of__int__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: int,W2: nat,X2: int] :
% 0.32/0.57        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X2 ) )
% 0.32/0.57        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_less_of_int_power_cancel_iff
% 0.32/0.57  thf(fact_3531_of__int__less__of__int__power__cancel__iff,axiom,
% 0.32/0.57      ! [B: int,W2: nat,X2: int] :
% 0.32/0.57        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X2 ) )
% 0.32/0.57        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_less_of_int_power_cancel_iff
% 0.32/0.57  thf(fact_3532_of__int__power__less__of__int__cancel__iff,axiom,
% 0.32/0.57      ! [X2: int,B: int,W2: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power_less_of_int_cancel_iff
% 0.32/0.57  thf(fact_3533_of__int__power__less__of__int__cancel__iff,axiom,
% 0.32/0.57      ! [X2: int,B: int,W2: nat] :
% 0.32/0.57        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power_less_of_int_cancel_iff
% 0.32/0.57  thf(fact_3534_of__int__power__less__of__int__cancel__iff,axiom,
% 0.32/0.57      ! [X2: int,B: int,W2: nat] :
% 0.32/0.57        ( ( ord_less_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 0.32/0.57        = ( ord_less_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_int_power_less_of_int_cancel_iff
% 0.32/0.57  thf(fact_3535_power__decreasing__iff,axiom,
% 0.32/0.57      ! [B: code_natural,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.57       => ( ( ord_le5570908160329646204atural @ B @ one_one_Code_natural )
% 0.32/0.57         => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ B @ M ) @ ( power_7079662738309270450atural @ B @ N ) )
% 0.32/0.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_decreasing_iff
% 0.32/0.57  thf(fact_3536_power__decreasing__iff,axiom,
% 0.32/0.57      ! [B: code_integer,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.57       => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 0.32/0.57         => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 0.32/0.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_decreasing_iff
% 0.32/0.57  thf(fact_3537_power__decreasing__iff,axiom,
% 0.32/0.57      ! [B: rat,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.32/0.57       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.32/0.57         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.32/0.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_decreasing_iff
% 0.32/0.57  thf(fact_3538_power__decreasing__iff,axiom,
% 0.32/0.57      ! [B: nat,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.32/0.57       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.32/0.57         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.32/0.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_decreasing_iff
% 0.32/0.57  thf(fact_3539_power__decreasing__iff,axiom,
% 0.32/0.57      ! [B: int,M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.57       => ( ( ord_less_int @ B @ one_one_int )
% 0.32/0.57         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.32/0.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_decreasing_iff
% 0.32/0.57  thf(fact_3540_of__nat__zero__less__power__iff,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X2 ) @ N ) )
% 0.32/0.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 0.32/0.57          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_zero_less_power_iff
% 0.32/0.57  thf(fact_3541_of__nat__zero__less__power__iff,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N ) )
% 0.32/0.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 0.32/0.57          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_zero_less_power_iff
% 0.32/0.57  thf(fact_3542_of__nat__zero__less__power__iff,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X2 ) @ N ) )
% 0.32/0.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 0.32/0.57          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_zero_less_power_iff
% 0.32/0.57  thf(fact_3543_of__nat__zero__less__power__iff,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N ) )
% 0.32/0.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 0.32/0.57          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_zero_less_power_iff
% 0.32/0.57  thf(fact_3544_of__nat__zero__less__power__iff,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ X2 ) @ N ) )
% 0.32/0.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 0.32/0.57          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_zero_less_power_iff
% 0.32/0.57  thf(fact_3545_pochhammer__of__nat,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( comm_s4660882817536571857er_int @ ( semiri1314217659103216013at_int @ X2 ) @ N )
% 0.32/0.57        = ( semiri1314217659103216013at_int @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_of_nat
% 0.32/0.57  thf(fact_3546_pochhammer__of__nat,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( comm_s4663373288045622133er_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N )
% 0.32/0.57        = ( semiri1316708129612266289at_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_of_nat
% 0.32/0.57  thf(fact_3547_pochhammer__of__nat,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( comm_s8582702949713902594nteger @ ( semiri4939895301339042750nteger @ X2 ) @ N )
% 0.32/0.57        = ( semiri4939895301339042750nteger @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_of_nat
% 0.32/0.57  thf(fact_3548_pochhammer__of__nat,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( comm_s4028243227959126397er_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N )
% 0.32/0.57        = ( semiri681578069525770553at_rat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_of_nat
% 0.32/0.57  thf(fact_3549_pochhammer__of__nat,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( comm_s7406298101470620109atural @ ( semiri3763490453095760265atural @ X2 ) @ N )
% 0.32/0.57        = ( semiri3763490453095760265atural @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_of_nat
% 0.32/0.57  thf(fact_3550_pochhammer__fact,axiom,
% 0.32/0.57      ( semiri1406184849735516958ct_int
% 0.32/0.57      = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_fact
% 0.32/0.57  thf(fact_3551_pochhammer__fact,axiom,
% 0.32/0.57      ( semiri3624122377584611663nteger
% 0.32/0.57      = ( comm_s8582702949713902594nteger @ one_one_Code_integer ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_fact
% 0.32/0.57  thf(fact_3552_pochhammer__fact,axiom,
% 0.32/0.57      ( semiri773545260158071498ct_rat
% 0.32/0.57      = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_fact
% 0.32/0.57  thf(fact_3553_pochhammer__fact,axiom,
% 0.32/0.57      ( semiri2447717529341329178atural
% 0.32/0.57      = ( comm_s7406298101470620109atural @ one_one_Code_natural ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_fact
% 0.32/0.57  thf(fact_3554_pochhammer__fact,axiom,
% 0.32/0.57      ( semiri1408675320244567234ct_nat
% 0.32/0.57      = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_fact
% 0.32/0.57  thf(fact_3555_of__nat__gbinomial,axiom,
% 0.32/0.57      ! [N: nat,K: nat] :
% 0.32/0.57        ( ( semiri681578069525770553at_rat @ ( gbinomial_nat @ N @ K ) )
% 0.32/0.57        = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 0.32/0.57  
% 0.32/0.57  % of_nat_gbinomial
% 0.32/0.57  thf(fact_3556_gbinomial__pochhammer,axiom,
% 0.32/0.57      ( gbinomial_rat
% 0.32/0.57      = ( ^ [A2: rat,K2: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A2 ) @ K2 ) ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_pochhammer
% 0.32/0.57  thf(fact_3557_gbinomial__ge__n__over__k__pow__k,axiom,
% 0.32/0.57      ! [K: nat,A: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 0.32/0.57       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_ge_n_over_k_pow_k
% 0.32/0.57  thf(fact_3558_fact__mono__nat,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.57       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_mono_nat
% 0.32/0.57  thf(fact_3559_fact__ge__self,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_self
% 0.32/0.57  thf(fact_3560_power__not__zero,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat] :
% 0.32/0.57        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.57       => ( ( power_8256067586552552935nteger @ A @ N )
% 0.32/0.57         != zero_z3403309356797280102nteger ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_not_zero
% 0.32/0.57  thf(fact_3561_power__not__zero,axiom,
% 0.32/0.57      ! [A: rat,N: nat] :
% 0.32/0.57        ( ( A != zero_zero_rat )
% 0.32/0.57       => ( ( power_power_rat @ A @ N )
% 0.32/0.57         != zero_zero_rat ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_not_zero
% 0.32/0.57  thf(fact_3562_power__not__zero,axiom,
% 0.32/0.57      ! [A: code_natural,N: nat] :
% 0.32/0.57        ( ( A != zero_z2226904508553997617atural )
% 0.32/0.57       => ( ( power_7079662738309270450atural @ A @ N )
% 0.32/0.57         != zero_z2226904508553997617atural ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_not_zero
% 0.32/0.57  thf(fact_3563_power__not__zero,axiom,
% 0.32/0.57      ! [A: int,N: nat] :
% 0.32/0.57        ( ( A != zero_zero_int )
% 0.32/0.57       => ( ( power_power_int @ A @ N )
% 0.32/0.57         != zero_zero_int ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_not_zero
% 0.32/0.57  thf(fact_3564_power__not__zero,axiom,
% 0.32/0.57      ! [A: nat,N: nat] :
% 0.32/0.57        ( ( A != zero_zero_nat )
% 0.32/0.57       => ( ( power_power_nat @ A @ N )
% 0.32/0.57         != zero_zero_nat ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_not_zero
% 0.32/0.57  thf(fact_3565_fact__nonzero,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri1406184849735516958ct_int @ N )
% 0.32/0.57       != zero_zero_int ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_nonzero
% 0.32/0.57  thf(fact_3566_fact__nonzero,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri3624122377584611663nteger @ N )
% 0.32/0.57       != zero_z3403309356797280102nteger ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_nonzero
% 0.32/0.57  thf(fact_3567_fact__nonzero,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri773545260158071498ct_rat @ N )
% 0.32/0.57       != zero_zero_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_nonzero
% 0.32/0.57  thf(fact_3568_fact__nonzero,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri2447717529341329178atural @ N )
% 0.32/0.57       != zero_z2226904508553997617atural ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_nonzero
% 0.32/0.57  thf(fact_3569_fact__nonzero,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( semiri1408675320244567234ct_nat @ N )
% 0.32/0.57       != zero_zero_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_nonzero
% 0.32/0.57  thf(fact_3570_pochhammer__same,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 0.32/0.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_same
% 0.32/0.57  thf(fact_3571_pochhammer__same,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 0.32/0.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_same
% 0.32/0.57  thf(fact_3572_pochhammer__same,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 0.32/0.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_same
% 0.32/0.57  thf(fact_3573_Ints__power,axiom,
% 0.32/0.57      ! [A: int,N: nat] :
% 0.32/0.57        ( ( member_int @ A @ ring_1_Ints_int )
% 0.32/0.57       => ( member_int @ ( power_power_int @ A @ N ) @ ring_1_Ints_int ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Ints_power
% 0.32/0.57  thf(fact_3574_gbinomial__pochhammer_H,axiom,
% 0.32/0.57      ( gbinomial_rat
% 0.32/0.57      = ( ^ [A2: rat,K2: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A2 @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_pochhammer'
% 0.32/0.57  thf(fact_3575_gbinomial__index__swap,axiom,
% 0.32/0.57      ! [K: nat,N: nat] :
% 0.32/0.57        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 0.32/0.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_index_swap
% 0.32/0.57  thf(fact_3576_gbinomial__negated__upper,axiom,
% 0.32/0.57      ( gbinomial_rat
% 0.32/0.57      = ( ^ [A2: rat,K2: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A2 ) @ one_one_rat ) @ K2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_negated_upper
% 0.32/0.57  thf(fact_3577_fact__less__mono__nat,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.57       => ( ( ord_less_nat @ M @ N )
% 0.32/0.57         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_less_mono_nat
% 0.32/0.57  thf(fact_3578_zero__le__power,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.57       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_le_power
% 0.32/0.57  thf(fact_3579_zero__le__power,axiom,
% 0.32/0.57      ! [A: code_natural,N: nat] :
% 0.32/0.57        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.57       => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_le_power
% 0.32/0.57  thf(fact_3580_zero__le__power,axiom,
% 0.32/0.57      ! [A: rat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.57       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_le_power
% 0.32/0.57  thf(fact_3581_zero__le__power,axiom,
% 0.32/0.57      ! [A: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.57       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_le_power
% 0.32/0.57  thf(fact_3582_zero__le__power,axiom,
% 0.32/0.57      ! [A: int,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.57       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_le_power
% 0.32/0.57  thf(fact_3583_power__mono,axiom,
% 0.32/0.57      ! [A: code_integer,B: code_integer,N: nat] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.57         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono
% 0.32/0.57  thf(fact_3584_power__mono,axiom,
% 0.32/0.57      ! [A: code_natural,B: code_natural,N: nat] :
% 0.32/0.57        ( ( ord_le1926595141338095240atural @ A @ B )
% 0.32/0.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.57         => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ B @ N ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono
% 0.32/0.57  thf(fact_3585_power__mono,axiom,
% 0.32/0.57      ! [A: rat,B: rat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.57         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono
% 0.32/0.57  thf(fact_3586_power__mono,axiom,
% 0.32/0.57      ! [A: nat,B: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.57         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono
% 0.32/0.57  thf(fact_3587_power__mono,axiom,
% 0.32/0.57      ! [A: int,B: int,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.57         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_mono
% 0.32/0.57  thf(fact_3588_zero__less__power,axiom,
% 0.32/0.57      ! [A: code_natural,N: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.57       => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_less_power
% 0.32/0.57  thf(fact_3589_zero__less__power,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.57       => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_less_power
% 0.32/0.57  thf(fact_3590_zero__less__power,axiom,
% 0.32/0.57      ! [A: rat,N: nat] :
% 0.32/0.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.57       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_less_power
% 0.32/0.57  thf(fact_3591_zero__less__power,axiom,
% 0.32/0.57      ! [A: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.57       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_less_power
% 0.32/0.57  thf(fact_3592_zero__less__power,axiom,
% 0.32/0.57      ! [A: int,N: nat] :
% 0.32/0.57        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.57       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % zero_less_power
% 0.32/0.57  thf(fact_3593_gbinomial__Suc__Suc,axiom,
% 0.32/0.57      ! [A: rat,K: nat] :
% 0.32/0.57        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.32/0.57        = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_Suc_Suc
% 0.32/0.57  thf(fact_3594_one__le__power,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.32/0.57       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % one_le_power
% 0.32/0.57  thf(fact_3595_one__le__power,axiom,
% 0.32/0.57      ! [A: code_natural,N: nat] :
% 0.32/0.57        ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ A )
% 0.32/0.57       => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % one_le_power
% 0.32/0.57  thf(fact_3596_one__le__power,axiom,
% 0.32/0.57      ! [A: rat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.32/0.57       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % one_le_power
% 0.32/0.57  thf(fact_3597_one__le__power,axiom,
% 0.32/0.57      ! [A: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.32/0.57       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % one_le_power
% 0.32/0.57  thf(fact_3598_one__le__power,axiom,
% 0.32/0.57      ! [A: int,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.32/0.57       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % one_le_power
% 0.32/0.57  thf(fact_3599_left__right__inverse__power,axiom,
% 0.32/0.57      ! [X2: code_natural,Y: code_natural,N: nat] :
% 0.32/0.57        ( ( ( times_2397367101498566445atural @ X2 @ Y )
% 0.32/0.57          = one_one_Code_natural )
% 0.32/0.57       => ( ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ X2 @ N ) @ ( power_7079662738309270450atural @ Y @ N ) )
% 0.32/0.57          = one_one_Code_natural ) ) ).
% 0.32/0.57  
% 0.32/0.57  % left_right_inverse_power
% 0.32/0.57  thf(fact_3600_left__right__inverse__power,axiom,
% 0.32/0.57      ! [X2: code_integer,Y: code_integer,N: nat] :
% 0.32/0.57        ( ( ( times_3573771949741848930nteger @ X2 @ Y )
% 0.32/0.57          = one_one_Code_integer )
% 0.32/0.57       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 0.32/0.57          = one_one_Code_integer ) ) ).
% 0.32/0.57  
% 0.32/0.57  % left_right_inverse_power
% 0.32/0.57  thf(fact_3601_left__right__inverse__power,axiom,
% 0.32/0.57      ! [X2: rat,Y: rat,N: nat] :
% 0.32/0.57        ( ( ( times_times_rat @ X2 @ Y )
% 0.32/0.57          = one_one_rat )
% 0.32/0.57       => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y @ N ) )
% 0.32/0.57          = one_one_rat ) ) ).
% 0.32/0.57  
% 0.32/0.57  % left_right_inverse_power
% 0.32/0.57  thf(fact_3602_left__right__inverse__power,axiom,
% 0.32/0.57      ! [X2: nat,Y: nat,N: nat] :
% 0.32/0.57        ( ( ( times_times_nat @ X2 @ Y )
% 0.32/0.57          = one_one_nat )
% 0.32/0.57       => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y @ N ) )
% 0.32/0.57          = one_one_nat ) ) ).
% 0.32/0.57  
% 0.32/0.57  % left_right_inverse_power
% 0.32/0.57  thf(fact_3603_left__right__inverse__power,axiom,
% 0.32/0.57      ! [X2: int,Y: int,N: nat] :
% 0.32/0.57        ( ( ( times_times_int @ X2 @ Y )
% 0.32/0.57          = one_one_int )
% 0.32/0.57       => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y @ N ) )
% 0.32/0.57          = one_one_int ) ) ).
% 0.32/0.57  
% 0.32/0.57  % left_right_inverse_power
% 0.32/0.57  thf(fact_3604_power__0,axiom,
% 0.32/0.57      ! [A: code_integer] :
% 0.32/0.57        ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_Code_integer ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0
% 0.32/0.57  thf(fact_3605_power__0,axiom,
% 0.32/0.57      ! [A: rat] :
% 0.32/0.57        ( ( power_power_rat @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0
% 0.32/0.57  thf(fact_3606_power__0,axiom,
% 0.32/0.57      ! [A: code_natural] :
% 0.32/0.57        ( ( power_7079662738309270450atural @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_Code_natural ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0
% 0.32/0.57  thf(fact_3607_power__0,axiom,
% 0.32/0.57      ! [A: int] :
% 0.32/0.57        ( ( power_power_int @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_int ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0
% 0.32/0.57  thf(fact_3608_power__0,axiom,
% 0.32/0.57      ! [A: nat] :
% 0.32/0.57        ( ( power_power_nat @ A @ zero_zero_nat )
% 0.32/0.57        = one_one_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % power_0
% 0.32/0.57  thf(fact_3609_power__one__over,axiom,
% 0.32/0.57      ! [A: rat,N: nat] :
% 0.32/0.57        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 0.32/0.57        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_one_over
% 0.32/0.57  thf(fact_3610_power__add,axiom,
% 0.32/0.57      ! [A: code_integer,M: nat,N: nat] :
% 0.32/0.57        ( ( power_8256067586552552935nteger @ A @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_add
% 0.32/0.57  thf(fact_3611_power__add,axiom,
% 0.32/0.57      ! [A: rat,M: nat,N: nat] :
% 0.32/0.57        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.57        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_add
% 0.32/0.57  thf(fact_3612_power__add,axiom,
% 0.32/0.57      ! [A: nat,M: nat,N: nat] :
% 0.32/0.57        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.57        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_add
% 0.32/0.57  thf(fact_3613_power__add,axiom,
% 0.32/0.57      ! [A: int,M: nat,N: nat] :
% 0.32/0.57        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.57        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_add
% 0.32/0.57  thf(fact_3614_fact__ge__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri3624122377584611663nteger @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_zero
% 0.32/0.57  thf(fact_3615_fact__ge__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( semiri2447717529341329178atural @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_zero
% 0.32/0.57  thf(fact_3616_fact__ge__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_zero
% 0.32/0.57  thf(fact_3617_fact__ge__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_zero
% 0.32/0.57  thf(fact_3618_fact__ge__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_zero
% 0.32/0.57  thf(fact_3619_gbinomial__of__nat__symmetric,axiom,
% 0.32/0.57      ! [K: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.57       => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 0.32/0.57          = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_of_nat_symmetric
% 0.32/0.57  thf(fact_3620_fact__gt__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( semiri2447717529341329178atural @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_gt_zero
% 0.32/0.57  thf(fact_3621_fact__gt__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri3624122377584611663nteger @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_gt_zero
% 0.32/0.57  thf(fact_3622_fact__gt__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_gt_zero
% 0.32/0.57  thf(fact_3623_fact__gt__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_gt_zero
% 0.32/0.57  thf(fact_3624_fact__gt__zero,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_gt_zero
% 0.32/0.57  thf(fact_3625_fact__not__neg,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ~ ( ord_le5570908160329646204atural @ ( semiri2447717529341329178atural @ N ) @ zero_z2226904508553997617atural ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_not_neg
% 0.32/0.57  thf(fact_3626_fact__not__neg,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ~ ( ord_le6747313008572928689nteger @ ( semiri3624122377584611663nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_not_neg
% 0.32/0.57  thf(fact_3627_fact__not__neg,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_not_neg
% 0.32/0.57  thf(fact_3628_fact__not__neg,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_not_neg
% 0.32/0.57  thf(fact_3629_fact__not__neg,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_not_neg
% 0.32/0.57  thf(fact_3630_fact__ge__1,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_1
% 0.32/0.57  thf(fact_3631_fact__ge__1,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( semiri2447717529341329178atural @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_1
% 0.32/0.57  thf(fact_3632_fact__ge__1,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_1
% 0.32/0.57  thf(fact_3633_fact__ge__1,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_1
% 0.32/0.57  thf(fact_3634_fact__ge__1,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_1
% 0.32/0.57  thf(fact_3635_fact__mono,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.57       => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_mono
% 0.32/0.57  thf(fact_3636_fact__mono,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.57       => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_mono
% 0.32/0.57  thf(fact_3637_fact__mono,axiom,
% 0.32/0.57      ! [M: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.57       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_mono
% 0.32/0.57  thf(fact_3638_pochhammer__pos,axiom,
% 0.32/0.57      ! [X2: code_natural,N: nat] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ X2 )
% 0.32/0.57       => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( comm_s7406298101470620109atural @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_pos
% 0.32/0.57  thf(fact_3639_pochhammer__pos,axiom,
% 0.32/0.57      ! [X2: code_integer,N: nat] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X2 )
% 0.32/0.57       => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( comm_s8582702949713902594nteger @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_pos
% 0.32/0.57  thf(fact_3640_pochhammer__pos,axiom,
% 0.32/0.57      ! [X2: rat,N: nat] :
% 0.32/0.57        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 0.32/0.57       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_pos
% 0.32/0.57  thf(fact_3641_pochhammer__pos,axiom,
% 0.32/0.57      ! [X2: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 0.32/0.57       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_pos
% 0.32/0.57  thf(fact_3642_pochhammer__pos,axiom,
% 0.32/0.57      ! [X2: int,N: nat] :
% 0.32/0.57        ( ( ord_less_int @ zero_zero_int @ X2 )
% 0.32/0.57       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_pos
% 0.32/0.57  thf(fact_3643_pochhammer__neq__0__mono,axiom,
% 0.32/0.57      ! [A: rat,M: nat,N: nat] :
% 0.32/0.57        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.32/0.57         != zero_zero_rat )
% 0.32/0.57       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.57         => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.32/0.57           != zero_zero_rat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_neq_0_mono
% 0.32/0.57  thf(fact_3644_pochhammer__eq__0__mono,axiom,
% 0.32/0.57      ! [A: rat,N: nat,M: nat] :
% 0.32/0.57        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.32/0.57          = zero_zero_rat )
% 0.32/0.57       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.57         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 0.32/0.57            = zero_zero_rat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_eq_0_mono
% 0.32/0.57  thf(fact_3645_gbinomial__minus,axiom,
% 0.32/0.57      ! [A: rat,K: nat] :
% 0.32/0.57        ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 0.32/0.57        = ( 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 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_minus
% 0.32/0.57  thf(fact_3646_gbinomial__addition__formula,axiom,
% 0.32/0.57      ! [A: rat,K: nat] :
% 0.32/0.57        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 0.32/0.57        = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_addition_formula
% 0.32/0.57  thf(fact_3647_gbinomial__absorb__comp,axiom,
% 0.32/0.57      ! [A: rat,K: nat] :
% 0.32/0.57        ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 0.32/0.57        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_absorb_comp
% 0.32/0.57  thf(fact_3648_gbinomial__mult__1_H,axiom,
% 0.32/0.57      ! [A: rat,K: nat] :
% 0.32/0.57        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 0.32/0.57        = ( 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 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_mult_1'
% 0.32/0.57  thf(fact_3649_gbinomial__mult__1,axiom,
% 0.32/0.57      ! [A: rat,K: nat] :
% 0.32/0.57        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 0.32/0.57        = ( 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 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % gbinomial_mult_1
% 0.32/0.57  thf(fact_3650_fact__ge__Suc__0__nat,axiom,
% 0.32/0.57      ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.57  
% 0.32/0.57  % fact_ge_Suc_0_nat
% 0.32/0.57  thf(fact_3651_pochhammer__minus,axiom,
% 0.32/0.57      ! [B: int,K: nat] :
% 0.32/0.57        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 0.32/0.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_minus
% 0.32/0.57  thf(fact_3652_pochhammer__minus,axiom,
% 0.32/0.57      ! [B: code_integer,K: nat] :
% 0.32/0.57        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 0.32/0.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_minus
% 0.32/0.57  thf(fact_3653_pochhammer__minus,axiom,
% 0.32/0.57      ! [B: rat,K: nat] :
% 0.32/0.57        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 0.32/0.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_minus
% 0.32/0.57  thf(fact_3654_pochhammer__minus_H,axiom,
% 0.32/0.57      ! [B: int,K: nat] :
% 0.32/0.57        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 0.32/0.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_minus'
% 0.32/0.57  thf(fact_3655_pochhammer__minus_H,axiom,
% 0.32/0.57      ! [B: code_integer,K: nat] :
% 0.32/0.57        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 0.32/0.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_minus'
% 0.32/0.57  thf(fact_3656_pochhammer__minus_H,axiom,
% 0.32/0.57      ! [B: rat,K: nat] :
% 0.32/0.57        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 0.32/0.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pochhammer_minus'
% 0.32/0.57  thf(fact_3657_power__less__imp__less__base,axiom,
% 0.32/0.57      ! [A: code_natural,N: nat,B: code_natural] :
% 0.32/0.57        ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ B @ N ) )
% 0.32/0.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.57         => ( ord_le5570908160329646204atural @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_less_imp_less_base
% 0.32/0.57  thf(fact_3658_power__less__imp__less__base,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat,B: code_integer] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 0.32/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.57         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_less_imp_less_base
% 0.32/0.57  thf(fact_3659_power__less__imp__less__base,axiom,
% 0.32/0.57      ! [A: rat,N: nat,B: rat] :
% 0.32/0.57        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.32/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.57         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_less_imp_less_base
% 0.32/0.57  thf(fact_3660_power__less__imp__less__base,axiom,
% 0.32/0.57      ! [A: nat,N: nat,B: nat] :
% 0.32/0.57        ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.32/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.57         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_less_imp_less_base
% 0.32/0.57  thf(fact_3661_power__less__imp__less__base,axiom,
% 0.32/0.57      ! [A: int,N: nat,B: int] :
% 0.32/0.57        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.32/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.57         => ( ord_less_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_less_imp_less_base
% 0.32/0.57  thf(fact_3662_power__le__one,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.57       => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.32/0.57         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_one
% 0.32/0.57  thf(fact_3663_power__le__one,axiom,
% 0.32/0.57      ! [A: code_natural,N: nat] :
% 0.32/0.57        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.32/0.57       => ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 0.32/0.57         => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N ) @ one_one_Code_natural ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_one
% 0.32/0.57  thf(fact_3664_power__le__one,axiom,
% 0.32/0.57      ! [A: rat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.57       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.32/0.57         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_one
% 0.32/0.57  thf(fact_3665_power__le__one,axiom,
% 0.32/0.57      ! [A: nat,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.57       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.32/0.57         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_one
% 0.32/0.57  thf(fact_3666_power__le__one,axiom,
% 0.32/0.57      ! [A: int,N: nat] :
% 0.32/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.57       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.32/0.57         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_one
% 0.32/0.57  thf(fact_3667_power__le__imp__le__base,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat,B: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ ( power_8256067586552552935nteger @ B @ ( suc @ N ) ) )
% 0.32/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.57         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_imp_le_base
% 0.32/0.57  thf(fact_3668_power__le__imp__le__base,axiom,
% 0.32/0.57      ! [A: code_natural,N: nat,B: code_natural] :
% 0.32/0.57        ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) @ ( power_7079662738309270450atural @ B @ ( suc @ N ) ) )
% 0.32/0.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.32/0.57         => ( ord_le1926595141338095240atural @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_imp_le_base
% 0.32/0.57  thf(fact_3669_power__le__imp__le__base,axiom,
% 0.32/0.57      ! [A: rat,N: nat,B: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.32/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.57         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_imp_le_base
% 0.32/0.57  thf(fact_3670_power__le__imp__le__base,axiom,
% 0.32/0.57      ! [A: nat,N: nat,B: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.32/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.57         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_imp_le_base
% 0.32/0.57  thf(fact_3671_power__le__imp__le__base,axiom,
% 0.32/0.57      ! [A: int,N: nat,B: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 0.32/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.57         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_le_imp_le_base
% 0.32/0.57  thf(fact_3672_power__inject__base,axiom,
% 0.32/0.57      ! [A: code_integer,N: nat,B: code_integer] :
% 0.32/0.57        ( ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 0.32/0.57          = ( power_8256067586552552935nteger @ B @ ( suc @ N ) ) )
% 0.32/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.57         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.57           => ( A = B ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % power_inject_base
% 0.33/0.57  thf(fact_3673_power__inject__base,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat,B: code_natural] :
% 0.33/0.57        ( ( ( power_7079662738309270450atural @ A @ ( suc @ N ) )
% 0.33/0.57          = ( power_7079662738309270450atural @ B @ ( suc @ N ) ) )
% 0.33/0.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.57         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.33/0.57           => ( A = B ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_inject_base
% 0.33/0.57  thf(fact_3674_power__inject__base,axiom,
% 0.33/0.57      ! [A: rat,N: nat,B: rat] :
% 0.33/0.57        ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.33/0.57          = ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.33/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.57         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.33/0.57           => ( A = B ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_inject_base
% 0.33/0.57  thf(fact_3675_power__inject__base,axiom,
% 0.33/0.57      ! [A: nat,N: nat,B: nat] :
% 0.33/0.57        ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.33/0.57          = ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.33/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.57         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.33/0.57           => ( A = B ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_inject_base
% 0.33/0.57  thf(fact_3676_power__inject__base,axiom,
% 0.33/0.57      ! [A: int,N: nat,B: int] :
% 0.33/0.57        ( ( ( power_power_int @ A @ ( suc @ N ) )
% 0.33/0.57          = ( power_power_int @ B @ ( suc @ N ) ) )
% 0.33/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.57         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.33/0.57           => ( A = B ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_inject_base
% 0.33/0.57  thf(fact_3677_power__gt1__lemma,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 0.33/0.57       => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1_lemma
% 0.33/0.57  thf(fact_3678_power__gt1__lemma,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.57       => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1_lemma
% 0.33/0.57  thf(fact_3679_power__gt1__lemma,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.57       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1_lemma
% 0.33/0.57  thf(fact_3680_power__gt1__lemma,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.57       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1_lemma
% 0.33/0.57  thf(fact_3681_power__gt1__lemma,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.57       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1_lemma
% 0.33/0.57  thf(fact_3682_power__less__power__Suc,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 0.33/0.57       => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N ) @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_power_Suc
% 0.33/0.57  thf(fact_3683_power__less__power__Suc,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.57       => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_power_Suc
% 0.33/0.57  thf(fact_3684_power__less__power__Suc,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.57       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_power_Suc
% 0.33/0.57  thf(fact_3685_power__less__power__Suc,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.57       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_power_Suc
% 0.33/0.57  thf(fact_3686_power__less__power__Suc,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.57       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_power_Suc
% 0.33/0.57  thf(fact_3687_power__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 0.33/0.57            = one_one_Code_integer ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 0.33/0.57            = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_0_left
% 0.33/0.57  thf(fact_3688_power__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.33/0.57            = one_one_rat ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.33/0.57            = zero_zero_rat ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_0_left
% 0.33/0.57  thf(fact_3689_power__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N )
% 0.33/0.57            = one_one_Code_natural ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N )
% 0.33/0.57            = zero_z2226904508553997617atural ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_0_left
% 0.33/0.57  thf(fact_3690_power__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( power_power_int @ zero_zero_int @ N )
% 0.33/0.57            = one_one_int ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( power_power_int @ zero_zero_int @ N )
% 0.33/0.57            = zero_zero_int ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_0_left
% 0.33/0.57  thf(fact_3691_power__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.33/0.57            = one_one_nat ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.33/0.57            = zero_zero_nat ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_0_left
% 0.33/0.57  thf(fact_3692_power__gt1,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 0.33/0.57       => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1
% 0.33/0.57  thf(fact_3693_power__gt1,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.57       => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1
% 0.33/0.57  thf(fact_3694_power__gt1,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.57       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1
% 0.33/0.57  thf(fact_3695_power__gt1,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.57       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1
% 0.33/0.57  thf(fact_3696_power__gt1,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.57       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_gt1
% 0.33/0.57  thf(fact_3697_power__less__imp__less__exp,axiom,
% 0.33/0.57      ! [A: code_natural,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 0.33/0.57       => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 0.33/0.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_imp_less_exp
% 0.33/0.57  thf(fact_3698_power__less__imp__less__exp,axiom,
% 0.33/0.57      ! [A: code_integer,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.57       => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.33/0.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_imp_less_exp
% 0.33/0.57  thf(fact_3699_power__less__imp__less__exp,axiom,
% 0.33/0.57      ! [A: rat,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.57       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.33/0.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_imp_less_exp
% 0.33/0.57  thf(fact_3700_power__less__imp__less__exp,axiom,
% 0.33/0.57      ! [A: nat,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.57       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.33/0.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_imp_less_exp
% 0.33/0.57  thf(fact_3701_power__less__imp__less__exp,axiom,
% 0.33/0.57      ! [A: int,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.57       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.33/0.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_less_imp_less_exp
% 0.33/0.57  thf(fact_3702_power__strict__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: code_natural] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 0.33/0.57         => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_increasing
% 0.33/0.57  thf(fact_3703_power__strict__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: code_integer] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.57         => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_increasing
% 0.33/0.57  thf(fact_3704_power__strict__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: rat] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.57         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_increasing
% 0.33/0.57  thf(fact_3705_power__strict__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: nat] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.57         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_increasing
% 0.33/0.57  thf(fact_3706_power__strict__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: int] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.57         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_increasing
% 0.33/0.57  thf(fact_3707_power__minus,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.33/0.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus
% 0.33/0.57  thf(fact_3708_power__minus,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.33/0.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus
% 0.33/0.57  thf(fact_3709_power__minus,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.33/0.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus
% 0.33/0.57  thf(fact_3710_power__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: code_integer] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.33/0.57         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_increasing
% 0.33/0.57  thf(fact_3711_power__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: code_natural] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ A )
% 0.33/0.57         => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_increasing
% 0.33/0.57  thf(fact_3712_power__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: rat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.33/0.57         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_increasing
% 0.33/0.57  thf(fact_3713_power__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.33/0.57         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_increasing
% 0.33/0.57  thf(fact_3714_power__increasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: int] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.33/0.57         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_increasing
% 0.33/0.57  thf(fact_3715_zero__power,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 0.33/0.57          = zero_z3403309356797280102nteger ) ) ).
% 0.33/0.57  
% 0.33/0.57  % zero_power
% 0.33/0.57  thf(fact_3716_zero__power,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.33/0.57          = zero_zero_rat ) ) ).
% 0.33/0.57  
% 0.33/0.57  % zero_power
% 0.33/0.57  thf(fact_3717_zero__power,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N )
% 0.33/0.57          = zero_z2226904508553997617atural ) ) ).
% 0.33/0.57  
% 0.33/0.57  % zero_power
% 0.33/0.57  thf(fact_3718_zero__power,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( power_power_int @ zero_zero_int @ N )
% 0.33/0.57          = zero_zero_int ) ) ).
% 0.33/0.57  
% 0.33/0.57  % zero_power
% 0.33/0.57  thf(fact_3719_zero__power,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.33/0.57          = zero_zero_nat ) ) ).
% 0.33/0.57  
% 0.33/0.57  % zero_power
% 0.33/0.57  thf(fact_3720_zero__le__power__abs,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 0.33/0.57  
% 0.33/0.57  % zero_le_power_abs
% 0.33/0.57  thf(fact_3721_zero__le__power__abs,axiom,
% 0.33/0.57      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 0.33/0.57  
% 0.33/0.57  % zero_le_power_abs
% 0.33/0.57  thf(fact_3722_zero__le__power__abs,axiom,
% 0.33/0.57      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 0.33/0.57  
% 0.33/0.57  % zero_le_power_abs
% 0.33/0.57  thf(fact_3723_fact__less__mono,axiom,
% 0.33/0.57      ! [M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.33/0.57       => ( ( ord_less_nat @ M @ N )
% 0.33/0.57         => ( ord_le6747313008572928689nteger @ ( semiri3624122377584611663nteger @ M ) @ ( semiri3624122377584611663nteger @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % fact_less_mono
% 0.33/0.57  thf(fact_3724_fact__less__mono,axiom,
% 0.33/0.57      ! [M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.33/0.57       => ( ( ord_less_nat @ M @ N )
% 0.33/0.57         => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % fact_less_mono
% 0.33/0.57  thf(fact_3725_fact__less__mono,axiom,
% 0.33/0.57      ! [M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.33/0.57       => ( ( ord_less_nat @ M @ N )
% 0.33/0.57         => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % fact_less_mono
% 0.33/0.57  thf(fact_3726_fact__less__mono,axiom,
% 0.33/0.57      ! [M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.33/0.57       => ( ( ord_less_nat @ M @ N )
% 0.33/0.57         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % fact_less_mono
% 0.33/0.57  thf(fact_3727_pochhammer__nonneg,axiom,
% 0.33/0.57      ! [X2: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ X2 )
% 0.33/0.57       => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( comm_s7406298101470620109atural @ X2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_nonneg
% 0.33/0.57  thf(fact_3728_pochhammer__nonneg,axiom,
% 0.33/0.57      ! [X2: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X2 )
% 0.33/0.57       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( comm_s8582702949713902594nteger @ X2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_nonneg
% 0.33/0.57  thf(fact_3729_pochhammer__nonneg,axiom,
% 0.33/0.57      ! [X2: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 0.33/0.57       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_nonneg
% 0.33/0.57  thf(fact_3730_pochhammer__nonneg,axiom,
% 0.33/0.57      ! [X2: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 0.33/0.57       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_nonneg
% 0.33/0.57  thf(fact_3731_pochhammer__nonneg,axiom,
% 0.33/0.57      ! [X2: int,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ zero_zero_int @ X2 )
% 0.33/0.57       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_nonneg
% 0.33/0.57  thf(fact_3732_pochhammer__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.33/0.57            = one_one_nat ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.33/0.57            = zero_zero_nat ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_0_left
% 0.33/0.57  thf(fact_3733_pochhammer__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.33/0.57            = one_one_int ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.33/0.57            = zero_zero_int ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_0_left
% 0.33/0.57  thf(fact_3734_pochhammer__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 0.33/0.57            = one_one_Code_integer ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 0.33/0.57            = zero_z3403309356797280102nteger ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_0_left
% 0.33/0.57  thf(fact_3735_pochhammer__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.33/0.57            = one_one_rat ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.33/0.57            = zero_zero_rat ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_0_left
% 0.33/0.57  thf(fact_3736_pochhammer__0__left,axiom,
% 0.33/0.57      ! [N: nat] :
% 0.33/0.57        ( ( ( N = zero_zero_nat )
% 0.33/0.57         => ( ( comm_s7406298101470620109atural @ zero_z2226904508553997617atural @ N )
% 0.33/0.57            = one_one_Code_natural ) )
% 0.33/0.57        & ( ( N != zero_zero_nat )
% 0.33/0.57         => ( ( comm_s7406298101470620109atural @ zero_z2226904508553997617atural @ N )
% 0.33/0.57            = zero_z2226904508553997617atural ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_0_left
% 0.33/0.57  thf(fact_3737_Suc__times__gbinomial,axiom,
% 0.33/0.57      ! [K: nat,A: rat] :
% 0.33/0.57        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 0.33/0.57        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % Suc_times_gbinomial
% 0.33/0.57  thf(fact_3738_gbinomial__absorption,axiom,
% 0.33/0.57      ! [K: nat,A: rat] :
% 0.33/0.57        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 0.33/0.57        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % gbinomial_absorption
% 0.33/0.57  thf(fact_3739_gbinomial__trinomial__revision,axiom,
% 0.33/0.57      ! [K: nat,M: nat,A: rat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ K @ M )
% 0.33/0.57       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 0.33/0.57          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % gbinomial_trinomial_revision
% 0.33/0.57  thf(fact_3740_power__Suc__less,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.57       => ( ( ord_le5570908160329646204atural @ A @ one_one_Code_natural )
% 0.33/0.57         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less
% 0.33/0.57  thf(fact_3741_power__Suc__less,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.57       => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.33/0.57         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less
% 0.33/0.57  thf(fact_3742_power__Suc__less,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.57       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.33/0.57         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less
% 0.33/0.57  thf(fact_3743_power__Suc__less,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.33/0.57       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.33/0.57         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less
% 0.33/0.57  thf(fact_3744_power__Suc__less,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ zero_zero_int @ A )
% 0.33/0.57       => ( ( ord_less_int @ A @ one_one_int )
% 0.33/0.57         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less
% 0.33/0.57  thf(fact_3745_power__Suc__le__self,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.57       => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.33/0.57         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_le_self
% 0.33/0.57  thf(fact_3746_power__Suc__le__self,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.57       => ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 0.33/0.57         => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_le_self
% 0.33/0.57  thf(fact_3747_power__Suc__le__self,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.57       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.33/0.57         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_le_self
% 0.33/0.57  thf(fact_3748_power__Suc__le__self,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.57       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.33/0.57         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_le_self
% 0.33/0.57  thf(fact_3749_power__Suc__le__self,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.57       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.33/0.57         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_le_self
% 0.33/0.57  thf(fact_3750_power__Suc__less__one,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.57       => ( ( ord_le5570908160329646204atural @ A @ one_one_Code_natural )
% 0.33/0.57         => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) @ one_one_Code_natural ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less_one
% 0.33/0.57  thf(fact_3751_power__Suc__less__one,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.57       => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.33/0.57         => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less_one
% 0.33/0.57  thf(fact_3752_power__Suc__less__one,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.57       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.33/0.57         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less_one
% 0.33/0.57  thf(fact_3753_power__Suc__less__one,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.33/0.57       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.33/0.57         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less_one
% 0.33/0.57  thf(fact_3754_power__Suc__less__one,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ zero_zero_int @ A )
% 0.33/0.57       => ( ( ord_less_int @ A @ one_one_int )
% 0.33/0.57         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_Suc_less_one
% 0.33/0.57  thf(fact_3755_power__strict__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: code_natural] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.57         => ( ( ord_le5570908160329646204atural @ A @ one_one_Code_natural )
% 0.33/0.57           => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N4 ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_decreasing
% 0.33/0.57  thf(fact_3756_power__strict__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: code_integer] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.57         => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.33/0.57           => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_decreasing
% 0.33/0.57  thf(fact_3757_power__strict__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: rat] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.33/0.57         => ( ( ord_less_rat @ A @ one_one_rat )
% 0.33/0.57           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_decreasing
% 0.33/0.57  thf(fact_3758_power__strict__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: nat] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.33/0.57         => ( ( ord_less_nat @ A @ one_one_nat )
% 0.33/0.57           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_decreasing
% 0.33/0.57  thf(fact_3759_power__strict__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: int] :
% 0.33/0.57        ( ( ord_less_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.33/0.57         => ( ( ord_less_int @ A @ one_one_int )
% 0.33/0.57           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_decreasing
% 0.33/0.57  thf(fact_3760_power__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: code_integer] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.57         => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.33/0.57           => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_decreasing
% 0.33/0.57  thf(fact_3761_power__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: code_natural] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.57         => ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 0.33/0.57           => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N4 ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_decreasing
% 0.33/0.57  thf(fact_3762_power__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: rat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.57         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.33/0.57           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_decreasing
% 0.33/0.57  thf(fact_3763_power__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.57         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.33/0.57           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_decreasing
% 0.33/0.57  thf(fact_3764_power__decreasing,axiom,
% 0.33/0.57      ! [N: nat,N4: nat,A: int] :
% 0.33/0.57        ( ( ord_less_eq_nat @ N @ N4 )
% 0.33/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.57         => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.33/0.57           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_decreasing
% 0.33/0.57  thf(fact_3765_power__eq__imp__eq__base,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat,B: code_integer] :
% 0.33/0.57        ( ( ( power_8256067586552552935nteger @ A @ N )
% 0.33/0.57          = ( power_8256067586552552935nteger @ B @ N ) )
% 0.33/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.57         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.33/0.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57             => ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_imp_eq_base
% 0.33/0.57  thf(fact_3766_power__eq__imp__eq__base,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat,B: code_natural] :
% 0.33/0.57        ( ( ( power_7079662738309270450atural @ A @ N )
% 0.33/0.57          = ( power_7079662738309270450atural @ B @ N ) )
% 0.33/0.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.57         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.33/0.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57             => ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_imp_eq_base
% 0.33/0.57  thf(fact_3767_power__eq__imp__eq__base,axiom,
% 0.33/0.57      ! [A: rat,N: nat,B: rat] :
% 0.33/0.57        ( ( ( power_power_rat @ A @ N )
% 0.33/0.57          = ( power_power_rat @ B @ N ) )
% 0.33/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.57         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.33/0.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57             => ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_imp_eq_base
% 0.33/0.57  thf(fact_3768_power__eq__imp__eq__base,axiom,
% 0.33/0.57      ! [A: nat,N: nat,B: nat] :
% 0.33/0.57        ( ( ( power_power_nat @ A @ N )
% 0.33/0.57          = ( power_power_nat @ B @ N ) )
% 0.33/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.57         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.33/0.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57             => ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_imp_eq_base
% 0.33/0.57  thf(fact_3769_power__eq__imp__eq__base,axiom,
% 0.33/0.57      ! [A: int,N: nat,B: int] :
% 0.33/0.57        ( ( ( power_power_int @ A @ N )
% 0.33/0.57          = ( power_power_int @ B @ N ) )
% 0.33/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.57         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.33/0.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57             => ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_imp_eq_base
% 0.33/0.57  thf(fact_3770_power__eq__iff__eq__base,axiom,
% 0.33/0.57      ! [N: nat,A: code_integer,B: code_integer] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.57         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.33/0.57           => ( ( ( power_8256067586552552935nteger @ A @ N )
% 0.33/0.57                = ( power_8256067586552552935nteger @ B @ N ) )
% 0.33/0.57              = ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_iff_eq_base
% 0.33/0.57  thf(fact_3771_power__eq__iff__eq__base,axiom,
% 0.33/0.57      ! [N: nat,A: code_natural,B: code_natural] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.57         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 0.33/0.57           => ( ( ( power_7079662738309270450atural @ A @ N )
% 0.33/0.57                = ( power_7079662738309270450atural @ B @ N ) )
% 0.33/0.57              = ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_iff_eq_base
% 0.33/0.57  thf(fact_3772_power__eq__iff__eq__base,axiom,
% 0.33/0.57      ! [N: nat,A: rat,B: rat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.57         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.33/0.57           => ( ( ( power_power_rat @ A @ N )
% 0.33/0.57                = ( power_power_rat @ B @ N ) )
% 0.33/0.57              = ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_iff_eq_base
% 0.33/0.57  thf(fact_3773_power__eq__iff__eq__base,axiom,
% 0.33/0.57      ! [N: nat,A: nat,B: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.57         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.33/0.57           => ( ( ( power_power_nat @ A @ N )
% 0.33/0.57                = ( power_power_nat @ B @ N ) )
% 0.33/0.57              = ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_iff_eq_base
% 0.33/0.57  thf(fact_3774_power__eq__iff__eq__base,axiom,
% 0.33/0.57      ! [N: nat,A: int,B: int] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.57         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.33/0.57           => ( ( ( power_power_int @ A @ N )
% 0.33/0.57                = ( power_power_int @ B @ N ) )
% 0.33/0.57              = ( A = B ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_iff_eq_base
% 0.33/0.57  thf(fact_3775_power__le__imp__le__exp,axiom,
% 0.33/0.57      ! [A: code_natural,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 0.33/0.57       => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 0.33/0.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_le_imp_le_exp
% 0.33/0.57  thf(fact_3776_power__le__imp__le__exp,axiom,
% 0.33/0.57      ! [A: code_integer,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.57       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.33/0.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_le_imp_le_exp
% 0.33/0.57  thf(fact_3777_power__le__imp__le__exp,axiom,
% 0.33/0.57      ! [A: rat,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.57       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.33/0.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_le_imp_le_exp
% 0.33/0.57  thf(fact_3778_power__le__imp__le__exp,axiom,
% 0.33/0.57      ! [A: nat,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.57       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.33/0.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_le_imp_le_exp
% 0.33/0.57  thf(fact_3779_power__le__imp__le__exp,axiom,
% 0.33/0.57      ! [A: int,M: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.57       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.33/0.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_le_imp_le_exp
% 0.33/0.57  thf(fact_3780_self__le__power,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % self_le_power
% 0.33/0.57  thf(fact_3781_self__le__power,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_le1926595141338095240atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % self_le_power
% 0.33/0.57  thf(fact_3782_self__le__power,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % self_le_power
% 0.33/0.57  thf(fact_3783_self__le__power,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % self_le_power
% 0.33/0.57  thf(fact_3784_self__le__power,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % self_le_power
% 0.33/0.57  thf(fact_3785_one__less__power,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % one_less_power
% 0.33/0.57  thf(fact_3786_one__less__power,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % one_less_power
% 0.33/0.57  thf(fact_3787_one__less__power,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ one_one_rat @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % one_less_power
% 0.33/0.57  thf(fact_3788_one__less__power,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ one_one_nat @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % one_less_power
% 0.33/0.57  thf(fact_3789_one__less__power,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ one_one_int @ A )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % one_less_power
% 0.33/0.57  thf(fact_3790_power__diff,axiom,
% 0.33/0.57      ! [A: nat,N: nat,M: nat] :
% 0.33/0.57        ( ( A != zero_zero_nat )
% 0.33/0.57       => ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.57         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 0.33/0.57            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_diff
% 0.33/0.57  thf(fact_3791_power__diff,axiom,
% 0.33/0.57      ! [A: int,N: nat,M: nat] :
% 0.33/0.57        ( ( A != zero_zero_int )
% 0.33/0.57       => ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.57         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 0.33/0.57            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_diff
% 0.33/0.57  thf(fact_3792_power__diff,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat,M: nat] :
% 0.33/0.57        ( ( A != zero_z3403309356797280102nteger )
% 0.33/0.57       => ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.57         => ( ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N ) )
% 0.33/0.57            = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_diff
% 0.33/0.57  thf(fact_3793_power__diff,axiom,
% 0.33/0.57      ! [A: rat,N: nat,M: nat] :
% 0.33/0.57        ( ( A != zero_zero_rat )
% 0.33/0.57       => ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.57         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 0.33/0.57            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_diff
% 0.33/0.57  thf(fact_3794_power__diff,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat,M: nat] :
% 0.33/0.57        ( ( A != zero_z2226904508553997617atural )
% 0.33/0.57       => ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.57         => ( ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N ) )
% 0.33/0.57            = ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_diff
% 0.33/0.57  thf(fact_3795_pochhammer__rec,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( comm_s7406298101470620109atural @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_2397367101498566445atural @ A @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec
% 0.33/0.57  thf(fact_3796_pochhammer__rec,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec
% 0.33/0.57  thf(fact_3797_pochhammer__rec,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec
% 0.33/0.57  thf(fact_3798_pochhammer__rec,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec
% 0.33/0.57  thf(fact_3799_pochhammer__rec,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec
% 0.33/0.57  thf(fact_3800_pochhammer__Suc,axiom,
% 0.33/0.57      ! [A: int,N: nat] :
% 0.33/0.57        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_Suc
% 0.33/0.57  thf(fact_3801_pochhammer__Suc,axiom,
% 0.33/0.57      ! [A: nat,N: nat] :
% 0.33/0.57        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_Suc
% 0.33/0.57  thf(fact_3802_pochhammer__Suc,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat] :
% 0.33/0.57        ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_Suc
% 0.33/0.57  thf(fact_3803_pochhammer__Suc,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_Suc
% 0.33/0.57  thf(fact_3804_pochhammer__Suc,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat] :
% 0.33/0.57        ( ( comm_s7406298101470620109atural @ A @ ( suc @ N ) )
% 0.33/0.57        = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ A @ N ) @ ( plus_p4538020629002901425atural @ A @ ( semiri3763490453095760265atural @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_Suc
% 0.33/0.57  thf(fact_3805_pochhammer__rec_H,axiom,
% 0.33/0.57      ! [Z2: int,N: nat] :
% 0.33/0.57        ( ( comm_s4660882817536571857er_int @ Z2 @ ( suc @ N ) )
% 0.33/0.57        = ( times_times_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec'
% 0.33/0.57  thf(fact_3806_pochhammer__rec_H,axiom,
% 0.33/0.57      ! [Z2: nat,N: nat] :
% 0.33/0.57        ( ( comm_s4663373288045622133er_nat @ Z2 @ ( suc @ N ) )
% 0.33/0.57        = ( times_times_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec'
% 0.33/0.57  thf(fact_3807_pochhammer__rec_H,axiom,
% 0.33/0.57      ! [Z2: code_integer,N: nat] :
% 0.33/0.57        ( ( comm_s8582702949713902594nteger @ Z2 @ ( suc @ N ) )
% 0.33/0.57        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z2 @ ( semiri4939895301339042750nteger @ N ) ) @ ( comm_s8582702949713902594nteger @ Z2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec'
% 0.33/0.57  thf(fact_3808_pochhammer__rec_H,axiom,
% 0.33/0.57      ! [Z2: rat,N: nat] :
% 0.33/0.57        ( ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N ) )
% 0.33/0.57        = ( times_times_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec'
% 0.33/0.57  thf(fact_3809_pochhammer__rec_H,axiom,
% 0.33/0.57      ! [Z2: code_natural,N: nat] :
% 0.33/0.57        ( ( comm_s7406298101470620109atural @ Z2 @ ( suc @ N ) )
% 0.33/0.57        = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ Z2 @ ( semiri3763490453095760265atural @ N ) ) @ ( comm_s7406298101470620109atural @ Z2 @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_rec'
% 0.33/0.57  thf(fact_3810_pochhammer__eq__0__iff,axiom,
% 0.33/0.57      ! [A: rat,N: nat] :
% 0.33/0.57        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.33/0.57          = zero_zero_rat )
% 0.33/0.57        = ( ? [K2: nat] :
% 0.33/0.57              ( ( ord_less_nat @ K2 @ N )
% 0.33/0.57              & ( A
% 0.33/0.57                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_eq_0_iff
% 0.33/0.57  thf(fact_3811_pochhammer__of__nat__eq__0__iff,axiom,
% 0.33/0.57      ! [N: nat,K: nat] :
% 0.33/0.57        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.33/0.57          = zero_zero_int )
% 0.33/0.57        = ( ord_less_nat @ N @ K ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_of_nat_eq_0_iff
% 0.33/0.57  thf(fact_3812_pochhammer__of__nat__eq__0__iff,axiom,
% 0.33/0.57      ! [N: nat,K: nat] :
% 0.33/0.57        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.33/0.57          = zero_z3403309356797280102nteger )
% 0.33/0.57        = ( ord_less_nat @ N @ K ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_of_nat_eq_0_iff
% 0.33/0.57  thf(fact_3813_pochhammer__of__nat__eq__0__iff,axiom,
% 0.33/0.57      ! [N: nat,K: nat] :
% 0.33/0.57        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.33/0.57          = zero_zero_rat )
% 0.33/0.57        = ( ord_less_nat @ N @ K ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_of_nat_eq_0_iff
% 0.33/0.57  thf(fact_3814_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.33/0.57      ! [N: nat,K: nat] :
% 0.33/0.57        ( ( ord_less_nat @ N @ K )
% 0.33/0.57       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.33/0.57          = zero_zero_int ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_of_nat_eq_0_lemma
% 0.33/0.57  thf(fact_3815_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.33/0.57      ! [N: nat,K: nat] :
% 0.33/0.57        ( ( ord_less_nat @ N @ K )
% 0.33/0.57       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.33/0.57          = zero_z3403309356797280102nteger ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_of_nat_eq_0_lemma
% 0.33/0.57  thf(fact_3816_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.33/0.57      ! [N: nat,K: nat] :
% 0.33/0.57        ( ( ord_less_nat @ N @ K )
% 0.33/0.57       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.33/0.57          = zero_zero_rat ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_of_nat_eq_0_lemma
% 0.33/0.57  thf(fact_3817_gbinomial__rec,axiom,
% 0.33/0.57      ! [A: rat,K: nat] :
% 0.33/0.57        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.33/0.57        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % gbinomial_rec
% 0.33/0.57  thf(fact_3818_gbinomial__factors,axiom,
% 0.33/0.57      ! [A: rat,K: nat] :
% 0.33/0.57        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.33/0.57        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % gbinomial_factors
% 0.33/0.57  thf(fact_3819_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.33/0.57      ! [K: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.57       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.33/0.57         != zero_zero_int ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_of_nat_eq_0_lemma'
% 0.33/0.57  thf(fact_3820_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.33/0.57      ! [K: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.57       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.33/0.57         != zero_z3403309356797280102nteger ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_of_nat_eq_0_lemma'
% 0.33/0.57  thf(fact_3821_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.33/0.57      ! [K: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.57       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.33/0.57         != zero_zero_rat ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_of_nat_eq_0_lemma'
% 0.33/0.57  thf(fact_3822_pochhammer__product_H,axiom,
% 0.33/0.57      ! [Z2: int,N: nat,M: nat] :
% 0.33/0.57        ( ( comm_s4660882817536571857er_int @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 0.33/0.57        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product'
% 0.33/0.57  thf(fact_3823_pochhammer__product_H,axiom,
% 0.33/0.57      ! [Z2: nat,N: nat,M: nat] :
% 0.33/0.57        ( ( comm_s4663373288045622133er_nat @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 0.33/0.57        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product'
% 0.33/0.57  thf(fact_3824_pochhammer__product_H,axiom,
% 0.33/0.57      ! [Z2: code_integer,N: nat,M: nat] :
% 0.33/0.57        ( ( comm_s8582702949713902594nteger @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 0.33/0.57        = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z2 @ N ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z2 @ ( semiri4939895301339042750nteger @ N ) ) @ M ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product'
% 0.33/0.57  thf(fact_3825_pochhammer__product_H,axiom,
% 0.33/0.57      ! [Z2: rat,N: nat,M: nat] :
% 0.33/0.57        ( ( comm_s4028243227959126397er_rat @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 0.33/0.57        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product'
% 0.33/0.57  thf(fact_3826_pochhammer__product_H,axiom,
% 0.33/0.57      ! [Z2: code_natural,N: nat,M: nat] :
% 0.33/0.57        ( ( comm_s7406298101470620109atural @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 0.33/0.57        = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ Z2 @ N ) @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ Z2 @ ( semiri3763490453095760265atural @ N ) ) @ M ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product'
% 0.33/0.57  thf(fact_3827_power__minus_H,axiom,
% 0.33/0.57      ! [X2: int,N: nat] :
% 0.33/0.57        ( ( nO_MATCH_int_int @ one_one_int @ X2 )
% 0.33/0.57       => ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ N )
% 0.33/0.57          = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ X2 @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus'
% 0.33/0.57  thf(fact_3828_power__minus_H,axiom,
% 0.33/0.57      ! [X2: code_integer,N: nat] :
% 0.33/0.57        ( ( nO_MAT8252062027627875367nteger @ one_one_Code_integer @ X2 )
% 0.33/0.57       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ N )
% 0.33/0.57          = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ X2 @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus'
% 0.33/0.57  thf(fact_3829_power__minus_H,axiom,
% 0.33/0.57      ! [X2: rat,N: nat] :
% 0.33/0.57        ( ( nO_MATCH_rat_rat @ one_one_rat @ X2 )
% 0.33/0.57       => ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ N )
% 0.33/0.57          = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ X2 @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus'
% 0.33/0.57  thf(fact_3830_power__strict__mono,axiom,
% 0.33/0.57      ! [A: code_natural,B: code_natural,N: nat] :
% 0.33/0.57        ( ( ord_le5570908160329646204atural @ A @ B )
% 0.33/0.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57           => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ B @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_mono
% 0.33/0.57  thf(fact_3831_power__strict__mono,axiom,
% 0.33/0.57      ! [A: code_integer,B: code_integer,N: nat] :
% 0.33/0.57        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.33/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57           => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_mono
% 0.33/0.57  thf(fact_3832_power__strict__mono,axiom,
% 0.33/0.57      ! [A: rat,B: rat,N: nat] :
% 0.33/0.57        ( ( ord_less_rat @ A @ B )
% 0.33/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.33/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57           => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_mono
% 0.33/0.57  thf(fact_3833_power__strict__mono,axiom,
% 0.33/0.57      ! [A: nat,B: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ A @ B )
% 0.33/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57           => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_mono
% 0.33/0.57  thf(fact_3834_power__strict__mono,axiom,
% 0.33/0.57      ! [A: int,B: int,N: nat] :
% 0.33/0.57        ( ( ord_less_int @ A @ B )
% 0.33/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57           => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_strict_mono
% 0.33/0.57  thf(fact_3835_power__diff__power__eq,axiom,
% 0.33/0.57      ! [A: nat,N: nat,M: nat] :
% 0.33/0.57        ( ( A != zero_zero_nat )
% 0.33/0.57       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.57           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.33/0.57              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.33/0.57          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.33/0.57           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.33/0.57              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_diff_power_eq
% 0.33/0.57  thf(fact_3836_power__diff__power__eq,axiom,
% 0.33/0.57      ! [A: int,N: nat,M: nat] :
% 0.33/0.57        ( ( A != zero_zero_int )
% 0.33/0.57       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.57           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.33/0.57              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.33/0.57          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.33/0.57           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.33/0.57              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_diff_power_eq
% 0.33/0.57  thf(fact_3837_power__diff__power__eq,axiom,
% 0.33/0.57      ! [A: code_integer,N: nat,M: nat] :
% 0.33/0.57        ( ( A != zero_z3403309356797280102nteger )
% 0.33/0.57       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.57           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.33/0.57              = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.33/0.57          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.33/0.57           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.33/0.57              = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_diff_power_eq
% 0.33/0.57  thf(fact_3838_power__diff__power__eq,axiom,
% 0.33/0.57      ! [A: code_natural,N: nat,M: nat] :
% 0.33/0.57        ( ( A != zero_z2226904508553997617atural )
% 0.33/0.57       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.57           => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 0.33/0.57              = ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.33/0.57          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.33/0.57           => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 0.33/0.57              = ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_diff_power_eq
% 0.33/0.57  thf(fact_3839_power__eq__if,axiom,
% 0.33/0.57      ( power_7079662738309270450atural
% 0.33/0.57      = ( ^ [P6: code_natural,M2: nat] : ( if_Code_natural @ ( M2 = zero_zero_nat ) @ one_one_Code_natural @ ( times_2397367101498566445atural @ P6 @ ( power_7079662738309270450atural @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_if
% 0.33/0.57  thf(fact_3840_power__eq__if,axiom,
% 0.33/0.57      ( power_8256067586552552935nteger
% 0.33/0.57      = ( ^ [P6: code_integer,M2: nat] : ( if_Code_integer @ ( M2 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P6 @ ( power_8256067586552552935nteger @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_if
% 0.33/0.57  thf(fact_3841_power__eq__if,axiom,
% 0.33/0.57      ( power_power_rat
% 0.33/0.57      = ( ^ [P6: rat,M2: nat] : ( if_rat @ ( M2 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_if
% 0.33/0.57  thf(fact_3842_power__eq__if,axiom,
% 0.33/0.57      ( power_power_nat
% 0.33/0.57      = ( ^ [P6: nat,M2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_if
% 0.33/0.57  thf(fact_3843_power__eq__if,axiom,
% 0.33/0.57      ( power_power_int
% 0.33/0.57      = ( ^ [P6: int,M2: nat] : ( if_int @ ( M2 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_eq_if
% 0.33/0.57  thf(fact_3844_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.33/0.57      ! [K: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.57       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 0.33/0.57          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % neg_one_power_add_eq_neg_one_power_diff
% 0.33/0.57  thf(fact_3845_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.33/0.57      ! [K: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.57       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 0.33/0.57          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % neg_one_power_add_eq_neg_one_power_diff
% 0.33/0.57  thf(fact_3846_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.33/0.57      ! [K: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.57       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 0.33/0.57          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % neg_one_power_add_eq_neg_one_power_diff
% 0.33/0.57  thf(fact_3847_power__minus__mult,axiom,
% 0.33/0.57      ! [N: nat,A: code_integer] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.33/0.57          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus_mult
% 0.33/0.57  thf(fact_3848_power__minus__mult,axiom,
% 0.33/0.57      ! [N: nat,A: rat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.33/0.57          = ( power_power_rat @ A @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus_mult
% 0.33/0.57  thf(fact_3849_power__minus__mult,axiom,
% 0.33/0.57      ! [N: nat,A: nat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.33/0.57          = ( power_power_nat @ A @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus_mult
% 0.33/0.57  thf(fact_3850_power__minus__mult,axiom,
% 0.33/0.57      ! [N: nat,A: int] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.33/0.57          = ( power_power_int @ A @ N ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % power_minus_mult
% 0.33/0.57  thf(fact_3851_gbinomial__reduce__nat,axiom,
% 0.33/0.57      ! [K: nat,A: rat] :
% 0.33/0.57        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.57       => ( ( gbinomial_rat @ A @ K )
% 0.33/0.57          = ( 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 ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % gbinomial_reduce_nat
% 0.33/0.57  thf(fact_3852_pochhammer__product,axiom,
% 0.33/0.57      ! [M: nat,N: nat,Z2: int] :
% 0.33/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.57       => ( ( comm_s4660882817536571857er_int @ Z2 @ N )
% 0.33/0.57          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product
% 0.33/0.57  thf(fact_3853_pochhammer__product,axiom,
% 0.33/0.57      ! [M: nat,N: nat,Z2: nat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.57       => ( ( comm_s4663373288045622133er_nat @ Z2 @ N )
% 0.33/0.57          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product
% 0.33/0.57  thf(fact_3854_pochhammer__product,axiom,
% 0.33/0.57      ! [M: nat,N: nat,Z2: code_integer] :
% 0.33/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.57       => ( ( comm_s8582702949713902594nteger @ Z2 @ N )
% 0.33/0.57          = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z2 @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z2 @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product
% 0.33/0.57  thf(fact_3855_pochhammer__product,axiom,
% 0.33/0.57      ! [M: nat,N: nat,Z2: rat] :
% 0.33/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.57       => ( ( comm_s4028243227959126397er_rat @ Z2 @ N )
% 0.33/0.57          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product
% 0.33/0.57  thf(fact_3856_pochhammer__product,axiom,
% 0.33/0.57      ! [M: nat,N: nat,Z2: code_natural] :
% 0.33/0.57        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.57       => ( ( comm_s7406298101470620109atural @ Z2 @ N )
% 0.33/0.57          = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ Z2 @ M ) @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ Z2 @ ( semiri3763490453095760265atural @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_product
% 0.33/0.57  thf(fact_3857_fact__num__eq__if,axiom,
% 0.33/0.57      ( semiri1406184849735516958ct_int
% 0.33/0.57      = ( ^ [M2: nat] : ( if_int @ ( M2 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % fact_num_eq_if
% 0.33/0.57  thf(fact_3858_fact__num__eq__if,axiom,
% 0.33/0.57      ( semiri3624122377584611663nteger
% 0.33/0.57      = ( ^ [M2: nat] : ( if_Code_integer @ ( M2 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % fact_num_eq_if
% 0.33/0.57  thf(fact_3859_fact__num__eq__if,axiom,
% 0.33/0.57      ( semiri773545260158071498ct_rat
% 0.33/0.57      = ( ^ [M2: nat] : ( if_rat @ ( M2 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % fact_num_eq_if
% 0.33/0.57  thf(fact_3860_fact__num__eq__if,axiom,
% 0.33/0.57      ( semiri2447717529341329178atural
% 0.33/0.57      = ( ^ [M2: nat] : ( if_Code_natural @ ( M2 = zero_zero_nat ) @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri2447717529341329178atural @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % fact_num_eq_if
% 0.33/0.57  thf(fact_3861_fact__num__eq__if,axiom,
% 0.33/0.57      ( semiri1408675320244567234ct_nat
% 0.33/0.57      = ( ^ [M2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % fact_num_eq_if
% 0.33/0.57  thf(fact_3862_gbinomial__code,axiom,
% 0.33/0.57      ( gbinomial_rat
% 0.33/0.57      = ( ^ [A2: rat,K2: nat] :
% 0.33/0.57            ( if_rat @ ( K2 = zero_zero_nat ) @ one_one_rat
% 0.33/0.57            @ ( divide_divide_rat
% 0.33/0.57              @ ( set_fo1949268297981939178at_rat
% 0.33/0.57                @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A2 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 0.33/0.57                @ zero_zero_nat
% 0.33/0.57                @ ( minus_minus_nat @ K2 @ one_one_nat )
% 0.33/0.57                @ one_one_rat )
% 0.33/0.57              @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % gbinomial_code
% 0.33/0.57  thf(fact_3863_pochhammer__code,axiom,
% 0.33/0.57      ( comm_s4660882817536571857er_int
% 0.33/0.57      = ( ^ [A2: int,N3: nat] :
% 0.33/0.57            ( if_int @ ( N3 = zero_zero_nat ) @ one_one_int
% 0.33/0.57            @ ( set_fo2581907887559384638at_int
% 0.33/0.57              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A2 @ ( semiri1314217659103216013at_int @ O ) ) )
% 0.33/0.57              @ zero_zero_nat
% 0.33/0.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.33/0.57              @ one_one_int ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_code
% 0.33/0.57  thf(fact_3864_pochhammer__code,axiom,
% 0.33/0.57      ( comm_s8582702949713902594nteger
% 0.33/0.57      = ( ^ [A2: code_integer,N3: nat] :
% 0.33/0.57            ( if_Code_integer @ ( N3 = zero_zero_nat ) @ one_one_Code_integer
% 0.33/0.57            @ ( set_fo1084959871951514735nteger
% 0.33/0.57              @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ ( semiri4939895301339042750nteger @ O ) ) )
% 0.33/0.57              @ zero_zero_nat
% 0.33/0.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.33/0.57              @ one_one_Code_integer ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_code
% 0.33/0.57  thf(fact_3865_pochhammer__code,axiom,
% 0.33/0.57      ( comm_s4028243227959126397er_rat
% 0.33/0.57      = ( ^ [A2: rat,N3: nat] :
% 0.33/0.57            ( if_rat @ ( N3 = zero_zero_nat ) @ one_one_rat
% 0.33/0.57            @ ( set_fo1949268297981939178at_rat
% 0.33/0.57              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A2 @ ( semiri681578069525770553at_rat @ O ) ) )
% 0.33/0.57              @ zero_zero_nat
% 0.33/0.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.33/0.57              @ one_one_rat ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_code
% 0.33/0.57  thf(fact_3866_pochhammer__code,axiom,
% 0.33/0.57      ( comm_s7406298101470620109atural
% 0.33/0.57      = ( ^ [A2: code_natural,N3: nat] :
% 0.33/0.57            ( if_Code_natural @ ( N3 = zero_zero_nat ) @ one_one_Code_natural
% 0.33/0.57            @ ( set_fo9131927060563008058atural
% 0.33/0.57              @ ^ [O: nat] : ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A2 @ ( semiri3763490453095760265atural @ O ) ) )
% 0.33/0.57              @ zero_zero_nat
% 0.33/0.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.33/0.57              @ one_one_Code_natural ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_code
% 0.33/0.57  thf(fact_3867_pochhammer__code,axiom,
% 0.33/0.57      ( comm_s4663373288045622133er_nat
% 0.33/0.57      = ( ^ [A2: nat,N3: nat] :
% 0.33/0.57            ( if_nat @ ( N3 = zero_zero_nat ) @ one_one_nat
% 0.33/0.57            @ ( set_fo2584398358068434914at_nat
% 0.33/0.57              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A2 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 0.33/0.57              @ zero_zero_nat
% 0.33/0.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 0.33/0.57              @ one_one_nat ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % pochhammer_code
% 0.33/0.57  thf(fact_3868_slice__nth,axiom,
% 0.33/0.57      ! [From: nat,To: nat,Xs: list_nat,I: nat] :
% 0.33/0.57        ( ( ord_less_nat @ From @ To )
% 0.33/0.57       => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 0.33/0.57         => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 0.33/0.57           => ( ( nth_nat @ ( slice_nat @ From @ To @ Xs ) @ I )
% 0.33/0.57              = ( nth_nat @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % slice_nth
% 0.33/0.57  thf(fact_3869_slice__nth,axiom,
% 0.33/0.57      ! [From: nat,To: nat,Xs: list_int,I: nat] :
% 0.33/0.57        ( ( ord_less_nat @ From @ To )
% 0.33/0.57       => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 0.33/0.57         => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 0.33/0.57           => ( ( nth_int @ ( slice_int @ From @ To @ Xs ) @ I )
% 0.33/0.57              = ( nth_int @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % slice_nth
% 0.33/0.57  thf(fact_3870_slice__nth,axiom,
% 0.33/0.57      ! [From: nat,To: nat,Xs: list_o,I: nat] :
% 0.33/0.57        ( ( ord_less_nat @ From @ To )
% 0.33/0.57       => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 0.33/0.57         => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 0.33/0.57           => ( ( nth_o @ ( slice_o @ From @ To @ Xs ) @ I )
% 0.33/0.57              = ( nth_o @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % slice_nth
% 0.33/0.57  thf(fact_3871_split__pos__lemma,axiom,
% 0.33/0.57      ! [K: int,P: int > int > $o,N: int] :
% 0.33/0.57        ( ( ord_less_int @ zero_zero_int @ K )
% 0.33/0.57       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.33/0.57          = ( ! [I2: int,J3: int] :
% 0.33/0.57                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.33/0.57                  & ( ord_less_int @ J3 @ K )
% 0.33/0.57                  & ( N
% 0.33/0.57                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 0.33/0.57               => ( P @ I2 @ J3 ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % split_pos_lemma
% 0.33/0.57  thf(fact_3872_split__neg__lemma,axiom,
% 0.33/0.57      ! [K: int,P: int > int > $o,N: int] :
% 0.33/0.57        ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.57       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.33/0.57          = ( ! [I2: int,J3: int] :
% 0.33/0.57                ( ( ( ord_less_int @ K @ J3 )
% 0.33/0.57                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.33/0.57                  & ( N
% 0.33/0.57                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 0.33/0.57               => ( P @ I2 @ J3 ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % split_neg_lemma
% 0.33/0.57  thf(fact_3873_verit__le__mono__div__int,axiom,
% 0.33/0.57      ! [A4: int,B4: int,N: int] :
% 0.33/0.57        ( ( ord_less_int @ A4 @ B4 )
% 0.33/0.57       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.33/0.57         => ( ord_less_eq_int
% 0.33/0.57            @ ( plus_plus_int @ ( divide_divide_int @ A4 @ N )
% 0.33/0.57              @ ( if_int
% 0.33/0.57                @ ( ( modulo_modulo_int @ B4 @ N )
% 0.33/0.57                  = zero_zero_int )
% 0.33/0.57                @ one_one_int
% 0.33/0.57                @ zero_zero_int ) )
% 0.33/0.57            @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % verit_le_mono_div_int
% 0.33/0.57  thf(fact_3874_verit__le__mono__div,axiom,
% 0.33/0.57      ! [A4: nat,B4: nat,N: nat] :
% 0.33/0.57        ( ( ord_less_nat @ A4 @ B4 )
% 0.33/0.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.57         => ( ord_less_eq_nat
% 0.33/0.57            @ ( plus_plus_nat @ ( divide_divide_nat @ A4 @ N )
% 0.33/0.57              @ ( if_nat
% 0.33/0.57                @ ( ( modulo_modulo_nat @ B4 @ N )
% 0.33/0.57                  = zero_zero_nat )
% 0.33/0.57                @ one_one_nat
% 0.33/0.57                @ zero_zero_nat ) )
% 0.33/0.57            @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % verit_le_mono_div
% 0.33/0.57  thf(fact_3875_le__divide__eq__numeral_I2_J,axiom,
% 0.33/0.57      ! [W2: num,B: rat,C: rat] :
% 0.33/0.57        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.33/0.57        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.57           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 0.33/0.57          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.57           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.57               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.33/0.57              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.57               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % le_divide_eq_numeral(2)
% 0.33/0.57  thf(fact_3876_numeral__eq__iff,axiom,
% 0.33/0.57      ! [M: num,N: num] :
% 0.33/0.57        ( ( ( numeral_numeral_int @ M )
% 0.33/0.57          = ( numeral_numeral_int @ N ) )
% 0.33/0.57        = ( M = N ) ) ).
% 0.33/0.57  
% 0.33/0.57  % numeral_eq_iff
% 0.33/0.57  thf(fact_3877_numeral__eq__iff,axiom,
% 0.33/0.57      ! [M: num,N: num] :
% 0.33/0.57        ( ( ( numeral_numeral_nat @ M )
% 0.33/0.57          = ( numeral_numeral_nat @ N ) )
% 0.33/0.57        = ( M = N ) ) ).
% 0.33/0.57  
% 0.33/0.57  % numeral_eq_iff
% 0.33/0.57  thf(fact_3878_numeral__eq__iff,axiom,
% 0.33/0.57      ! [M: num,N: num] :
% 0.33/0.57        ( ( ( numera6620942414471956472nteger @ M )
% 0.33/0.57          = ( numera6620942414471956472nteger @ N ) )
% 0.33/0.57        = ( M = N ) ) ).
% 0.33/0.57  
% 0.33/0.57  % numeral_eq_iff
% 0.33/0.57  thf(fact_3879_numeral__eq__iff,axiom,
% 0.33/0.57      ! [M: num,N: num] :
% 0.33/0.57        ( ( ( numeral_numeral_rat @ M )
% 0.33/0.57          = ( numeral_numeral_rat @ N ) )
% 0.33/0.57        = ( M = N ) ) ).
% 0.33/0.57  
% 0.33/0.57  % numeral_eq_iff
% 0.33/0.57  thf(fact_3880_numeral__eq__iff,axiom,
% 0.33/0.57      ! [M: num,N: num] :
% 0.33/0.57        ( ( ( numera5444537566228673987atural @ M )
% 0.33/0.57          = ( numera5444537566228673987atural @ N ) )
% 0.33/0.57        = ( M = N ) ) ).
% 0.33/0.57  
% 0.33/0.57  % numeral_eq_iff
% 0.33/0.57  thf(fact_3881_int__eq__iff__numeral,axiom,
% 0.33/0.57      ! [M: nat,V: num] :
% 0.33/0.57        ( ( ( semiri1314217659103216013at_int @ M )
% 0.33/0.57          = ( numeral_numeral_int @ V ) )
% 0.33/0.57        = ( M
% 0.33/0.57          = ( numeral_numeral_nat @ V ) ) ) ).
% 0.33/0.57  
% 0.33/0.57  % int_eq_iff_numeral
% 0.33/0.57  thf(fact_3882_nat__numeral,axiom,
% 0.33/0.57      ! [K: num] :
% 0.33/0.57        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 0.33/0.57        = ( numeral_numeral_nat @ K ) ) ).
% 0.33/0.57  
% 0.33/0.57  % nat_numeral
% 0.33/0.57  thf(fact_3883_numeral__le__iff,axiom,
% 0.33/0.57      ! [M: num,N: num] :
% 0.33/0.57        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.57        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_le_iff
% 0.33/0.58  thf(fact_3884_numeral__le__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 0.33/0.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_le_iff
% 0.33/0.58  thf(fact_3885_numeral__le__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_le_iff
% 0.33/0.58  thf(fact_3886_numeral__le__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_le_iff
% 0.33/0.58  thf(fact_3887_numeral__le__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_le_iff
% 0.33/0.58  thf(fact_3888_numeral__less__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( ord_less_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_less_iff
% 0.33/0.58  thf(fact_3889_numeral__less__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( ord_less_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_less_iff
% 0.33/0.58  thf(fact_3890_numeral__less__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.58        = ( ord_less_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_less_iff
% 0.33/0.58  thf(fact_3891_numeral__less__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( ord_less_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_less_iff
% 0.33/0.58  thf(fact_3892_numeral__less__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 0.33/0.58        = ( ord_less_num @ M @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_less_iff
% 0.33/0.58  thf(fact_3893_numeral__plus__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_plus_numeral
% 0.33/0.58  thf(fact_3894_numeral__plus__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_plus_numeral
% 0.33/0.58  thf(fact_3895_numeral__plus__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.58        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_plus_numeral
% 0.33/0.58  thf(fact_3896_numeral__plus__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_plus_numeral
% 0.33/0.58  thf(fact_3897_numeral__plus__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 0.33/0.58        = ( numera5444537566228673987atural @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_plus_numeral
% 0.33/0.58  thf(fact_3898_add__numeral__left,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: int] :
% 0.33/0.58        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % add_numeral_left
% 0.33/0.58  thf(fact_3899_add__numeral__left,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: nat] :
% 0.33/0.58        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % add_numeral_left
% 0.33/0.58  thf(fact_3900_add__numeral__left,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: code_integer] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % add_numeral_left
% 0.33/0.58  thf(fact_3901_add__numeral__left,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: rat] :
% 0.33/0.58        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % add_numeral_left
% 0.33/0.58  thf(fact_3902_add__numeral__left,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: code_natural] :
% 0.33/0.58        ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % add_numeral_left
% 0.33/0.58  thf(fact_3903_numeral__times__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_times_numeral
% 0.33/0.58  thf(fact_3904_numeral__times__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_times_numeral
% 0.33/0.58  thf(fact_3905_numeral__times__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.58        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_times_numeral
% 0.33/0.58  thf(fact_3906_numeral__times__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_times_numeral
% 0.33/0.58  thf(fact_3907_numeral__times__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 0.33/0.58        = ( numera5444537566228673987atural @ ( times_times_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_times_numeral
% 0.33/0.58  thf(fact_3908_mult__numeral__left__semiring__numeral,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: int] :
% 0.33/0.58        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_numeral_left_semiring_numeral
% 0.33/0.58  thf(fact_3909_mult__numeral__left__semiring__numeral,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: nat] :
% 0.33/0.58        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_numeral_left_semiring_numeral
% 0.33/0.58  thf(fact_3910_mult__numeral__left__semiring__numeral,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: code_integer] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_numeral_left_semiring_numeral
% 0.33/0.58  thf(fact_3911_mult__numeral__left__semiring__numeral,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: rat] :
% 0.33/0.58        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_numeral_left_semiring_numeral
% 0.33/0.58  thf(fact_3912_mult__numeral__left__semiring__numeral,axiom,
% 0.33/0.58      ! [V: num,W2: num,Z2: code_natural] :
% 0.33/0.58        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ W2 ) @ Z2 ) )
% 0.33/0.58        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_numeral_left_semiring_numeral
% 0.33/0.58  thf(fact_3913_neg__numeral__eq__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.33/0.58          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.58        = ( M = N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_eq_iff
% 0.33/0.58  thf(fact_3914_neg__numeral__eq__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.33/0.58          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.33/0.58        = ( M = N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_eq_iff
% 0.33/0.58  thf(fact_3915_neg__numeral__eq__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.33/0.58          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.33/0.58        = ( M = N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_eq_iff
% 0.33/0.58  thf(fact_3916_power__zero__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( numeral_numeral_nat @ K ) )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % power_zero_numeral
% 0.33/0.58  thf(fact_3917_power__zero__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 0.33/0.58        = zero_zero_rat ) ).
% 0.33/0.58  
% 0.33/0.58  % power_zero_numeral
% 0.33/0.58  thf(fact_3918_power__zero__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ ( numeral_numeral_nat @ K ) )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % power_zero_numeral
% 0.33/0.58  thf(fact_3919_power__zero__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % power_zero_numeral
% 0.33/0.58  thf(fact_3920_power__zero__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % power_zero_numeral
% 0.33/0.58  thf(fact_3921_mod__self,axiom,
% 0.33/0.58      ! [A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ A @ A )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_self
% 0.33/0.58  thf(fact_3922_mod__self,axiom,
% 0.33/0.58      ! [A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ A @ A )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_self
% 0.33/0.58  thf(fact_3923_mod__self,axiom,
% 0.33/0.58      ! [A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ A @ A )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_self
% 0.33/0.58  thf(fact_3924_mod__self,axiom,
% 0.33/0.58      ! [A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ A @ A )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_self
% 0.33/0.58  thf(fact_3925_mod__by__0,axiom,
% 0.33/0.58      ! [A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_by_0
% 0.33/0.58  thf(fact_3926_mod__by__0,axiom,
% 0.33/0.58      ! [A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_by_0
% 0.33/0.58  thf(fact_3927_mod__by__0,axiom,
% 0.33/0.58      ! [A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_by_0
% 0.33/0.58  thf(fact_3928_mod__by__0,axiom,
% 0.33/0.58      ! [A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ A @ zero_z2226904508553997617atural )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_by_0
% 0.33/0.58  thf(fact_3929_mod__0,axiom,
% 0.33/0.58      ! [A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_0
% 0.33/0.58  thf(fact_3930_mod__0,axiom,
% 0.33/0.58      ! [A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_0
% 0.33/0.58  thf(fact_3931_mod__0,axiom,
% 0.33/0.58      ! [A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_0
% 0.33/0.58  thf(fact_3932_mod__0,axiom,
% 0.33/0.58      ! [A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_0
% 0.33/0.58  thf(fact_3933_bits__mod__0,axiom,
% 0.33/0.58      ! [A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_0
% 0.33/0.58  thf(fact_3934_bits__mod__0,axiom,
% 0.33/0.58      ! [A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_0
% 0.33/0.58  thf(fact_3935_bits__mod__0,axiom,
% 0.33/0.58      ! [A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_0
% 0.33/0.58  thf(fact_3936_bits__mod__0,axiom,
% 0.33/0.58      ! [A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_0
% 0.33/0.58  thf(fact_3937_power__add__numeral,axiom,
% 0.33/0.58      ! [A: code_integer,M: num,N: num] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.33/0.58        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_add_numeral
% 0.33/0.58  thf(fact_3938_power__add__numeral,axiom,
% 0.33/0.58      ! [A: rat,M: num,N: num] :
% 0.33/0.58        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.33/0.58        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_add_numeral
% 0.33/0.58  thf(fact_3939_power__add__numeral,axiom,
% 0.33/0.58      ! [A: nat,M: num,N: num] :
% 0.33/0.58        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.33/0.58        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_add_numeral
% 0.33/0.58  thf(fact_3940_power__add__numeral,axiom,
% 0.33/0.58      ! [A: int,M: num,N: num] :
% 0.33/0.58        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.33/0.58        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_add_numeral
% 0.33/0.58  thf(fact_3941_power__add__numeral2,axiom,
% 0.33/0.58      ! [A: code_integer,M: num,N: num,B: code_integer] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.33/0.58        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_add_numeral2
% 0.33/0.58  thf(fact_3942_power__add__numeral2,axiom,
% 0.33/0.58      ! [A: rat,M: num,N: num,B: rat] :
% 0.33/0.58        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.33/0.58        = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_add_numeral2
% 0.33/0.58  thf(fact_3943_power__add__numeral2,axiom,
% 0.33/0.58      ! [A: nat,M: num,N: num,B: nat] :
% 0.33/0.58        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.33/0.58        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_add_numeral2
% 0.33/0.58  thf(fact_3944_power__add__numeral2,axiom,
% 0.33/0.58      ! [A: int,M: num,N: num,B: int] :
% 0.33/0.58        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.33/0.58        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_add_numeral2
% 0.33/0.58  thf(fact_3945_of__nat__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_numeral
% 0.33/0.58  thf(fact_3946_of__nat__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( numeral_numeral_nat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_numeral
% 0.33/0.58  thf(fact_3947_of__nat__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( semiri4939895301339042750nteger @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_numeral
% 0.33/0.58  thf(fact_3948_of__nat__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_numeral
% 0.33/0.58  thf(fact_3949_of__nat__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( semiri3763490453095760265atural @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( numera5444537566228673987atural @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_numeral
% 0.33/0.58  thf(fact_3950_mod__add__self1,axiom,
% 0.33/0.58      ! [B: int,A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.33/0.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_self1
% 0.33/0.58  thf(fact_3951_mod__add__self1,axiom,
% 0.33/0.58      ! [B: nat,A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.33/0.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_self1
% 0.33/0.58  thf(fact_3952_mod__add__self1,axiom,
% 0.33/0.58      ! [B: code_integer,A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.33/0.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_self1
% 0.33/0.58  thf(fact_3953_mod__add__self1,axiom,
% 0.33/0.58      ! [B: code_natural,A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 0.33/0.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_self1
% 0.33/0.58  thf(fact_3954_mod__add__self2,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.33/0.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_self2
% 0.33/0.58  thf(fact_3955_mod__add__self2,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.33/0.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_self2
% 0.33/0.58  thf(fact_3956_mod__add__self2,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.33/0.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_self2
% 0.33/0.58  thf(fact_3957_mod__add__self2,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 0.33/0.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_self2
% 0.33/0.58  thf(fact_3958_abs__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % abs_numeral
% 0.33/0.58  thf(fact_3959_abs__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.58        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % abs_numeral
% 0.33/0.58  thf(fact_3960_abs__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % abs_numeral
% 0.33/0.58  thf(fact_3961_of__int__eq__numeral__iff,axiom,
% 0.33/0.58      ! [Z2: int,N: num] :
% 0.33/0.58        ( ( ( ring_1_of_int_int @ Z2 )
% 0.33/0.58          = ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( Z2
% 0.33/0.58          = ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_eq_numeral_iff
% 0.33/0.58  thf(fact_3962_of__int__eq__numeral__iff,axiom,
% 0.33/0.58      ! [Z2: int,N: num] :
% 0.33/0.58        ( ( ( ring_18347121197199848620nteger @ Z2 )
% 0.33/0.58          = ( numera6620942414471956472nteger @ N ) )
% 0.33/0.58        = ( Z2
% 0.33/0.58          = ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_eq_numeral_iff
% 0.33/0.58  thf(fact_3963_of__int__eq__numeral__iff,axiom,
% 0.33/0.58      ! [Z2: int,N: num] :
% 0.33/0.58        ( ( ( ring_1_of_int_rat @ Z2 )
% 0.33/0.58          = ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( Z2
% 0.33/0.58          = ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_eq_numeral_iff
% 0.33/0.58  thf(fact_3964_of__int__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 0.33/0.58        = ( numeral_numeral_int @ K ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_numeral
% 0.33/0.58  thf(fact_3965_of__int__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( ring_18347121197199848620nteger @ ( numeral_numeral_int @ K ) )
% 0.33/0.58        = ( numera6620942414471956472nteger @ K ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_numeral
% 0.33/0.58  thf(fact_3966_of__int__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 0.33/0.58        = ( numeral_numeral_rat @ K ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_numeral
% 0.33/0.58  thf(fact_3967_power__int__add__numeral,axiom,
% 0.33/0.58      ! [X2: rat,M: num,N: num] :
% 0.33/0.58        ( ( times_times_rat @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ M ) ) @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.58        = ( power_int_rat @ X2 @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_int_add_numeral
% 0.33/0.58  thf(fact_3968_power__int__add__numeral2,axiom,
% 0.33/0.58      ! [X2: rat,M: num,N: num,B: rat] :
% 0.33/0.58        ( ( times_times_rat @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ M ) ) @ ( times_times_rat @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ N ) ) @ B ) )
% 0.33/0.58        = ( times_times_rat @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_int_add_numeral2
% 0.33/0.58  thf(fact_3969_floor__numeral,axiom,
% 0.33/0.58      ! [V: num] :
% 0.33/0.58        ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 0.33/0.58        = ( numeral_numeral_int @ V ) ) ).
% 0.33/0.58  
% 0.33/0.58  % floor_numeral
% 0.33/0.58  thf(fact_3970_ceiling__numeral,axiom,
% 0.33/0.58      ! [V: num] :
% 0.33/0.58        ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 0.33/0.58        = ( numeral_numeral_int @ V ) ) ).
% 0.33/0.58  
% 0.33/0.58  % ceiling_numeral
% 0.33/0.58  thf(fact_3971_distrib__right__numeral,axiom,
% 0.33/0.58      ! [A: int,B: int,V: num] :
% 0.33/0.58        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.33/0.58        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_right_numeral
% 0.33/0.58  thf(fact_3972_distrib__right__numeral,axiom,
% 0.33/0.58      ! [A: nat,B: nat,V: num] :
% 0.33/0.58        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 0.33/0.58        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_right_numeral
% 0.33/0.58  thf(fact_3973_distrib__right__numeral,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer,V: num] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_right_numeral
% 0.33/0.58  thf(fact_3974_distrib__right__numeral,axiom,
% 0.33/0.58      ! [A: rat,B: rat,V: num] :
% 0.33/0.58        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.33/0.58        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_right_numeral
% 0.33/0.58  thf(fact_3975_distrib__right__numeral,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural,V: num] :
% 0.33/0.58        ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ ( numera5444537566228673987atural @ V ) )
% 0.33/0.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ V ) ) @ ( times_2397367101498566445atural @ B @ ( numera5444537566228673987atural @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_right_numeral
% 0.33/0.58  thf(fact_3976_distrib__left__numeral,axiom,
% 0.33/0.58      ! [V: num,B: int,C: int] :
% 0.33/0.58        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 0.33/0.58        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_left_numeral
% 0.33/0.58  thf(fact_3977_distrib__left__numeral,axiom,
% 0.33/0.58      ! [V: num,B: nat,C: nat] :
% 0.33/0.58        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.33/0.58        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_left_numeral
% 0.33/0.58  thf(fact_3978_distrib__left__numeral,axiom,
% 0.33/0.58      ! [V: num,B: code_integer,C: code_integer] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_left_numeral
% 0.33/0.58  thf(fact_3979_distrib__left__numeral,axiom,
% 0.33/0.58      ! [V: num,B: rat,C: rat] :
% 0.33/0.58        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 0.33/0.58        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_left_numeral
% 0.33/0.58  thf(fact_3980_distrib__left__numeral,axiom,
% 0.33/0.58      ! [V: num,B: code_natural,C: code_natural] :
% 0.33/0.58        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ B @ C ) )
% 0.33/0.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ B ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % distrib_left_numeral
% 0.33/0.58  thf(fact_3981_neg__numeral__le__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.33/0.58        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_iff
% 0.33/0.58  thf(fact_3982_neg__numeral__le__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.33/0.58        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_iff
% 0.33/0.58  thf(fact_3983_neg__numeral__le__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.58        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_iff
% 0.33/0.58  thf(fact_3984_left__diff__distrib__numeral,axiom,
% 0.33/0.58      ! [A: int,B: int,V: num] :
% 0.33/0.58        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.33/0.58        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % left_diff_distrib_numeral
% 0.33/0.58  thf(fact_3985_left__diff__distrib__numeral,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer,V: num] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 0.33/0.58        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % left_diff_distrib_numeral
% 0.33/0.58  thf(fact_3986_left__diff__distrib__numeral,axiom,
% 0.33/0.58      ! [A: rat,B: rat,V: num] :
% 0.33/0.58        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.33/0.58        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % left_diff_distrib_numeral
% 0.33/0.58  thf(fact_3987_right__diff__distrib__numeral,axiom,
% 0.33/0.58      ! [V: num,B: int,C: int] :
% 0.33/0.58        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 0.33/0.58        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % right_diff_distrib_numeral
% 0.33/0.58  thf(fact_3988_right__diff__distrib__numeral,axiom,
% 0.33/0.58      ! [V: num,B: code_integer,C: code_integer] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.33/0.58        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % right_diff_distrib_numeral
% 0.33/0.58  thf(fact_3989_right__diff__distrib__numeral,axiom,
% 0.33/0.58      ! [V: num,B: rat,C: rat] :
% 0.33/0.58        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 0.33/0.58        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % right_diff_distrib_numeral
% 0.33/0.58  thf(fact_3990_neg__numeral__less__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.58        = ( ord_less_num @ N @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_iff
% 0.33/0.58  thf(fact_3991_neg__numeral__less__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.33/0.58        = ( ord_less_num @ N @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_iff
% 0.33/0.58  thf(fact_3992_neg__numeral__less__iff,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.33/0.58        = ( ord_less_num @ N @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_iff
% 0.33/0.58  thf(fact_3993_semiring__norm_I168_J,axiom,
% 0.33/0.58      ! [V: num,W2: num,Y: int] :
% 0.33/0.58        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 0.33/0.58        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % semiring_norm(168)
% 0.33/0.58  thf(fact_3994_semiring__norm_I168_J,axiom,
% 0.33/0.58      ! [V: num,W2: num,Y: code_integer] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % semiring_norm(168)
% 0.33/0.58  thf(fact_3995_semiring__norm_I168_J,axiom,
% 0.33/0.58      ! [V: num,W2: num,Y: rat] :
% 0.33/0.58        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 0.33/0.58        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % semiring_norm(168)
% 0.33/0.58  thf(fact_3996_add__neg__numeral__simps_I3_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % add_neg_numeral_simps(3)
% 0.33/0.58  thf(fact_3997_add__neg__numeral__simps_I3_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.33/0.58        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % add_neg_numeral_simps(3)
% 0.33/0.58  thf(fact_3998_add__neg__numeral__simps_I3_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.33/0.58        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % add_neg_numeral_simps(3)
% 0.33/0.58  thf(fact_3999_mult__neg__numeral__simps_I3_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_neg_numeral_simps(3)
% 0.33/0.58  thf(fact_4000_mult__neg__numeral__simps_I3_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.33/0.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_neg_numeral_simps(3)
% 0.33/0.58  thf(fact_4001_mult__neg__numeral__simps_I3_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.33/0.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_neg_numeral_simps(3)
% 0.33/0.58  thf(fact_4002_mult__neg__numeral__simps_I2_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_neg_numeral_simps(2)
% 0.33/0.58  thf(fact_4003_mult__neg__numeral__simps_I2_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_neg_numeral_simps(2)
% 0.33/0.58  thf(fact_4004_mult__neg__numeral__simps_I2_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_neg_numeral_simps(2)
% 0.33/0.58  thf(fact_4005_mult__neg__numeral__simps_I1_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.58        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_neg_numeral_simps(1)
% 0.33/0.58  thf(fact_4006_mult__neg__numeral__simps_I1_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.33/0.58        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_neg_numeral_simps(1)
% 0.33/0.58  thf(fact_4007_mult__neg__numeral__simps_I1_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.33/0.58        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_neg_numeral_simps(1)
% 0.33/0.58  thf(fact_4008_diff__numeral__simps_I3_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % diff_numeral_simps(3)
% 0.33/0.58  thf(fact_4009_diff__numeral__simps_I3_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % diff_numeral_simps(3)
% 0.33/0.58  thf(fact_4010_diff__numeral__simps_I3_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % diff_numeral_simps(3)
% 0.33/0.58  thf(fact_4011_diff__numeral__simps_I2_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.58        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % diff_numeral_simps(2)
% 0.33/0.58  thf(fact_4012_diff__numeral__simps_I2_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.33/0.58        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % diff_numeral_simps(2)
% 0.33/0.58  thf(fact_4013_diff__numeral__simps_I2_J,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.33/0.58        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % diff_numeral_simps(2)
% 0.33/0.58  thf(fact_4014_mod__mult__self2__is__0,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self2_is_0
% 0.33/0.58  thf(fact_4015_mod__mult__self2__is__0,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self2_is_0
% 0.33/0.58  thf(fact_4016_mod__mult__self2__is__0,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self2_is_0
% 0.33/0.58  thf(fact_4017_mod__mult__self2__is__0,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self2_is_0
% 0.33/0.58  thf(fact_4018_mod__mult__self1__is__0,axiom,
% 0.33/0.58      ! [B: int,A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self1_is_0
% 0.33/0.58  thf(fact_4019_mod__mult__self1__is__0,axiom,
% 0.33/0.58      ! [B: nat,A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self1_is_0
% 0.33/0.58  thf(fact_4020_mod__mult__self1__is__0,axiom,
% 0.33/0.58      ! [B: code_integer,A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self1_is_0
% 0.33/0.58  thf(fact_4021_mod__mult__self1__is__0,axiom,
% 0.33/0.58      ! [B: code_natural,A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self1_is_0
% 0.33/0.58  thf(fact_4022_mod__by__1,axiom,
% 0.33/0.58      ! [A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_by_1
% 0.33/0.58  thf(fact_4023_mod__by__1,axiom,
% 0.33/0.58      ! [A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_by_1
% 0.33/0.58  thf(fact_4024_mod__by__1,axiom,
% 0.33/0.58      ! [A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_by_1
% 0.33/0.58  thf(fact_4025_mod__by__1,axiom,
% 0.33/0.58      ! [A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_by_1
% 0.33/0.58  thf(fact_4026_bits__mod__by__1,axiom,
% 0.33/0.58      ! [A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_by_1
% 0.33/0.58  thf(fact_4027_bits__mod__by__1,axiom,
% 0.33/0.58      ! [A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_by_1
% 0.33/0.58  thf(fact_4028_bits__mod__by__1,axiom,
% 0.33/0.58      ! [A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_by_1
% 0.33/0.58  thf(fact_4029_bits__mod__by__1,axiom,
% 0.33/0.58      ! [A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_by_1
% 0.33/0.58  thf(fact_4030_mod__mult__self1,axiom,
% 0.33/0.58      ! [A: int,C: int,B: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.33/0.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self1
% 0.33/0.58  thf(fact_4031_mod__mult__self1,axiom,
% 0.33/0.58      ! [A: nat,C: nat,B: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.33/0.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self1
% 0.33/0.58  thf(fact_4032_mod__mult__self1,axiom,
% 0.33/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 0.33/0.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self1
% 0.33/0.58  thf(fact_4033_mod__mult__self1,axiom,
% 0.33/0.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 0.33/0.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self1
% 0.33/0.58  thf(fact_4034_mod__mult__self2,axiom,
% 0.33/0.58      ! [A: int,B: int,C: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.33/0.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self2
% 0.33/0.58  thf(fact_4035_mod__mult__self2,axiom,
% 0.33/0.58      ! [A: nat,B: nat,C: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.33/0.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self2
% 0.33/0.58  thf(fact_4036_mod__mult__self2,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 0.33/0.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self2
% 0.33/0.58  thf(fact_4037_mod__mult__self2,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 0.33/0.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self2
% 0.33/0.58  thf(fact_4038_mod__mult__self3,axiom,
% 0.33/0.58      ! [C: int,B: int,A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.33/0.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self3
% 0.33/0.58  thf(fact_4039_mod__mult__self3,axiom,
% 0.33/0.58      ! [C: nat,B: nat,A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.33/0.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self3
% 0.33/0.58  thf(fact_4040_mod__mult__self3,axiom,
% 0.33/0.58      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 0.33/0.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self3
% 0.33/0.58  thf(fact_4041_mod__mult__self3,axiom,
% 0.33/0.58      ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 0.33/0.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self3
% 0.33/0.58  thf(fact_4042_mod__mult__self4,axiom,
% 0.33/0.58      ! [B: int,C: int,A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.33/0.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self4
% 0.33/0.58  thf(fact_4043_mod__mult__self4,axiom,
% 0.33/0.58      ! [B: nat,C: nat,A: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.33/0.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self4
% 0.33/0.58  thf(fact_4044_mod__mult__self4,axiom,
% 0.33/0.58      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 0.33/0.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self4
% 0.33/0.58  thf(fact_4045_mod__mult__self4,axiom,
% 0.33/0.58      ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 0.33/0.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_self4
% 0.33/0.58  thf(fact_4046_mod__div__trivial,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_trivial
% 0.33/0.58  thf(fact_4047_mod__div__trivial,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_trivial
% 0.33/0.58  thf(fact_4048_mod__div__trivial,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_trivial
% 0.33/0.58  thf(fact_4049_mod__div__trivial,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural] :
% 0.33/0.58        ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_trivial
% 0.33/0.58  thf(fact_4050_bits__mod__div__trivial,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_div_trivial
% 0.33/0.58  thf(fact_4051_bits__mod__div__trivial,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_div_trivial
% 0.33/0.58  thf(fact_4052_bits__mod__div__trivial,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_div_trivial
% 0.33/0.58  thf(fact_4053_bits__mod__div__trivial,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural] :
% 0.33/0.58        ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 0.33/0.58        = zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % bits_mod_div_trivial
% 0.33/0.58  thf(fact_4054_abs__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.58        = ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % abs_neg_numeral
% 0.33/0.58  thf(fact_4055_abs__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.33/0.58        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % abs_neg_numeral
% 0.33/0.58  thf(fact_4056_abs__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.33/0.58        = ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % abs_neg_numeral
% 0.33/0.58  thf(fact_4057_power__int__mult__distrib__numeral1,axiom,
% 0.33/0.58      ! [W2: num,Y: rat,M: int] :
% 0.33/0.58        ( ( power_int_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Y ) @ M )
% 0.33/0.58        = ( times_times_rat @ ( power_int_rat @ ( numeral_numeral_rat @ W2 ) @ M ) @ ( power_int_rat @ Y @ M ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_int_mult_distrib_numeral1
% 0.33/0.58  thf(fact_4058_power__int__mult__distrib__numeral2,axiom,
% 0.33/0.58      ! [X2: rat,W2: num,M: int] :
% 0.33/0.58        ( ( power_int_rat @ ( times_times_rat @ X2 @ ( numeral_numeral_rat @ W2 ) ) @ M )
% 0.33/0.58        = ( times_times_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ ( numeral_numeral_rat @ W2 ) @ M ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_int_mult_distrib_numeral2
% 0.33/0.58  thf(fact_4059_mod__by__Suc__0,axiom,
% 0.33/0.58      ! [M: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_by_Suc_0
% 0.33/0.58  thf(fact_4060_nat__neg__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.33/0.58        = zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_neg_numeral
% 0.33/0.58  thf(fact_4061_nat__power__eq__Suc__0__iff,axiom,
% 0.33/0.58      ! [X2: nat,M: nat] :
% 0.33/0.58        ( ( ( power_power_nat @ X2 @ M )
% 0.33/0.58          = ( suc @ zero_zero_nat ) )
% 0.33/0.58        = ( ( M = zero_zero_nat )
% 0.33/0.58          | ( X2
% 0.33/0.58            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_power_eq_Suc_0_iff
% 0.33/0.58  thf(fact_4062_power__Suc__0,axiom,
% 0.33/0.58      ! [N: nat] :
% 0.33/0.58        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.58        = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_Suc_0
% 0.33/0.58  thf(fact_4063_nat__zero__less__power__iff,axiom,
% 0.33/0.58      ! [X2: nat,N: nat] :
% 0.33/0.58        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X2 @ N ) )
% 0.33/0.58        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 0.33/0.58          | ( N = zero_zero_nat ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_zero_less_power_iff
% 0.33/0.58  thf(fact_4064_diff__nat__numeral,axiom,
% 0.33/0.58      ! [V: num,V2: num] :
% 0.33/0.58        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V2 ) )
% 0.33/0.58        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % diff_nat_numeral
% 0.33/0.58  thf(fact_4065_nat__eq__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ( nat2 @ Y )
% 0.33/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_eq_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4066_numeral__power__eq__nat__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: int] :
% 0.33/0.58        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 0.33/0.58          = ( nat2 @ Y ) )
% 0.33/0.58        = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_eq_nat_cancel_iff
% 0.33/0.58  thf(fact_4067_dbl__simps_I1_J,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % dbl_simps(1)
% 0.33/0.58  thf(fact_4068_dbl__simps_I1_J,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.33/0.58        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % dbl_simps(1)
% 0.33/0.58  thf(fact_4069_dbl__simps_I1_J,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.33/0.58        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % dbl_simps(1)
% 0.33/0.58  thf(fact_4070_le__divide__eq__numeral1_I1_J,axiom,
% 0.33/0.58      ! [A: rat,B: rat,W2: num] :
% 0.33/0.58        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 0.33/0.58        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % le_divide_eq_numeral1(1)
% 0.33/0.58  thf(fact_4071_divide__le__eq__numeral1_I1_J,axiom,
% 0.33/0.58      ! [B: rat,W2: num,A: rat] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 0.33/0.58        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % divide_le_eq_numeral1(1)
% 0.33/0.58  thf(fact_4072_eq__divide__eq__numeral1_I1_J,axiom,
% 0.33/0.58      ! [A: rat,B: rat,W2: num] :
% 0.33/0.58        ( ( A
% 0.33/0.58          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 0.33/0.58        = ( ( ( ( numeral_numeral_rat @ W2 )
% 0.33/0.58             != zero_zero_rat )
% 0.33/0.58           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.58              = B ) )
% 0.33/0.58          & ( ( ( numeral_numeral_rat @ W2 )
% 0.33/0.58              = zero_zero_rat )
% 0.33/0.58           => ( A = zero_zero_rat ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % eq_divide_eq_numeral1(1)
% 0.33/0.58  thf(fact_4073_divide__eq__eq__numeral1_I1_J,axiom,
% 0.33/0.58      ! [B: rat,W2: num,A: rat] :
% 0.33/0.58        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.58          = A )
% 0.33/0.58        = ( ( ( ( numeral_numeral_rat @ W2 )
% 0.33/0.58             != zero_zero_rat )
% 0.33/0.58           => ( B
% 0.33/0.58              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.33/0.58          & ( ( ( numeral_numeral_rat @ W2 )
% 0.33/0.58              = zero_zero_rat )
% 0.33/0.58           => ( A = zero_zero_rat ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % divide_eq_eq_numeral1(1)
% 0.33/0.58  thf(fact_4074_divide__less__eq__numeral1_I1_J,axiom,
% 0.33/0.58      ! [B: rat,W2: num,A: rat] :
% 0.33/0.58        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 0.33/0.58        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % divide_less_eq_numeral1(1)
% 0.33/0.58  thf(fact_4075_less__divide__eq__numeral1_I1_J,axiom,
% 0.33/0.58      ! [A: rat,B: rat,W2: num] :
% 0.33/0.58        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 0.33/0.58        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % less_divide_eq_numeral1(1)
% 0.33/0.58  thf(fact_4076_mod__minus1__right,axiom,
% 0.33/0.58      ! [A: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.58        = zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_minus1_right
% 0.33/0.58  thf(fact_4077_mod__minus1__right,axiom,
% 0.33/0.58      ! [A: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.58        = zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_minus1_right
% 0.33/0.58  thf(fact_4078_of__int__numeral__le__iff,axiom,
% 0.33/0.58      ! [N: num,Z2: int] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_numeral_le_iff
% 0.33/0.58  thf(fact_4079_of__int__numeral__le__iff,axiom,
% 0.33/0.58      ! [N: num,Z2: int] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z2 ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_numeral_le_iff
% 0.33/0.58  thf(fact_4080_of__int__numeral__le__iff,axiom,
% 0.33/0.58      ! [N: num,Z2: int] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_numeral_le_iff
% 0.33/0.58  thf(fact_4081_of__int__le__numeral__iff,axiom,
% 0.33/0.58      ! [Z2: int,N: num] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_le_numeral_iff
% 0.33/0.58  thf(fact_4082_of__int__le__numeral__iff,axiom,
% 0.33/0.58      ! [Z2: int,N: num] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_le_numeral_iff
% 0.33/0.58  thf(fact_4083_of__int__le__numeral__iff,axiom,
% 0.33/0.58      ! [Z2: int,N: num] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_le_numeral_iff
% 0.33/0.58  thf(fact_4084_of__int__numeral__less__iff,axiom,
% 0.33/0.58      ! [N: num,Z2: int] :
% 0.33/0.58        ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.33/0.58        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_numeral_less_iff
% 0.33/0.58  thf(fact_4085_of__int__numeral__less__iff,axiom,
% 0.33/0.58      ! [N: num,Z2: int] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 0.33/0.58        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_numeral_less_iff
% 0.33/0.58  thf(fact_4086_of__int__numeral__less__iff,axiom,
% 0.33/0.58      ! [N: num,Z2: int] :
% 0.33/0.58        ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z2 ) )
% 0.33/0.58        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_numeral_less_iff
% 0.33/0.58  thf(fact_4087_of__int__less__numeral__iff,axiom,
% 0.33/0.58      ! [Z2: int,N: num] :
% 0.33/0.58        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.58        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_less_numeral_iff
% 0.33/0.58  thf(fact_4088_of__int__less__numeral__iff,axiom,
% 0.33/0.58      ! [Z2: int,N: num] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.58        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_less_numeral_iff
% 0.33/0.58  thf(fact_4089_of__int__less__numeral__iff,axiom,
% 0.33/0.58      ! [Z2: int,N: num] :
% 0.33/0.58        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N ) )
% 0.33/0.58        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_less_numeral_iff
% 0.33/0.58  thf(fact_4090_numeral__le__floor,axiom,
% 0.33/0.58      ! [V: num,X2: rat] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_le_floor
% 0.33/0.58  thf(fact_4091_floor__less__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 0.33/0.58        = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % floor_less_numeral
% 0.33/0.58  thf(fact_4092_ceiling__le__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 0.33/0.58        = ( ord_less_eq_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % ceiling_le_numeral
% 0.33/0.58  thf(fact_4093_numeral__less__ceiling,axiom,
% 0.33/0.58      ! [V: num,X2: rat] :
% 0.33/0.58        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_less_ceiling
% 0.33/0.58  thf(fact_4094_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: nat] :
% 0.33/0.58        ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 0.33/0.58          = ( semiri1314217659103216013at_int @ Y ) )
% 0.33/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4095_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: nat] :
% 0.33/0.58        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 0.33/0.58          = ( semiri1316708129612266289at_nat @ Y ) )
% 0.33/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4096_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: nat] :
% 0.33/0.58        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N )
% 0.33/0.58          = ( semiri4939895301339042750nteger @ Y ) )
% 0.33/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4097_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: nat] :
% 0.33/0.58        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 0.33/0.58          = ( semiri681578069525770553at_rat @ Y ) )
% 0.33/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4098_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: nat] :
% 0.33/0.58        ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ X2 ) @ N )
% 0.33/0.58          = ( semiri3763490453095760265atural @ Y ) )
% 0.33/0.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_eq_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4099_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: nat,X2: num,N: nat] :
% 0.33/0.58        ( ( ( semiri1314217659103216013at_int @ Y )
% 0.33/0.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4100_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: nat,X2: num,N: nat] :
% 0.33/0.58        ( ( ( semiri1316708129612266289at_nat @ Y )
% 0.33/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4101_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: nat,X2: num,N: nat] :
% 0.33/0.58        ( ( ( semiri4939895301339042750nteger @ Y )
% 0.33/0.58          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4102_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: nat,X2: num,N: nat] :
% 0.33/0.58        ( ( ( semiri681578069525770553at_rat @ Y )
% 0.33/0.58          = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4103_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: nat,X2: num,N: nat] :
% 0.33/0.58        ( ( ( semiri3763490453095760265atural @ Y )
% 0.33/0.58          = ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ X2 ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % real_of_nat_eq_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4104_Suc__mod__mult__self1,axiom,
% 0.33/0.58      ! [M: nat,K: nat,N: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 0.33/0.58        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Suc_mod_mult_self1
% 0.33/0.58  thf(fact_4105_Suc__mod__mult__self2,axiom,
% 0.33/0.58      ! [M: nat,N: nat,K: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 0.33/0.58        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Suc_mod_mult_self2
% 0.33/0.58  thf(fact_4106_Suc__mod__mult__self3,axiom,
% 0.33/0.58      ! [K: nat,N: nat,M: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 0.33/0.58        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Suc_mod_mult_self3
% 0.33/0.58  thf(fact_4107_Suc__mod__mult__self4,axiom,
% 0.33/0.58      ! [N: nat,K: nat,M: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 0.33/0.58        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Suc_mod_mult_self4
% 0.33/0.58  thf(fact_4108_floor__neg__numeral,axiom,
% 0.33/0.58      ! [V: num] :
% 0.33/0.58        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % floor_neg_numeral
% 0.33/0.58  thf(fact_4109_ceiling__add__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 0.33/0.58        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % ceiling_add_numeral
% 0.33/0.58  thf(fact_4110_floor__diff__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 0.33/0.58        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % floor_diff_numeral
% 0.33/0.58  thf(fact_4111_ceiling__neg__numeral,axiom,
% 0.33/0.58      ! [V: num] :
% 0.33/0.58        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % ceiling_neg_numeral
% 0.33/0.58  thf(fact_4112_Suc__times__numeral__mod__eq,axiom,
% 0.33/0.58      ! [K: num,N: nat] :
% 0.33/0.58        ( ( ( numeral_numeral_nat @ K )
% 0.33/0.58         != one_one_nat )
% 0.33/0.58       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 0.33/0.58          = one_one_nat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Suc_times_numeral_mod_eq
% 0.33/0.58  thf(fact_4113_ceiling__diff__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 0.33/0.58        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % ceiling_diff_numeral
% 0.33/0.58  thf(fact_4114_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ( ring_1_of_int_int @ Y )
% 0.33/0.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_eq_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4115_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ( ring_18347121197199848620nteger @ Y )
% 0.33/0.58          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_eq_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4116_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ( ring_1_of_int_rat @ Y )
% 0.33/0.58          = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_eq_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4117_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: int] :
% 0.33/0.58        ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 0.33/0.58          = ( ring_1_of_int_int @ Y ) )
% 0.33/0.58        = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_eq_of_int_cancel_iff
% 0.33/0.58  thf(fact_4118_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: int] :
% 0.33/0.58        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N )
% 0.33/0.58          = ( ring_18347121197199848620nteger @ Y ) )
% 0.33/0.58        = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_eq_of_int_cancel_iff
% 0.33/0.58  thf(fact_4119_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: int] :
% 0.33/0.58        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 0.33/0.58          = ( ring_1_of_int_rat @ Y ) )
% 0.33/0.58        = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_eq_of_int_cancel_iff
% 0.33/0.58  thf(fact_4120_mod__neg__neg__trivial,axiom,
% 0.33/0.58      ! [K: int,L: int] :
% 0.33/0.58        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.33/0.58       => ( ( ord_less_int @ L @ K )
% 0.33/0.58         => ( ( modulo_modulo_int @ K @ L )
% 0.33/0.58            = K ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_neg_neg_trivial
% 0.33/0.58  thf(fact_4121_mod__pos__pos__trivial,axiom,
% 0.33/0.58      ! [K: int,L: int] :
% 0.33/0.58        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.58       => ( ( ord_less_int @ K @ L )
% 0.33/0.58         => ( ( modulo_modulo_int @ K @ L )
% 0.33/0.58            = K ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_pos_pos_trivial
% 0.33/0.58  thf(fact_4122_le__divide__eq__numeral1_I2_J,axiom,
% 0.33/0.58      ! [A: rat,B: rat,W2: num] :
% 0.33/0.58        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.33/0.58        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % le_divide_eq_numeral1(2)
% 0.33/0.58  thf(fact_4123_divide__le__eq__numeral1_I2_J,axiom,
% 0.33/0.58      ! [B: rat,W2: num,A: rat] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 0.33/0.58        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % divide_le_eq_numeral1(2)
% 0.33/0.58  thf(fact_4124_eq__divide__eq__numeral1_I2_J,axiom,
% 0.33/0.58      ! [A: rat,B: rat,W2: num] :
% 0.33/0.58        ( ( A
% 0.33/0.58          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.33/0.58        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.58             != zero_zero_rat )
% 0.33/0.58           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.33/0.58              = B ) )
% 0.33/0.58          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.58              = zero_zero_rat )
% 0.33/0.58           => ( A = zero_zero_rat ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % eq_divide_eq_numeral1(2)
% 0.33/0.58  thf(fact_4125_divide__eq__eq__numeral1_I2_J,axiom,
% 0.33/0.58      ! [B: rat,W2: num,A: rat] :
% 0.33/0.58        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.33/0.58          = A )
% 0.33/0.58        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.58             != zero_zero_rat )
% 0.33/0.58           => ( B
% 0.33/0.58              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 0.33/0.58          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.58              = zero_zero_rat )
% 0.33/0.58           => ( A = zero_zero_rat ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % divide_eq_eq_numeral1(2)
% 0.33/0.58  thf(fact_4126_less__divide__eq__numeral1_I2_J,axiom,
% 0.33/0.58      ! [A: rat,B: rat,W2: num] :
% 0.33/0.58        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.33/0.58        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % less_divide_eq_numeral1(2)
% 0.33/0.58  thf(fact_4127_divide__less__eq__numeral1_I2_J,axiom,
% 0.33/0.58      ! [B: rat,W2: num,A: rat] :
% 0.33/0.58        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 0.33/0.58        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % divide_less_eq_numeral1(2)
% 0.33/0.58  thf(fact_4128_dbl__dec__simps_I1_J,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % dbl_dec_simps(1)
% 0.33/0.58  thf(fact_4129_dbl__dec__simps_I1_J,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.33/0.58        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % dbl_dec_simps(1)
% 0.33/0.58  thf(fact_4130_dbl__dec__simps_I1_J,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.33/0.58        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % dbl_dec_simps(1)
% 0.33/0.58  thf(fact_4131_dbl__inc__simps_I1_J,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % dbl_inc_simps(1)
% 0.33/0.58  thf(fact_4132_dbl__inc__simps_I1_J,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.33/0.58        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % dbl_inc_simps(1)
% 0.33/0.58  thf(fact_4133_dbl__inc__simps_I1_J,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.33/0.58        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % dbl_inc_simps(1)
% 0.33/0.58  thf(fact_4134_nat__numeral__diff__1,axiom,
% 0.33/0.58      ! [V: num] :
% 0.33/0.58        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 0.33/0.58        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_numeral_diff_1
% 0.33/0.58  thf(fact_4135_numeral__power__less__nat__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 0.33/0.58        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_less_nat_cancel_iff
% 0.33/0.58  thf(fact_4136_nat__less__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 0.33/0.58        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_less_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4137_nat__le__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_le_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4138_numeral__power__le__nat__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_le_nat_cancel_iff
% 0.33/0.58  thf(fact_4139_numeral__less__floor,axiom,
% 0.33/0.58      ! [V: num,X2: rat] :
% 0.33/0.58        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_less_floor
% 0.33/0.58  thf(fact_4140_floor__le__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 0.33/0.58        = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % floor_le_numeral
% 0.33/0.58  thf(fact_4141_ceiling__less__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 0.33/0.58        = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % ceiling_less_numeral
% 0.33/0.58  thf(fact_4142_numeral__le__ceiling,axiom,
% 0.33/0.58      ! [V: num,X2: rat] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_le_ceiling
% 0.33/0.58  thf(fact_4143_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 0.33/0.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_less_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4144_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 0.33/0.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_less_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4145_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 0.33/0.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_less_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4146_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_less_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4147_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I ) @ N ) @ ( semiri3763490453095760265atural @ X2 ) )
% 0.33/0.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_less_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4148_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_less_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4149_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_less_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4150_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_less_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4151_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_less_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4152_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ X2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_less_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4153_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_le_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4154_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ X2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_le_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4155_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_le_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4156_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_le_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4157_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [X2: nat,I: num,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_le_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4158_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 0.33/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_le_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4159_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I ) @ N ) @ ( semiri3763490453095760265atural @ X2 ) )
% 0.33/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_le_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4160_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_le_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4161_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 0.33/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_le_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4162_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.33/0.58      ! [I: num,N: nat,X2: nat] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 0.33/0.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_le_of_nat_cancel_iff
% 0.33/0.58  thf(fact_4163_neg__numeral__le__floor,axiom,
% 0.33/0.58      ! [V: num,X2: rat] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_floor
% 0.33/0.58  thf(fact_4164_floor__less__neg__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.33/0.58        = ( ord_less_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % floor_less_neg_numeral
% 0.33/0.58  thf(fact_4165_ceiling__le__neg__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.33/0.58        = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % ceiling_le_neg_numeral
% 0.33/0.58  thf(fact_4166_neg__numeral__less__ceiling,axiom,
% 0.33/0.58      ! [V: num,X2: rat] :
% 0.33/0.58        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_ceiling
% 0.33/0.58  thf(fact_4167_of__int__le__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_le_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4168_of__int__le__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_le_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4169_of__int__le__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_le_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4170_numeral__power__le__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_le_of_int_cancel_iff
% 0.33/0.58  thf(fact_4171_numeral__power__le__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_le_of_int_cancel_iff
% 0.33/0.58  thf(fact_4172_numeral__power__le__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_le_of_int_cancel_iff
% 0.33/0.58  thf(fact_4173_numeral__power__less__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.33/0.58        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_less_of_int_cancel_iff
% 0.33/0.58  thf(fact_4174_numeral__power__less__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.33/0.58        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_less_of_int_cancel_iff
% 0.33/0.58  thf(fact_4175_numeral__power__less__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.33/0.58        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_power_less_of_int_cancel_iff
% 0.33/0.58  thf(fact_4176_of__int__less__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 0.33/0.58        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_less_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4177_of__int__less__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 0.33/0.58        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_less_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4178_of__int__less__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 0.33/0.58        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_less_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4179_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ( ring_1_of_int_int @ Y )
% 0.33/0.58          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_eq_neg_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4180_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ( ring_18347121197199848620nteger @ Y )
% 0.33/0.58          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_eq_neg_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4181_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [Y: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ( ring_1_of_int_rat @ Y )
% 0.33/0.58          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 0.33/0.58        = ( Y
% 0.33/0.58          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_eq_neg_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4182_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: int] :
% 0.33/0.58        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 0.33/0.58          = ( ring_1_of_int_int @ Y ) )
% 0.33/0.58        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_power_eq_of_int_cancel_iff
% 0.33/0.58  thf(fact_4183_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: int] :
% 0.33/0.58        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N )
% 0.33/0.58          = ( ring_18347121197199848620nteger @ Y ) )
% 0.33/0.58        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_power_eq_of_int_cancel_iff
% 0.33/0.58  thf(fact_4184_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,Y: int] :
% 0.33/0.58        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N )
% 0.33/0.58          = ( ring_1_of_int_rat @ Y ) )
% 0.33/0.58        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 0.33/0.58          = Y ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_power_eq_of_int_cancel_iff
% 0.33/0.58  thf(fact_4185_neg__numeral__less__floor,axiom,
% 0.33/0.58      ! [V: num,X2: rat] :
% 0.33/0.58        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_floor
% 0.33/0.58  thf(fact_4186_floor__le__neg__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.33/0.58        = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % floor_le_neg_numeral
% 0.33/0.58  thf(fact_4187_ceiling__less__neg__numeral,axiom,
% 0.33/0.58      ! [X2: rat,V: num] :
% 0.33/0.58        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.33/0.58        = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % ceiling_less_neg_numeral
% 0.33/0.58  thf(fact_4188_neg__numeral__le__ceiling,axiom,
% 0.33/0.58      ! [V: num,X2: rat] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 0.33/0.58        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_ceiling
% 0.33/0.58  thf(fact_4189_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_le_neg_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4190_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_le_neg_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4191_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 0.33/0.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_le_neg_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4192_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_power_le_of_int_cancel_iff
% 0.33/0.58  thf(fact_4193_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_power_le_of_int_cancel_iff
% 0.33/0.58  thf(fact_4194_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.33/0.58        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_power_le_of_int_cancel_iff
% 0.33/0.58  thf(fact_4195_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.33/0.58        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_power_less_of_int_cancel_iff
% 0.33/0.58  thf(fact_4196_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.33/0.58        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_power_less_of_int_cancel_iff
% 0.33/0.58  thf(fact_4197_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.33/0.58      ! [X2: num,N: nat,A: int] :
% 0.33/0.58        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.33/0.58        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_power_less_of_int_cancel_iff
% 0.33/0.58  thf(fact_4198_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 0.33/0.58        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_less_neg_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4199_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 0.33/0.58        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_less_neg_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4200_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.33/0.58      ! [A: int,X2: num,N: nat] :
% 0.33/0.58        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 0.33/0.58        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_less_neg_numeral_power_cancel_iff
% 0.33/0.58  thf(fact_4201_zmod__int,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 0.33/0.58        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zmod_int
% 0.33/0.58  thf(fact_4202_nat__numeral__as__int,axiom,
% 0.33/0.58      ( numeral_numeral_nat
% 0.33/0.58      = ( ^ [I2: num] : ( nat2 @ ( numeral_numeral_int @ I2 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_numeral_as_int
% 0.33/0.58  thf(fact_4203_int__ops_I3_J,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 0.33/0.58        = ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % int_ops(3)
% 0.33/0.58  thf(fact_4204_of__nat__mod,axiom,
% 0.33/0.58      ! [M: nat,N: nat] :
% 0.33/0.58        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 0.33/0.58        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_mod
% 0.33/0.58  thf(fact_4205_of__nat__mod,axiom,
% 0.33/0.58      ! [M: nat,N: nat] :
% 0.33/0.58        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 0.33/0.58        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_mod
% 0.33/0.58  thf(fact_4206_of__nat__mod,axiom,
% 0.33/0.58      ! [M: nat,N: nat] :
% 0.33/0.58        ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 0.33/0.58        = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_mod
% 0.33/0.58  thf(fact_4207_of__nat__mod,axiom,
% 0.33/0.58      ! [M: nat,N: nat] :
% 0.33/0.58        ( ( semiri3763490453095760265atural @ ( modulo_modulo_nat @ M @ N ) )
% 0.33/0.58        = ( modulo8411746178871703098atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_nat_mod
% 0.33/0.58  thf(fact_4208_mod__add__eq,axiom,
% 0.33/0.58      ! [A: int,C: int,B: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.33/0.58        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_eq
% 0.33/0.58  thf(fact_4209_mod__add__eq,axiom,
% 0.33/0.58      ! [A: nat,C: nat,B: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.33/0.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_eq
% 0.33/0.58  thf(fact_4210_mod__add__eq,axiom,
% 0.33/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.33/0.58        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_eq
% 0.33/0.58  thf(fact_4211_mod__add__eq,axiom,
% 0.33/0.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 0.33/0.58        = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_eq
% 0.33/0.58  thf(fact_4212_mod__add__cong,axiom,
% 0.33/0.58      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 0.33/0.58        ( ( ( modulo_modulo_int @ A @ C )
% 0.33/0.58          = ( modulo_modulo_int @ A5 @ C ) )
% 0.33/0.58       => ( ( ( modulo_modulo_int @ B @ C )
% 0.33/0.58            = ( modulo_modulo_int @ B5 @ C ) )
% 0.33/0.58         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.58            = ( modulo_modulo_int @ ( plus_plus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_cong
% 0.33/0.58  thf(fact_4213_mod__add__cong,axiom,
% 0.33/0.58      ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 0.33/0.58        ( ( ( modulo_modulo_nat @ A @ C )
% 0.33/0.58          = ( modulo_modulo_nat @ A5 @ C ) )
% 0.33/0.58       => ( ( ( modulo_modulo_nat @ B @ C )
% 0.33/0.58            = ( modulo_modulo_nat @ B5 @ C ) )
% 0.33/0.58         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.58            = ( modulo_modulo_nat @ ( plus_plus_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_cong
% 0.33/0.58  thf(fact_4214_mod__add__cong,axiom,
% 0.33/0.58      ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 0.33/0.58        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.33/0.58          = ( modulo364778990260209775nteger @ A5 @ C ) )
% 0.33/0.58       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 0.33/0.58            = ( modulo364778990260209775nteger @ B5 @ C ) )
% 0.33/0.58         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.33/0.58            = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_cong
% 0.33/0.58  thf(fact_4215_mod__add__cong,axiom,
% 0.33/0.58      ! [A: code_natural,C: code_natural,A5: code_natural,B: code_natural,B5: code_natural] :
% 0.33/0.58        ( ( ( modulo8411746178871703098atural @ A @ C )
% 0.33/0.58          = ( modulo8411746178871703098atural @ A5 @ C ) )
% 0.33/0.58       => ( ( ( modulo8411746178871703098atural @ B @ C )
% 0.33/0.58            = ( modulo8411746178871703098atural @ B5 @ C ) )
% 0.33/0.58         => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 0.33/0.58            = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_cong
% 0.33/0.58  thf(fact_4216_mod__add__left__eq,axiom,
% 0.33/0.58      ! [A: int,C: int,B: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.33/0.58        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_left_eq
% 0.33/0.58  thf(fact_4217_mod__add__left__eq,axiom,
% 0.33/0.58      ! [A: nat,C: nat,B: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.33/0.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_left_eq
% 0.33/0.58  thf(fact_4218_mod__add__left__eq,axiom,
% 0.33/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 0.33/0.58        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_left_eq
% 0.33/0.58  thf(fact_4219_mod__add__left__eq,axiom,
% 0.33/0.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ B ) @ C )
% 0.33/0.58        = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_left_eq
% 0.33/0.58  thf(fact_4220_mod__add__right__eq,axiom,
% 0.33/0.58      ! [A: int,B: int,C: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.33/0.58        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_right_eq
% 0.33/0.58  thf(fact_4221_mod__add__right__eq,axiom,
% 0.33/0.58      ! [A: nat,B: nat,C: nat] :
% 0.33/0.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.33/0.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_right_eq
% 0.33/0.58  thf(fact_4222_mod__add__right__eq,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.33/0.58        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_right_eq
% 0.33/0.58  thf(fact_4223_mod__add__right__eq,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 0.33/0.58        = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_add_right_eq
% 0.33/0.58  thf(fact_4224_zero__neq__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( zero_zero_int
% 0.33/0.58       != ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_neq_numeral
% 0.33/0.58  thf(fact_4225_zero__neq__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( zero_zero_nat
% 0.33/0.58       != ( numeral_numeral_nat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_neq_numeral
% 0.33/0.58  thf(fact_4226_zero__neq__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( zero_z3403309356797280102nteger
% 0.33/0.58       != ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_neq_numeral
% 0.33/0.58  thf(fact_4227_zero__neq__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( zero_zero_rat
% 0.33/0.58       != ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_neq_numeral
% 0.33/0.58  thf(fact_4228_zero__neq__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( zero_z2226904508553997617atural
% 0.33/0.58       != ( numera5444537566228673987atural @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_neq_numeral
% 0.33/0.58  thf(fact_4229_mod__less__eq__dividend,axiom,
% 0.33/0.58      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_less_eq_dividend
% 0.33/0.58  thf(fact_4230_neg__numeral__neq__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.33/0.58       != ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_neq_numeral
% 0.33/0.58  thf(fact_4231_neg__numeral__neq__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.33/0.58       != ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_neq_numeral
% 0.33/0.58  thf(fact_4232_neg__numeral__neq__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.33/0.58       != ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_neq_numeral
% 0.33/0.58  thf(fact_4233_numeral__neq__neg__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( numeral_numeral_int @ M )
% 0.33/0.58       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_neq_neg_numeral
% 0.33/0.58  thf(fact_4234_numeral__neq__neg__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( numera6620942414471956472nteger @ M )
% 0.33/0.58       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_neq_neg_numeral
% 0.33/0.58  thf(fact_4235_numeral__neq__neg__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ( ( numeral_numeral_rat @ M )
% 0.33/0.58       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_neq_neg_numeral
% 0.33/0.58  thf(fact_4236_nat__mod__as__int,axiom,
% 0.33/0.58      ( modulo_modulo_nat
% 0.33/0.58      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_mod_as_int
% 0.33/0.58  thf(fact_4237_Ints__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( member_int @ ( numeral_numeral_int @ N ) @ ring_1_Ints_int ) ).
% 0.33/0.58  
% 0.33/0.58  % Ints_numeral
% 0.33/0.58  thf(fact_4238_Ints__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( member_Code_integer @ ( numera6620942414471956472nteger @ N ) @ ring_11222124179247155820nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % Ints_numeral
% 0.33/0.58  thf(fact_4239_Ints__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( member_rat @ ( numeral_numeral_rat @ N ) @ ring_1_Ints_rat ) ).
% 0.33/0.58  
% 0.33/0.58  % Ints_numeral
% 0.33/0.58  thf(fact_4240_nat__mod__distrib,axiom,
% 0.33/0.58      ! [X2: int,Y: int] :
% 0.33/0.58        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.33/0.58       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.58         => ( ( nat2 @ ( modulo_modulo_int @ X2 @ Y ) )
% 0.33/0.58            = ( modulo_modulo_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_mod_distrib
% 0.33/0.58  thf(fact_4241_mod__abs__eq__div__nat,axiom,
% 0.33/0.58      ! [K: int,L: int] :
% 0.33/0.58        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 0.33/0.58        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_abs_eq_div_nat
% 0.33/0.58  thf(fact_4242_of__int__neg__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.33/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_neg_numeral
% 0.33/0.58  thf(fact_4243_of__int__neg__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.33/0.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_neg_numeral
% 0.33/0.58  thf(fact_4244_of__int__neg__numeral,axiom,
% 0.33/0.58      ! [K: num] :
% 0.33/0.58        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.33/0.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % of_int_neg_numeral
% 0.33/0.58  thf(fact_4245_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.58       => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.33/0.58  thf(fact_4246_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.58       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.33/0.58  thf(fact_4247_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.58       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.33/0.58  thf(fact_4248_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.33/0.58      ! [B: int,A: int] :
% 0.33/0.58        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.58       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.33/0.58  thf(fact_4249_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.33/0.58      ! [B: nat,A: nat] :
% 0.33/0.58        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.33/0.58       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.33/0.58  thf(fact_4250_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.33/0.58      ! [B: code_integer,A: code_integer] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.33/0.58       => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.33/0.58  thf(fact_4251_mod__eqE,axiom,
% 0.33/0.58      ! [A: int,C: int,B: int] :
% 0.33/0.58        ( ( ( modulo_modulo_int @ A @ C )
% 0.33/0.58          = ( modulo_modulo_int @ B @ C ) )
% 0.33/0.58       => ~ ! [D5: int] :
% 0.33/0.58              ( B
% 0.33/0.58             != ( plus_plus_int @ A @ ( times_times_int @ C @ D5 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_eqE
% 0.33/0.58  thf(fact_4252_mod__eqE,axiom,
% 0.33/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.33/0.58        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.33/0.58          = ( modulo364778990260209775nteger @ B @ C ) )
% 0.33/0.58       => ~ ! [D5: code_integer] :
% 0.33/0.58              ( B
% 0.33/0.58             != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D5 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_eqE
% 0.33/0.58  thf(fact_4253_mod__eq__self__iff__div__eq__0,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( ( modulo_modulo_int @ A @ B )
% 0.33/0.58          = A )
% 0.33/0.58        = ( ( divide_divide_int @ A @ B )
% 0.33/0.58          = zero_zero_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_eq_self_iff_div_eq_0
% 0.33/0.58  thf(fact_4254_mod__eq__self__iff__div__eq__0,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( ( modulo_modulo_nat @ A @ B )
% 0.33/0.58          = A )
% 0.33/0.58        = ( ( divide_divide_nat @ A @ B )
% 0.33/0.58          = zero_zero_nat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_eq_self_iff_div_eq_0
% 0.33/0.58  thf(fact_4255_mod__eq__self__iff__div__eq__0,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.33/0.58          = A )
% 0.33/0.58        = ( ( divide6298287555418463151nteger @ A @ B )
% 0.33/0.58          = zero_z3403309356797280102nteger ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_eq_self_iff_div_eq_0
% 0.33/0.58  thf(fact_4256_mod__eq__self__iff__div__eq__0,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural] :
% 0.33/0.58        ( ( ( modulo8411746178871703098atural @ A @ B )
% 0.33/0.58          = A )
% 0.33/0.58        = ( ( divide5121882707175180666atural @ A @ B )
% 0.33/0.58          = zero_z2226904508553997617atural ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_eq_self_iff_div_eq_0
% 0.33/0.58  thf(fact_4257_div__add1__eq,axiom,
% 0.33/0.58      ! [A: int,B: int,C: int] :
% 0.33/0.58        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.33/0.58        = ( 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 ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % div_add1_eq
% 0.33/0.58  thf(fact_4258_div__add1__eq,axiom,
% 0.33/0.58      ! [A: nat,B: nat,C: nat] :
% 0.33/0.58        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.33/0.58        = ( 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 ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % div_add1_eq
% 0.33/0.58  thf(fact_4259_div__add1__eq,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58        ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % div_add1_eq
% 0.33/0.58  thf(fact_4260_div__add1__eq,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.58        ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 0.33/0.58        = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % div_add1_eq
% 0.33/0.58  thf(fact_4261_nth__rotate1,axiom,
% 0.33/0.58      ! [N: nat,Xs: list_nat] :
% 0.33/0.58        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.33/0.58       => ( ( nth_nat @ ( rotate1_nat @ Xs ) @ N )
% 0.33/0.58          = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nth_rotate1
% 0.33/0.58  thf(fact_4262_nth__rotate1,axiom,
% 0.33/0.58      ! [N: nat,Xs: list_int] :
% 0.33/0.58        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.33/0.58       => ( ( nth_int @ ( rotate1_int @ Xs ) @ N )
% 0.33/0.58          = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nth_rotate1
% 0.33/0.58  thf(fact_4263_nth__rotate1,axiom,
% 0.33/0.58      ! [N: nat,Xs: list_o] :
% 0.33/0.58        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.33/0.58       => ( ( nth_o @ ( rotate1_o @ Xs ) @ N )
% 0.33/0.58          = ( nth_o @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nth_rotate1
% 0.33/0.58  thf(fact_4264_list__eq__iff__nth__eq,axiom,
% 0.33/0.58      ( ( ^ [Y3: list_nat,Z: list_nat] : ( Y3 = Z ) )
% 0.33/0.58      = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 0.33/0.58            ( ( ( size_size_list_nat @ Xs3 )
% 0.33/0.58              = ( size_size_list_nat @ Ys3 ) )
% 0.33/0.58            & ! [I2: nat] :
% 0.33/0.58                ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs3 ) )
% 0.33/0.58               => ( ( nth_nat @ Xs3 @ I2 )
% 0.33/0.58                  = ( nth_nat @ Ys3 @ I2 ) ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % list_eq_iff_nth_eq
% 0.33/0.58  thf(fact_4265_list__eq__iff__nth__eq,axiom,
% 0.33/0.58      ( ( ^ [Y3: list_int,Z: list_int] : ( Y3 = Z ) )
% 0.33/0.58      = ( ^ [Xs3: list_int,Ys3: list_int] :
% 0.33/0.58            ( ( ( size_size_list_int @ Xs3 )
% 0.33/0.58              = ( size_size_list_int @ Ys3 ) )
% 0.33/0.58            & ! [I2: nat] :
% 0.33/0.58                ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs3 ) )
% 0.33/0.58               => ( ( nth_int @ Xs3 @ I2 )
% 0.33/0.58                  = ( nth_int @ Ys3 @ I2 ) ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % list_eq_iff_nth_eq
% 0.33/0.58  thf(fact_4266_list__eq__iff__nth__eq,axiom,
% 0.33/0.58      ( ( ^ [Y3: list_o,Z: list_o] : ( Y3 = Z ) )
% 0.33/0.58      = ( ^ [Xs3: list_o,Ys3: list_o] :
% 0.33/0.58            ( ( ( size_size_list_o @ Xs3 )
% 0.33/0.58              = ( size_size_list_o @ Ys3 ) )
% 0.33/0.58            & ! [I2: nat] :
% 0.33/0.58                ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs3 ) )
% 0.33/0.58               => ( ( nth_o @ Xs3 @ I2 )
% 0.33/0.58                  = ( nth_o @ Ys3 @ I2 ) ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % list_eq_iff_nth_eq
% 0.33/0.58  thf(fact_4267_Skolem__list__nth,axiom,
% 0.33/0.58      ! [K: nat,P: nat > nat > $o] :
% 0.33/0.58        ( ( ! [I2: nat] :
% 0.33/0.58              ( ( ord_less_nat @ I2 @ K )
% 0.33/0.58             => ? [X5: nat] : ( P @ I2 @ X5 ) ) )
% 0.33/0.58        = ( ? [Xs3: list_nat] :
% 0.33/0.58              ( ( ( size_size_list_nat @ Xs3 )
% 0.33/0.58                = K )
% 0.33/0.58              & ! [I2: nat] :
% 0.33/0.58                  ( ( ord_less_nat @ I2 @ K )
% 0.33/0.58                 => ( P @ I2 @ ( nth_nat @ Xs3 @ I2 ) ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Skolem_list_nth
% 0.33/0.58  thf(fact_4268_Skolem__list__nth,axiom,
% 0.33/0.58      ! [K: nat,P: nat > int > $o] :
% 0.33/0.58        ( ( ! [I2: nat] :
% 0.33/0.58              ( ( ord_less_nat @ I2 @ K )
% 0.33/0.58             => ? [X5: int] : ( P @ I2 @ X5 ) ) )
% 0.33/0.58        = ( ? [Xs3: list_int] :
% 0.33/0.58              ( ( ( size_size_list_int @ Xs3 )
% 0.33/0.58                = K )
% 0.33/0.58              & ! [I2: nat] :
% 0.33/0.58                  ( ( ord_less_nat @ I2 @ K )
% 0.33/0.58                 => ( P @ I2 @ ( nth_int @ Xs3 @ I2 ) ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Skolem_list_nth
% 0.33/0.58  thf(fact_4269_Skolem__list__nth,axiom,
% 0.33/0.58      ! [K: nat,P: nat > $o > $o] :
% 0.33/0.58        ( ( ! [I2: nat] :
% 0.33/0.58              ( ( ord_less_nat @ I2 @ K )
% 0.33/0.58             => ? [X5: $o] : ( P @ I2 @ X5 ) ) )
% 0.33/0.58        = ( ? [Xs3: list_o] :
% 0.33/0.58              ( ( ( size_size_list_o @ Xs3 )
% 0.33/0.58                = K )
% 0.33/0.58              & ! [I2: nat] :
% 0.33/0.58                  ( ( ord_less_nat @ I2 @ K )
% 0.33/0.58                 => ( P @ I2 @ ( nth_o @ Xs3 @ I2 ) ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Skolem_list_nth
% 0.33/0.58  thf(fact_4270_nth__equalityI,axiom,
% 0.33/0.58      ! [Xs: list_nat,Ys: list_nat] :
% 0.33/0.58        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.58          = ( size_size_list_nat @ Ys ) )
% 0.33/0.58       => ( ! [I3: nat] :
% 0.33/0.58              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.33/0.58             => ( ( nth_nat @ Xs @ I3 )
% 0.33/0.58                = ( nth_nat @ Ys @ I3 ) ) )
% 0.33/0.58         => ( Xs = Ys ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nth_equalityI
% 0.33/0.58  thf(fact_4271_nth__equalityI,axiom,
% 0.33/0.58      ! [Xs: list_int,Ys: list_int] :
% 0.33/0.58        ( ( ( size_size_list_int @ Xs )
% 0.33/0.58          = ( size_size_list_int @ Ys ) )
% 0.33/0.58       => ( ! [I3: nat] :
% 0.33/0.58              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 0.33/0.58             => ( ( nth_int @ Xs @ I3 )
% 0.33/0.58                = ( nth_int @ Ys @ I3 ) ) )
% 0.33/0.58         => ( Xs = Ys ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nth_equalityI
% 0.33/0.58  thf(fact_4272_nth__equalityI,axiom,
% 0.33/0.58      ! [Xs: list_o,Ys: list_o] :
% 0.33/0.58        ( ( ( size_size_list_o @ Xs )
% 0.33/0.58          = ( size_size_list_o @ Ys ) )
% 0.33/0.58       => ( ! [I3: nat] :
% 0.33/0.58              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 0.33/0.58             => ( ( nth_o @ Xs @ I3 )
% 0.33/0.58                = ( nth_o @ Ys @ I3 ) ) )
% 0.33/0.58         => ( Xs = Ys ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nth_equalityI
% 0.33/0.58  thf(fact_4273_obtain__list__from__elements,axiom,
% 0.33/0.58      ! [N: nat,P: nat > nat > $o] :
% 0.33/0.58        ( ! [I3: nat] :
% 0.33/0.58            ( ( ord_less_nat @ I3 @ N )
% 0.33/0.58           => ? [Li: nat] : ( P @ Li @ I3 ) )
% 0.33/0.58       => ~ ! [L3: list_nat] :
% 0.33/0.58              ( ( ( size_size_list_nat @ L3 )
% 0.33/0.58                = N )
% 0.33/0.58             => ~ ! [I4: nat] :
% 0.33/0.58                    ( ( ord_less_nat @ I4 @ N )
% 0.33/0.58                   => ( P @ ( nth_nat @ L3 @ I4 ) @ I4 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % obtain_list_from_elements
% 0.33/0.58  thf(fact_4274_obtain__list__from__elements,axiom,
% 0.33/0.58      ! [N: nat,P: int > nat > $o] :
% 0.33/0.58        ( ! [I3: nat] :
% 0.33/0.58            ( ( ord_less_nat @ I3 @ N )
% 0.33/0.58           => ? [Li: int] : ( P @ Li @ I3 ) )
% 0.33/0.58       => ~ ! [L3: list_int] :
% 0.33/0.58              ( ( ( size_size_list_int @ L3 )
% 0.33/0.58                = N )
% 0.33/0.58             => ~ ! [I4: nat] :
% 0.33/0.58                    ( ( ord_less_nat @ I4 @ N )
% 0.33/0.58                   => ( P @ ( nth_int @ L3 @ I4 ) @ I4 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % obtain_list_from_elements
% 0.33/0.58  thf(fact_4275_obtain__list__from__elements,axiom,
% 0.33/0.58      ! [N: nat,P: $o > nat > $o] :
% 0.33/0.58        ( ! [I3: nat] :
% 0.33/0.58            ( ( ord_less_nat @ I3 @ N )
% 0.33/0.58           => ? [Li: $o] : ( P @ Li @ I3 ) )
% 0.33/0.58       => ~ ! [L3: list_o] :
% 0.33/0.58              ( ( ( size_size_list_o @ L3 )
% 0.33/0.58                = N )
% 0.33/0.58             => ~ ! [I4: nat] :
% 0.33/0.58                    ( ( ord_less_nat @ I4 @ N )
% 0.33/0.58                   => ( P @ ( nth_o @ L3 @ I4 ) @ I4 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % obtain_list_from_elements
% 0.33/0.58  thf(fact_4276_mod__Suc,axiom,
% 0.33/0.58      ! [M: nat,N: nat] :
% 0.33/0.58        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.33/0.58            = N )
% 0.33/0.58         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.33/0.58            = zero_zero_nat ) )
% 0.33/0.58        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.33/0.58           != N )
% 0.33/0.58         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.33/0.58            = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_Suc
% 0.33/0.58  thf(fact_4277_mod__less__divisor,axiom,
% 0.33/0.58      ! [N: nat,M: nat] :
% 0.33/0.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.58       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_less_divisor
% 0.33/0.58  thf(fact_4278_gcd__nat__induct,axiom,
% 0.33/0.58      ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.33/0.58        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 0.33/0.58       => ( ! [M4: nat,N2: nat] :
% 0.33/0.58              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.58             => ( ( P @ N2 @ ( modulo_modulo_nat @ M4 @ N2 ) )
% 0.33/0.58               => ( P @ M4 @ N2 ) ) )
% 0.33/0.58         => ( P @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % gcd_nat_induct
% 0.33/0.58  thf(fact_4279_zero__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_le_numeral
% 0.33/0.58  thf(fact_4280_zero__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( numera5444537566228673987atural @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_le_numeral
% 0.33/0.58  thf(fact_4281_zero__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_le_numeral
% 0.33/0.58  thf(fact_4282_zero__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_le_numeral
% 0.33/0.58  thf(fact_4283_zero__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_le_numeral
% 0.33/0.58  thf(fact_4284_not__numeral__le__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_zero
% 0.33/0.58  thf(fact_4285_not__numeral__le__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N ) @ zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_zero
% 0.33/0.58  thf(fact_4286_not__numeral__le__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_zero
% 0.33/0.58  thf(fact_4287_not__numeral__le__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_zero
% 0.33/0.58  thf(fact_4288_not__numeral__le__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_zero
% 0.33/0.58  thf(fact_4289_mod__Suc__le__divisor,axiom,
% 0.33/0.58      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_Suc_le_divisor
% 0.33/0.58  thf(fact_4290_zero__less__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_less_numeral
% 0.33/0.58  thf(fact_4291_zero__less__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_less_numeral
% 0.33/0.58  thf(fact_4292_zero__less__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_less_numeral
% 0.33/0.58  thf(fact_4293_zero__less__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_less_numeral
% 0.33/0.58  thf(fact_4294_zero__less__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( numera5444537566228673987atural @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_less_numeral
% 0.33/0.58  thf(fact_4295_not__numeral__less__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_zero
% 0.33/0.58  thf(fact_4296_not__numeral__less__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_zero
% 0.33/0.58  thf(fact_4297_not__numeral__less__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_zero
% 0.33/0.58  thf(fact_4298_not__numeral__less__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_zero
% 0.33/0.58  thf(fact_4299_not__numeral__less__zero,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N ) @ zero_z2226904508553997617atural ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_zero
% 0.33/0.58  thf(fact_4300_one__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_le_numeral
% 0.33/0.58  thf(fact_4301_one__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_le_numeral
% 0.33/0.58  thf(fact_4302_one__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_le_numeral
% 0.33/0.58  thf(fact_4303_one__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_le_numeral
% 0.33/0.58  thf(fact_4304_one__le__numeral,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_le_numeral
% 0.33/0.58  thf(fact_4305_nat__power__less__imp__less,axiom,
% 0.33/0.58      ! [I: nat,M: nat,N: nat] :
% 0.33/0.58        ( ( ord_less_nat @ zero_zero_nat @ I )
% 0.33/0.58       => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 0.33/0.58         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_power_less_imp_less
% 0.33/0.58  thf(fact_4306_mod__eq__0D,axiom,
% 0.33/0.58      ! [M: nat,D: nat] :
% 0.33/0.58        ( ( ( modulo_modulo_nat @ M @ D )
% 0.33/0.58          = zero_zero_nat )
% 0.33/0.58       => ? [Q4: nat] :
% 0.33/0.58            ( M
% 0.33/0.58            = ( times_times_nat @ D @ Q4 ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_eq_0D
% 0.33/0.58  thf(fact_4307_zmod__le__nonneg__dividend,axiom,
% 0.33/0.58      ! [M: int,K: int] :
% 0.33/0.58        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.33/0.58       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zmod_le_nonneg_dividend
% 0.33/0.58  thf(fact_4308_Euclidean__Division_Opos__mod__bound,axiom,
% 0.33/0.58      ! [L: int,K: int] :
% 0.33/0.58        ( ( ord_less_int @ zero_zero_int @ L )
% 0.33/0.58       => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Euclidean_Division.pos_mod_bound
% 0.33/0.58  thf(fact_4309_neg__mod__bound,axiom,
% 0.33/0.58      ! [L: int,K: int] :
% 0.33/0.58        ( ( ord_less_int @ L @ zero_zero_int )
% 0.33/0.58       => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_mod_bound
% 0.33/0.58  thf(fact_4310_not__numeral__less__one,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_one
% 0.33/0.58  thf(fact_4311_not__numeral__less__one,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_one
% 0.33/0.58  thf(fact_4312_not__numeral__less__one,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_one
% 0.33/0.58  thf(fact_4313_not__numeral__less__one,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_one
% 0.33/0.58  thf(fact_4314_not__numeral__less__one,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_one
% 0.33/0.58  thf(fact_4315_le__mod__geq,axiom,
% 0.33/0.58      ! [N: nat,M: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.58       => ( ( modulo_modulo_nat @ M @ N )
% 0.33/0.58          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % le_mod_geq
% 0.33/0.58  thf(fact_4316_not__numeral__le__neg__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_neg_numeral
% 0.33/0.58  thf(fact_4317_not__numeral__le__neg__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_neg_numeral
% 0.33/0.58  thf(fact_4318_not__numeral__le__neg__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_neg_numeral
% 0.33/0.58  thf(fact_4319_neg__numeral__le__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_numeral
% 0.33/0.58  thf(fact_4320_neg__numeral__le__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_numeral
% 0.33/0.58  thf(fact_4321_neg__numeral__le__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_numeral
% 0.33/0.58  thf(fact_4322_zero__neq__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( zero_zero_int
% 0.33/0.58       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_neq_neg_numeral
% 0.33/0.58  thf(fact_4323_zero__neq__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( zero_z3403309356797280102nteger
% 0.33/0.58       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_neq_neg_numeral
% 0.33/0.58  thf(fact_4324_zero__neq__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( zero_zero_rat
% 0.33/0.58       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zero_neq_neg_numeral
% 0.33/0.58  thf(fact_4325_one__plus__numeral__commute,axiom,
% 0.33/0.58      ! [X2: num] :
% 0.33/0.58        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 0.33/0.58        = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_plus_numeral_commute
% 0.33/0.58  thf(fact_4326_one__plus__numeral__commute,axiom,
% 0.33/0.58      ! [X2: num] :
% 0.33/0.58        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 0.33/0.58        = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_plus_numeral_commute
% 0.33/0.58  thf(fact_4327_one__plus__numeral__commute,axiom,
% 0.33/0.58      ! [X2: num] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X2 ) )
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X2 ) @ one_one_Code_integer ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_plus_numeral_commute
% 0.33/0.58  thf(fact_4328_one__plus__numeral__commute,axiom,
% 0.33/0.58      ! [X2: num] :
% 0.33/0.58        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 0.33/0.58        = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_plus_numeral_commute
% 0.33/0.58  thf(fact_4329_one__plus__numeral__commute,axiom,
% 0.33/0.58      ! [X2: num] :
% 0.33/0.58        ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X2 ) )
% 0.33/0.58        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X2 ) @ one_one_Code_natural ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_plus_numeral_commute
% 0.33/0.58  thf(fact_4330_zmod__eq__0D,axiom,
% 0.33/0.58      ! [M: int,D: int] :
% 0.33/0.58        ( ( ( modulo_modulo_int @ M @ D )
% 0.33/0.58          = zero_zero_int )
% 0.33/0.58       => ? [Q4: int] :
% 0.33/0.58            ( M
% 0.33/0.58            = ( times_times_int @ D @ Q4 ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zmod_eq_0D
% 0.33/0.58  thf(fact_4331_zmod__eq__0__iff,axiom,
% 0.33/0.58      ! [M: int,D: int] :
% 0.33/0.58        ( ( ( modulo_modulo_int @ M @ D )
% 0.33/0.58          = zero_zero_int )
% 0.33/0.58        = ( ? [Q6: int] :
% 0.33/0.58              ( M
% 0.33/0.58              = ( times_times_int @ D @ Q6 ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zmod_eq_0_iff
% 0.33/0.58  thf(fact_4332_zmod__zminus2__not__zero,axiom,
% 0.33/0.58      ! [K: int,L: int] :
% 0.33/0.58        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 0.33/0.58         != zero_zero_int )
% 0.33/0.58       => ( ( modulo_modulo_int @ K @ L )
% 0.33/0.58         != zero_zero_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zmod_zminus2_not_zero
% 0.33/0.58  thf(fact_4333_zmod__zminus1__not__zero,axiom,
% 0.33/0.58      ! [K: int,L: int] :
% 0.33/0.58        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.33/0.58         != zero_zero_int )
% 0.33/0.58       => ( ( modulo_modulo_int @ K @ L )
% 0.33/0.58         != zero_zero_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zmod_zminus1_not_zero
% 0.33/0.58  thf(fact_4334_neg__numeral__less__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_numeral
% 0.33/0.58  thf(fact_4335_neg__numeral__less__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_numeral
% 0.33/0.58  thf(fact_4336_neg__numeral__less__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_numeral
% 0.33/0.58  thf(fact_4337_not__numeral__less__neg__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_neg_numeral
% 0.33/0.58  thf(fact_4338_not__numeral__less__neg__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_neg_numeral
% 0.33/0.58  thf(fact_4339_not__numeral__less__neg__numeral,axiom,
% 0.33/0.58      ! [M: num,N: num] :
% 0.33/0.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_neg_numeral
% 0.33/0.58  thf(fact_4340_nat__mod__eq__iff,axiom,
% 0.33/0.58      ! [X2: nat,N: nat,Y: nat] :
% 0.33/0.58        ( ( ( modulo_modulo_nat @ X2 @ N )
% 0.33/0.58          = ( modulo_modulo_nat @ Y @ N ) )
% 0.33/0.58        = ( ? [Q1: nat,Q22: nat] :
% 0.33/0.58              ( ( plus_plus_nat @ X2 @ ( times_times_nat @ N @ Q1 ) )
% 0.33/0.58              = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_mod_eq_iff
% 0.33/0.58  thf(fact_4341_numeral__neq__neg__one,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( numeral_numeral_int @ N )
% 0.33/0.58       != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_neq_neg_one
% 0.33/0.58  thf(fact_4342_numeral__neq__neg__one,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( numera6620942414471956472nteger @ N )
% 0.33/0.58       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_neq_neg_one
% 0.33/0.58  thf(fact_4343_numeral__neq__neg__one,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( ( numeral_numeral_rat @ N )
% 0.33/0.58       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % numeral_neq_neg_one
% 0.33/0.58  thf(fact_4344_one__neq__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( one_one_int
% 0.33/0.58       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_neq_neg_numeral
% 0.33/0.58  thf(fact_4345_one__neq__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( one_one_Code_integer
% 0.33/0.58       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_neq_neg_numeral
% 0.33/0.58  thf(fact_4346_one__neq__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ( one_one_rat
% 0.33/0.58       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % one_neq_neg_numeral
% 0.33/0.58  thf(fact_4347_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.33/0.58       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.33/0.58         => ( ( modulo364778990260209775nteger @ A @ B )
% 0.33/0.58            = A ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.mod_less
% 0.33/0.58  thf(fact_4348_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.33/0.58       => ( ( ord_less_nat @ A @ B )
% 0.33/0.58         => ( ( modulo_modulo_nat @ A @ B )
% 0.33/0.58            = A ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.mod_less
% 0.33/0.58  thf(fact_4349_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.58       => ( ( ord_less_int @ A @ B )
% 0.33/0.58         => ( ( modulo_modulo_int @ A @ B )
% 0.33/0.58            = A ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.mod_less
% 0.33/0.58  thf(fact_4350_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.33/0.58      ! [B: code_integer,A: code_integer] :
% 0.33/0.58        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.33/0.58       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.33/0.58  thf(fact_4351_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.33/0.58      ! [B: nat,A: nat] :
% 0.33/0.58        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.33/0.58       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.33/0.58  thf(fact_4352_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.33/0.58      ! [B: int,A: int] :
% 0.33/0.58        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.58       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.33/0.58  thf(fact_4353_div__mult1__eq,axiom,
% 0.33/0.58      ! [A: int,B: int,C: int] :
% 0.33/0.58        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 0.33/0.58        = ( 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 ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % div_mult1_eq
% 0.33/0.58  thf(fact_4354_div__mult1__eq,axiom,
% 0.33/0.58      ! [A: nat,B: nat,C: nat] :
% 0.33/0.58        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.33/0.58        = ( 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 ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % div_mult1_eq
% 0.33/0.58  thf(fact_4355_div__mult1__eq,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58        ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % div_mult1_eq
% 0.33/0.58  thf(fact_4356_div__mult1__eq,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.58        ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 0.33/0.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % div_mult1_eq
% 0.33/0.58  thf(fact_4357_cancel__div__mod__rules_I2_J,axiom,
% 0.33/0.58      ! [B: int,A: int,C: int] :
% 0.33/0.58        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.33/0.58        = ( plus_plus_int @ A @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % cancel_div_mod_rules(2)
% 0.33/0.58  thf(fact_4358_cancel__div__mod__rules_I2_J,axiom,
% 0.33/0.58      ! [B: nat,A: nat,C: nat] :
% 0.33/0.58        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.33/0.58        = ( plus_plus_nat @ A @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % cancel_div_mod_rules(2)
% 0.33/0.58  thf(fact_4359_cancel__div__mod__rules_I2_J,axiom,
% 0.33/0.58      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % cancel_div_mod_rules(2)
% 0.33/0.58  thf(fact_4360_cancel__div__mod__rules_I2_J,axiom,
% 0.33/0.58      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.33/0.58        ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 0.33/0.58        = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % cancel_div_mod_rules(2)
% 0.33/0.58  thf(fact_4361_cancel__div__mod__rules_I1_J,axiom,
% 0.33/0.58      ! [A: int,B: int,C: int] :
% 0.33/0.58        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.33/0.58        = ( plus_plus_int @ A @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % cancel_div_mod_rules(1)
% 0.33/0.58  thf(fact_4362_cancel__div__mod__rules_I1_J,axiom,
% 0.33/0.58      ! [A: nat,B: nat,C: nat] :
% 0.33/0.58        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.33/0.58        = ( plus_plus_nat @ A @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % cancel_div_mod_rules(1)
% 0.33/0.58  thf(fact_4363_cancel__div__mod__rules_I1_J,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % cancel_div_mod_rules(1)
% 0.33/0.58  thf(fact_4364_cancel__div__mod__rules_I1_J,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.33/0.58        ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 0.33/0.58        = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 0.33/0.58  
% 0.33/0.58  % cancel_div_mod_rules(1)
% 0.33/0.58  thf(fact_4365_mod__div__decomp,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( A
% 0.33/0.58        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_decomp
% 0.33/0.58  thf(fact_4366_mod__div__decomp,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( A
% 0.33/0.58        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_decomp
% 0.33/0.58  thf(fact_4367_mod__div__decomp,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( A
% 0.33/0.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_decomp
% 0.33/0.58  thf(fact_4368_mod__div__decomp,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural] :
% 0.33/0.58        ( A
% 0.33/0.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_decomp
% 0.33/0.58  thf(fact_4369_div__mult__mod__eq,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % div_mult_mod_eq
% 0.33/0.58  thf(fact_4370_div__mult__mod__eq,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % div_mult_mod_eq
% 0.33/0.58  thf(fact_4371_div__mult__mod__eq,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % div_mult_mod_eq
% 0.33/0.58  thf(fact_4372_div__mult__mod__eq,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural] :
% 0.33/0.58        ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % div_mult_mod_eq
% 0.33/0.58  thf(fact_4373_mod__div__mult__eq,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_mult_eq
% 0.33/0.58  thf(fact_4374_mod__div__mult__eq,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_mult_eq
% 0.33/0.58  thf(fact_4375_mod__div__mult__eq,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_mult_eq
% 0.33/0.58  thf(fact_4376_mod__div__mult__eq,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural] :
% 0.33/0.58        ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_div_mult_eq
% 0.33/0.58  thf(fact_4377_mod__mult__div__eq,axiom,
% 0.33/0.58      ! [A: int,B: int] :
% 0.33/0.58        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_div_eq
% 0.33/0.58  thf(fact_4378_mod__mult__div__eq,axiom,
% 0.33/0.58      ! [A: nat,B: nat] :
% 0.33/0.58        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_div_eq
% 0.33/0.58  thf(fact_4379_mod__mult__div__eq,axiom,
% 0.33/0.58      ! [A: code_integer,B: code_integer] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_div_eq
% 0.33/0.58  thf(fact_4380_mod__mult__div__eq,axiom,
% 0.33/0.58      ! [A: code_natural,B: code_natural] :
% 0.33/0.58        ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_mult_div_eq
% 0.33/0.58  thf(fact_4381_mult__div__mod__eq,axiom,
% 0.33/0.58      ! [B: int,A: int] :
% 0.33/0.58        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_div_mod_eq
% 0.33/0.58  thf(fact_4382_mult__div__mod__eq,axiom,
% 0.33/0.58      ! [B: nat,A: nat] :
% 0.33/0.58        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_div_mod_eq
% 0.33/0.58  thf(fact_4383_mult__div__mod__eq,axiom,
% 0.33/0.58      ! [B: code_integer,A: code_integer] :
% 0.33/0.58        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_div_mod_eq
% 0.33/0.58  thf(fact_4384_mult__div__mod__eq,axiom,
% 0.33/0.58      ! [B: code_natural,A: code_natural] :
% 0.33/0.58        ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.33/0.58        = A ) ).
% 0.33/0.58  
% 0.33/0.58  % mult_div_mod_eq
% 0.33/0.58  thf(fact_4385_mod__le__divisor,axiom,
% 0.33/0.58      ! [N: nat,M: nat] :
% 0.33/0.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.58       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_le_divisor
% 0.33/0.58  thf(fact_4386_fact__mod,axiom,
% 0.33/0.58      ! [M: nat,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.58       => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 0.33/0.58          = zero_zero_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % fact_mod
% 0.33/0.58  thf(fact_4387_fact__mod,axiom,
% 0.33/0.58      ! [M: nat,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.58       => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 0.33/0.58          = zero_z3403309356797280102nteger ) ) ).
% 0.33/0.58  
% 0.33/0.58  % fact_mod
% 0.33/0.58  thf(fact_4388_fact__mod,axiom,
% 0.33/0.58      ! [M: nat,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.58       => ( ( modulo8411746178871703098atural @ ( semiri2447717529341329178atural @ N ) @ ( semiri2447717529341329178atural @ M ) )
% 0.33/0.58          = zero_z2226904508553997617atural ) ) ).
% 0.33/0.58  
% 0.33/0.58  % fact_mod
% 0.33/0.58  thf(fact_4389_fact__mod,axiom,
% 0.33/0.58      ! [M: nat,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.58       => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 0.33/0.58          = zero_zero_nat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % fact_mod
% 0.33/0.58  thf(fact_4390_neg__numeral__le__zero,axiom,
% 0.33/0.58      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_zero
% 0.33/0.58  thf(fact_4391_neg__numeral__le__zero,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_zero
% 0.33/0.58  thf(fact_4392_neg__numeral__le__zero,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_zero
% 0.33/0.58  thf(fact_4393_not__zero__le__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_zero_le_neg_numeral
% 0.33/0.58  thf(fact_4394_not__zero__le__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_zero_le_neg_numeral
% 0.33/0.58  thf(fact_4395_not__zero__le__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_zero_le_neg_numeral
% 0.33/0.58  thf(fact_4396_power__gt__expt,axiom,
% 0.33/0.58      ! [N: nat,K: nat] :
% 0.33/0.58        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.58       => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % power_gt_expt
% 0.33/0.58  thf(fact_4397_not__zero__less__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_zero_less_neg_numeral
% 0.33/0.58  thf(fact_4398_not__zero__less__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_zero_less_neg_numeral
% 0.33/0.58  thf(fact_4399_not__zero__less__neg__numeral,axiom,
% 0.33/0.58      ! [N: num] :
% 0.33/0.58        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_zero_less_neg_numeral
% 0.33/0.58  thf(fact_4400_neg__numeral__less__zero,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_zero
% 0.33/0.58  thf(fact_4401_neg__numeral__less__zero,axiom,
% 0.33/0.58      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_zero
% 0.33/0.58  thf(fact_4402_neg__numeral__less__zero,axiom,
% 0.33/0.58      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_zero
% 0.33/0.58  thf(fact_4403_nat__one__le__power,axiom,
% 0.33/0.58      ! [I: nat,N: nat] :
% 0.33/0.58        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 0.33/0.58       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_one_le_power
% 0.33/0.58  thf(fact_4404_not__one__le__neg__numeral,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_one_le_neg_numeral
% 0.33/0.58  thf(fact_4405_not__one__le__neg__numeral,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_one_le_neg_numeral
% 0.33/0.58  thf(fact_4406_not__one__le__neg__numeral,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_one_le_neg_numeral
% 0.33/0.58  thf(fact_4407_not__numeral__le__neg__one,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_neg_one
% 0.33/0.58  thf(fact_4408_not__numeral__le__neg__one,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_neg_one
% 0.33/0.58  thf(fact_4409_not__numeral__le__neg__one,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_le_neg_one
% 0.33/0.58  thf(fact_4410_neg__numeral__le__neg__one,axiom,
% 0.33/0.58      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_neg_one
% 0.33/0.58  thf(fact_4411_neg__numeral__le__neg__one,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_neg_one
% 0.33/0.58  thf(fact_4412_neg__numeral__le__neg__one,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_neg_one
% 0.33/0.58  thf(fact_4413_neg__one__le__numeral,axiom,
% 0.33/0.58      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_one_le_numeral
% 0.33/0.58  thf(fact_4414_neg__one__le__numeral,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_one_le_numeral
% 0.33/0.58  thf(fact_4415_neg__one__le__numeral,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_one_le_numeral
% 0.33/0.58  thf(fact_4416_neg__numeral__le__one,axiom,
% 0.33/0.58      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_one
% 0.33/0.58  thf(fact_4417_neg__numeral__le__one,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_one
% 0.33/0.58  thf(fact_4418_neg__numeral__le__one,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_le_one
% 0.33/0.58  thf(fact_4419_neg__mod__sign,axiom,
% 0.33/0.58      ! [L: int,K: int] :
% 0.33/0.58        ( ( ord_less_int @ L @ zero_zero_int )
% 0.33/0.58       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_mod_sign
% 0.33/0.58  thf(fact_4420_Euclidean__Division_Opos__mod__sign,axiom,
% 0.33/0.58      ! [L: int,K: int] :
% 0.33/0.58        ( ( ord_less_int @ zero_zero_int @ L )
% 0.33/0.58       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % Euclidean_Division.pos_mod_sign
% 0.33/0.58  thf(fact_4421_neg__mod__conj,axiom,
% 0.33/0.58      ! [B: int,A: int] :
% 0.33/0.58        ( ( ord_less_int @ B @ zero_zero_int )
% 0.33/0.58       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 0.33/0.58          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_mod_conj
% 0.33/0.58  thf(fact_4422_pos__mod__conj,axiom,
% 0.33/0.58      ! [B: int,A: int] :
% 0.33/0.58        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.58       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 0.33/0.58          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % pos_mod_conj
% 0.33/0.58  thf(fact_4423_zmod__trivial__iff,axiom,
% 0.33/0.58      ! [I: int,K: int] :
% 0.33/0.58        ( ( ( modulo_modulo_int @ I @ K )
% 0.33/0.58          = I )
% 0.33/0.58        = ( ( K = zero_zero_int )
% 0.33/0.58          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.33/0.58            & ( ord_less_int @ I @ K ) )
% 0.33/0.58          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.33/0.58            & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % zmod_trivial_iff
% 0.33/0.58  thf(fact_4424_eq__divide__eq__numeral_I1_J,axiom,
% 0.33/0.58      ! [W2: num,B: rat,C: rat] :
% 0.33/0.58        ( ( ( numeral_numeral_rat @ W2 )
% 0.33/0.58          = ( divide_divide_rat @ B @ C ) )
% 0.33/0.58        = ( ( ( C != zero_zero_rat )
% 0.33/0.58           => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C )
% 0.33/0.58              = B ) )
% 0.33/0.58          & ( ( C = zero_zero_rat )
% 0.33/0.58           => ( ( numeral_numeral_rat @ W2 )
% 0.33/0.58              = zero_zero_rat ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % eq_divide_eq_numeral(1)
% 0.33/0.58  thf(fact_4425_divide__eq__eq__numeral_I1_J,axiom,
% 0.33/0.58      ! [B: rat,C: rat,W2: num] :
% 0.33/0.58        ( ( ( divide_divide_rat @ B @ C )
% 0.33/0.58          = ( numeral_numeral_rat @ W2 ) )
% 0.33/0.58        = ( ( ( C != zero_zero_rat )
% 0.33/0.58           => ( B
% 0.33/0.58              = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.33/0.58          & ( ( C = zero_zero_rat )
% 0.33/0.58           => ( ( numeral_numeral_rat @ W2 )
% 0.33/0.58              = zero_zero_rat ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % divide_eq_eq_numeral(1)
% 0.33/0.58  thf(fact_4426_nat__mod__eq__lemma,axiom,
% 0.33/0.58      ! [X2: nat,N: nat,Y: nat] :
% 0.33/0.58        ( ( ( modulo_modulo_nat @ X2 @ N )
% 0.33/0.58          = ( modulo_modulo_nat @ Y @ N ) )
% 0.33/0.58       => ( ( ord_less_eq_nat @ Y @ X2 )
% 0.33/0.58         => ? [Q4: nat] :
% 0.33/0.58              ( X2
% 0.33/0.58              = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q4 ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % nat_mod_eq_lemma
% 0.33/0.58  thf(fact_4427_mod__eq__nat2E,axiom,
% 0.33/0.58      ! [M: nat,Q2: nat,N: nat] :
% 0.33/0.58        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.33/0.58          = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.33/0.58       => ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.58         => ~ ! [S2: nat] :
% 0.33/0.58                ( N
% 0.33/0.58               != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_eq_nat2E
% 0.33/0.58  thf(fact_4428_mod__eq__nat1E,axiom,
% 0.33/0.58      ! [M: nat,Q2: nat,N: nat] :
% 0.33/0.58        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.33/0.58          = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.33/0.58       => ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.58         => ~ ! [S2: nat] :
% 0.33/0.58                ( M
% 0.33/0.58               != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 0.33/0.58  
% 0.33/0.58  % mod_eq_nat1E
% 0.33/0.58  thf(fact_4429_neg__numeral__less__one,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_one
% 0.33/0.58  thf(fact_4430_neg__numeral__less__one,axiom,
% 0.33/0.58      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_one
% 0.33/0.58  thf(fact_4431_neg__numeral__less__one,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_numeral_less_one
% 0.33/0.58  thf(fact_4432_neg__one__less__numeral,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_one_less_numeral
% 0.33/0.58  thf(fact_4433_neg__one__less__numeral,axiom,
% 0.33/0.58      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_one_less_numeral
% 0.33/0.58  thf(fact_4434_neg__one__less__numeral,axiom,
% 0.33/0.58      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.33/0.58  
% 0.33/0.58  % neg_one_less_numeral
% 0.33/0.58  thf(fact_4435_not__numeral__less__neg__one,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_neg_one
% 0.33/0.58  thf(fact_4436_not__numeral__less__neg__one,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_neg_one
% 0.33/0.58  thf(fact_4437_not__numeral__less__neg__one,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.58  
% 0.33/0.58  % not_numeral_less_neg_one
% 0.33/0.58  thf(fact_4438_not__one__less__neg__numeral,axiom,
% 0.33/0.58      ! [M: num] :
% 0.33/0.58        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % not_one_less_neg_numeral
% 0.33/0.59  thf(fact_4439_not__one__less__neg__numeral,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % not_one_less_neg_numeral
% 0.33/0.59  thf(fact_4440_not__one__less__neg__numeral,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % not_one_less_neg_numeral
% 0.33/0.59  thf(fact_4441_not__neg__one__less__neg__numeral,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % not_neg_one_less_neg_numeral
% 0.33/0.59  thf(fact_4442_not__neg__one__less__neg__numeral,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % not_neg_one_less_neg_numeral
% 0.33/0.59  thf(fact_4443_not__neg__one__less__neg__numeral,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % not_neg_one_less_neg_numeral
% 0.33/0.59  thf(fact_4444_div__less__mono,axiom,
% 0.33/0.59      ! [A4: nat,B4: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ A4 @ B4 )
% 0.33/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59         => ( ( ( modulo_modulo_nat @ A4 @ N )
% 0.33/0.59              = zero_zero_nat )
% 0.33/0.59           => ( ( ( modulo_modulo_nat @ B4 @ N )
% 0.33/0.59                = zero_zero_nat )
% 0.33/0.59             => ( ord_less_nat @ ( divide_divide_nat @ A4 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % div_less_mono
% 0.33/0.59  thf(fact_4445_abs__mod__less,axiom,
% 0.33/0.59      ! [L: int,K: int] :
% 0.33/0.59        ( ( L != zero_zero_int )
% 0.33/0.59       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % abs_mod_less
% 0.33/0.59  thf(fact_4446_zmod__zminus1__eq__if,axiom,
% 0.33/0.59      ! [A: int,B: int] :
% 0.33/0.59        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59            = zero_zero_int )
% 0.33/0.59         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.33/0.59            = zero_zero_int ) )
% 0.33/0.59        & ( ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59           != zero_zero_int )
% 0.33/0.59         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.33/0.59            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zmod_zminus1_eq_if
% 0.33/0.59  thf(fact_4447_zmod__zminus2__eq__if,axiom,
% 0.33/0.59      ! [A: int,B: int] :
% 0.33/0.59        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59            = zero_zero_int )
% 0.33/0.59         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.33/0.59            = zero_zero_int ) )
% 0.33/0.59        & ( ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59           != zero_zero_int )
% 0.33/0.59         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.33/0.59            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zmod_zminus2_eq_if
% 0.33/0.59  thf(fact_4448_zdiv__mono__strict,axiom,
% 0.33/0.59      ! [A4: int,B4: int,N: int] :
% 0.33/0.59        ( ( ord_less_int @ A4 @ B4 )
% 0.33/0.59       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.33/0.59         => ( ( ( modulo_modulo_int @ A4 @ N )
% 0.33/0.59              = zero_zero_int )
% 0.33/0.59           => ( ( ( modulo_modulo_int @ B4 @ N )
% 0.33/0.59                = zero_zero_int )
% 0.33/0.59             => ( ord_less_int @ ( divide_divide_int @ A4 @ N ) @ ( divide_divide_int @ B4 @ N ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdiv_mono_strict
% 0.33/0.59  thf(fact_4449_mod__mult2__eq,axiom,
% 0.33/0.59      ! [M: nat,N: nat,Q2: nat] :
% 0.33/0.59        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 0.33/0.59        = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_mult2_eq
% 0.33/0.59  thf(fact_4450_div__mod__decomp,axiom,
% 0.33/0.59      ! [A4: nat,N: nat] :
% 0.33/0.59        ( A4
% 0.33/0.59        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A4 @ N ) @ N ) @ ( modulo_modulo_nat @ A4 @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % div_mod_decomp
% 0.33/0.59  thf(fact_4451_fact__le__power,axiom,
% 0.33/0.59      ! [N: nat] : ( ord_le3102999989581377725nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri4939895301339042750nteger @ ( power_power_nat @ N @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % fact_le_power
% 0.33/0.59  thf(fact_4452_fact__le__power,axiom,
% 0.33/0.59      ! [N: nat] : ( ord_le1926595141338095240atural @ ( semiri2447717529341329178atural @ N ) @ ( semiri3763490453095760265atural @ ( power_power_nat @ N @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % fact_le_power
% 0.33/0.59  thf(fact_4453_fact__le__power,axiom,
% 0.33/0.59      ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % fact_le_power
% 0.33/0.59  thf(fact_4454_fact__le__power,axiom,
% 0.33/0.59      ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % fact_le_power
% 0.33/0.59  thf(fact_4455_fact__le__power,axiom,
% 0.33/0.59      ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % fact_le_power
% 0.33/0.59  thf(fact_4456_div__mod__decomp__int,axiom,
% 0.33/0.59      ! [A4: int,N: int] :
% 0.33/0.59        ( A4
% 0.33/0.59        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A4 @ N ) @ N ) @ ( modulo_modulo_int @ A4 @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % div_mod_decomp_int
% 0.33/0.59  thf(fact_4457_fact__div__fact__le__pow,axiom,
% 0.33/0.59      ! [R: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ R @ N )
% 0.33/0.59       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % fact_div_fact_le_pow
% 0.33/0.59  thf(fact_4458_mod__mult2__eq_H,axiom,
% 0.33/0.59      ! [A: int,M: nat,N: nat] :
% 0.33/0.59        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.33/0.59        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_mult2_eq'
% 0.33/0.59  thf(fact_4459_mod__mult2__eq_H,axiom,
% 0.33/0.59      ! [A: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.33/0.59        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_mult2_eq'
% 0.33/0.59  thf(fact_4460_mod__mult2__eq_H,axiom,
% 0.33/0.59      ! [A: code_integer,M: nat,N: nat] :
% 0.33/0.59        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 0.33/0.59        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_mult2_eq'
% 0.33/0.59  thf(fact_4461_mod__mult2__eq_H,axiom,
% 0.33/0.59      ! [A: code_natural,M: nat,N: nat] :
% 0.33/0.59        ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) )
% 0.33/0.59        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_mult2_eq'
% 0.33/0.59  thf(fact_4462_split__mod,axiom,
% 0.33/0.59      ! [P: nat > $o,M: nat,N: nat] :
% 0.33/0.59        ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 0.33/0.59        = ( ( ( N = zero_zero_nat )
% 0.33/0.59           => ( P @ M ) )
% 0.33/0.59          & ( ( N != zero_zero_nat )
% 0.33/0.59           => ! [I2: nat,J3: nat] :
% 0.33/0.59                ( ( ord_less_nat @ J3 @ N )
% 0.33/0.59               => ( ( M
% 0.33/0.59                    = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 0.33/0.59                 => ( P @ J3 ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % split_mod
% 0.33/0.59  thf(fact_4463_less__divide__eq__numeral_I1_J,axiom,
% 0.33/0.59      ! [W2: num,B: rat,C: rat] :
% 0.33/0.59        ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 0.33/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 0.33/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.33/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % less_divide_eq_numeral(1)
% 0.33/0.59  thf(fact_4464_divide__less__eq__numeral_I1_J,axiom,
% 0.33/0.59      ! [B: rat,C: rat,W2: num] :
% 0.33/0.59        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.33/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 0.33/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % divide_less_eq_numeral(1)
% 0.33/0.59  thf(fact_4465_field__char__0__class_Oof__nat__div,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 0.33/0.59        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % field_char_0_class.of_nat_div
% 0.33/0.59  thf(fact_4466_eq__divide__eq__numeral_I2_J,axiom,
% 0.33/0.59      ! [W2: num,B: rat,C: rat] :
% 0.33/0.59        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.59          = ( divide_divide_rat @ B @ C ) )
% 0.33/0.59        = ( ( ( C != zero_zero_rat )
% 0.33/0.59           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C )
% 0.33/0.59              = B ) )
% 0.33/0.59          & ( ( C = zero_zero_rat )
% 0.33/0.59           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.59              = zero_zero_rat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % eq_divide_eq_numeral(2)
% 0.33/0.59  thf(fact_4467_divide__eq__eq__numeral_I2_J,axiom,
% 0.33/0.59      ! [B: rat,C: rat,W2: num] :
% 0.33/0.59        ( ( ( divide_divide_rat @ B @ C )
% 0.33/0.59          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.33/0.59        = ( ( ( C != zero_zero_rat )
% 0.33/0.59           => ( B
% 0.33/0.59              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.33/0.59          & ( ( C = zero_zero_rat )
% 0.33/0.59           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.59              = zero_zero_rat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % divide_eq_eq_numeral(2)
% 0.33/0.59  thf(fact_4468_mod__pos__neg__trivial,axiom,
% 0.33/0.59      ! [K: int,L: int] :
% 0.33/0.59        ( ( ord_less_int @ zero_zero_int @ K )
% 0.33/0.59       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.33/0.59         => ( ( modulo_modulo_int @ K @ L )
% 0.33/0.59            = ( plus_plus_int @ K @ L ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_pos_neg_trivial
% 0.33/0.59  thf(fact_4469_mod__pos__geq,axiom,
% 0.33/0.59      ! [L: int,K: int] :
% 0.33/0.59        ( ( ord_less_int @ zero_zero_int @ L )
% 0.33/0.59       => ( ( ord_less_eq_int @ L @ K )
% 0.33/0.59         => ( ( modulo_modulo_int @ K @ L )
% 0.33/0.59            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_pos_geq
% 0.33/0.59  thf(fact_4470_array__of__list__make,axiom,
% 0.33/0.59      ( array_of_list_nat
% 0.33/0.59      = ( ^ [Xs3: list_nat] : ( array_make_nat @ ( size_size_list_nat @ Xs3 ) @ ( nth_nat @ Xs3 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % array_of_list_make
% 0.33/0.59  thf(fact_4471_array__of__list__make,axiom,
% 0.33/0.59      ( array_of_list_int
% 0.33/0.59      = ( ^ [Xs3: list_int] : ( array_make_int @ ( size_size_list_int @ Xs3 ) @ ( nth_int @ Xs3 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % array_of_list_make
% 0.33/0.59  thf(fact_4472_array__of__list__make,axiom,
% 0.33/0.59      ( array_of_list_o
% 0.33/0.59      = ( ^ [Xs3: list_o] : ( array_make_o @ ( size_size_list_o @ Xs3 ) @ ( nth_o @ Xs3 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % array_of_list_make
% 0.33/0.59  thf(fact_4473_nat__power__eq,axiom,
% 0.33/0.59      ! [Z2: int,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.33/0.59       => ( ( nat2 @ ( power_power_int @ Z2 @ N ) )
% 0.33/0.59          = ( power_power_nat @ ( nat2 @ Z2 ) @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_power_eq
% 0.33/0.59  thf(fact_4474_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.33/0.59      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.33/0.59        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.33/0.59       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.33/0.59          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.33/0.59  thf(fact_4475_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.33/0.59      ! [C: nat,A: nat,B: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.33/0.59       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.33/0.59          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.33/0.59  thf(fact_4476_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.33/0.59      ! [C: int,A: int,B: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.33/0.59       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.33/0.59          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.33/0.59  thf(fact_4477_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.33/0.59      ( set_fo2584398358068434914at_nat
% 0.33/0.59      = ( ^ [F3: nat > nat > nat,A2: nat,B2: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B2 @ A2 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A2 @ one_one_nat ) @ B2 @ ( F3 @ A2 @ Acc ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % fold_atLeastAtMost_nat.simps
% 0.33/0.59  thf(fact_4478_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.33/0.59      ! [X2: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 0.33/0.59        ( ( ( set_fo2584398358068434914at_nat @ X2 @ Xa @ Xb @ Xc )
% 0.33/0.59          = Y )
% 0.33/0.59       => ( ( ( ord_less_nat @ Xb @ Xa )
% 0.33/0.59           => ( Y = Xc ) )
% 0.33/0.59          & ( ~ ( ord_less_nat @ Xb @ Xa )
% 0.33/0.59           => ( Y
% 0.33/0.59              = ( set_fo2584398358068434914at_nat @ X2 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X2 @ Xa @ Xc ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % fold_atLeastAtMost_nat.elims
% 0.33/0.59  thf(fact_4479_divide__le__eq__numeral_I1_J,axiom,
% 0.33/0.59      ! [B: rat,C: rat,W2: num] :
% 0.33/0.59        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 0.33/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.33/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 0.33/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % divide_le_eq_numeral(1)
% 0.33/0.59  thf(fact_4480_le__divide__eq__numeral_I1_J,axiom,
% 0.33/0.59      ! [W2: num,B: rat,C: rat] :
% 0.33/0.59        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 0.33/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 0.33/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 0.33/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % le_divide_eq_numeral(1)
% 0.33/0.59  thf(fact_4481_Suc__times__mod__eq,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.33/0.59       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 0.33/0.59          = one_one_nat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_times_mod_eq
% 0.33/0.59  thf(fact_4482_divide__less__eq__numeral_I2_J,axiom,
% 0.33/0.59      ! [B: rat,C: rat,W2: num] :
% 0.33/0.59        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.33/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.33/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 0.33/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % divide_less_eq_numeral(2)
% 0.33/0.59  thf(fact_4483_less__divide__eq__numeral_I2_J,axiom,
% 0.33/0.59      ! [W2: num,B: rat,C: rat] :
% 0.33/0.59        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.33/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 0.33/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.33/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % less_divide_eq_numeral(2)
% 0.33/0.59  thf(fact_4484_int__mod__pos__eq,axiom,
% 0.33/0.59      ! [A: int,B: int,Q2: int,R: int] :
% 0.33/0.59        ( ( A
% 0.33/0.59          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.33/0.59       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.33/0.59         => ( ( ord_less_int @ R @ B )
% 0.33/0.59           => ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59              = R ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % int_mod_pos_eq
% 0.33/0.59  thf(fact_4485_int__mod__neg__eq,axiom,
% 0.33/0.59      ! [A: int,B: int,Q2: int,R: int] :
% 0.33/0.59        ( ( A
% 0.33/0.59          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.33/0.59       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.33/0.59         => ( ( ord_less_int @ B @ R )
% 0.33/0.59           => ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59              = R ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % int_mod_neg_eq
% 0.33/0.59  thf(fact_4486_split__zmod,axiom,
% 0.33/0.59      ! [P: int > $o,N: int,K: int] :
% 0.33/0.59        ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 0.33/0.59        = ( ( ( K = zero_zero_int )
% 0.33/0.59           => ( P @ N ) )
% 0.33/0.59          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.33/0.59           => ! [I2: int,J3: int] :
% 0.33/0.59                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.33/0.59                  & ( ord_less_int @ J3 @ K )
% 0.33/0.59                  & ( N
% 0.33/0.59                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 0.33/0.59               => ( P @ J3 ) ) )
% 0.33/0.59          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.59           => ! [I2: int,J3: int] :
% 0.33/0.59                ( ( ( ord_less_int @ K @ J3 )
% 0.33/0.59                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.33/0.59                  & ( N
% 0.33/0.59                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 0.33/0.59               => ( P @ J3 ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % split_zmod
% 0.33/0.59  thf(fact_4487_minus__mod__int__eq,axiom,
% 0.33/0.59      ! [L: int,K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.33/0.59       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.33/0.59          = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % minus_mod_int_eq
% 0.33/0.59  thf(fact_4488_zmod__minus1,axiom,
% 0.33/0.59      ! [B: int] :
% 0.33/0.59        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.59       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.33/0.59          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zmod_minus1
% 0.33/0.59  thf(fact_4489_zmod__zmult2__eq,axiom,
% 0.33/0.59      ! [C: int,A: int,B: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.33/0.59       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.33/0.59          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zmod_zmult2_eq
% 0.33/0.59  thf(fact_4490_zdiv__zminus1__eq__if,axiom,
% 0.33/0.59      ! [B: int,A: int] :
% 0.33/0.59        ( ( B != zero_zero_int )
% 0.33/0.59       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59              = zero_zero_int )
% 0.33/0.59           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.33/0.59              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.33/0.59          & ( ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59             != zero_zero_int )
% 0.33/0.59           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.33/0.59              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdiv_zminus1_eq_if
% 0.33/0.59  thf(fact_4491_zdiv__zminus2__eq__if,axiom,
% 0.33/0.59      ! [B: int,A: int] :
% 0.33/0.59        ( ( B != zero_zero_int )
% 0.33/0.59       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59              = zero_zero_int )
% 0.33/0.59           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.33/0.59              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.33/0.59          & ( ( ( modulo_modulo_int @ A @ B )
% 0.33/0.59             != zero_zero_int )
% 0.33/0.59           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.33/0.59              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdiv_zminus2_eq_if
% 0.33/0.59  thf(fact_4492_divide__le__eq__numeral_I2_J,axiom,
% 0.33/0.59      ! [B: rat,C: rat,W2: num] :
% 0.33/0.59        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.33/0.59        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 0.33/0.59          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.33/0.59           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 0.33/0.59              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.33/0.59               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % divide_le_eq_numeral(2)
% 0.33/0.59  thf(fact_4493_sorted__in__between,axiom,
% 0.33/0.59      ! [I: nat,J: nat,L: list_o,X2: $o] :
% 0.33/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.33/0.59       => ( ( ord_less_nat @ I @ J )
% 0.33/0.59         => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 0.33/0.59           => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 0.33/0.59             => ( ( ord_less_eq_o @ ( nth_o @ L @ I ) @ X2 )
% 0.33/0.59               => ( ( ord_less_o @ X2 @ ( nth_o @ L @ J ) )
% 0.33/0.59                 => ~ ! [K3: nat] :
% 0.33/0.59                        ( ( ord_less_eq_nat @ I @ K3 )
% 0.33/0.59                       => ( ( ord_less_nat @ K3 @ J )
% 0.33/0.59                         => ( ( ord_less_eq_o @ ( nth_o @ L @ K3 ) @ X2 )
% 0.33/0.59                           => ~ ( ord_less_o @ X2 @ ( nth_o @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_in_between
% 0.33/0.59  thf(fact_4494_sorted__in__between,axiom,
% 0.33/0.59      ! [I: nat,J: nat,L: list_Code_integer,X2: code_integer] :
% 0.33/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.33/0.59       => ( ( ord_less_nat @ I @ J )
% 0.33/0.59         => ( ( ord_less_nat @ J @ ( size_s3445333598471063425nteger @ L ) )
% 0.33/0.59           => ( ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ L )
% 0.33/0.59             => ( ( ord_le3102999989581377725nteger @ ( nth_Code_integer @ L @ I ) @ X2 )
% 0.33/0.59               => ( ( ord_le6747313008572928689nteger @ X2 @ ( nth_Code_integer @ L @ J ) )
% 0.33/0.59                 => ~ ! [K3: nat] :
% 0.33/0.59                        ( ( ord_less_eq_nat @ I @ K3 )
% 0.33/0.59                       => ( ( ord_less_nat @ K3 @ J )
% 0.33/0.59                         => ( ( ord_le3102999989581377725nteger @ ( nth_Code_integer @ L @ K3 ) @ X2 )
% 0.33/0.59                           => ~ ( ord_le6747313008572928689nteger @ X2 @ ( nth_Code_integer @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_in_between
% 0.33/0.59  thf(fact_4495_sorted__in__between,axiom,
% 0.33/0.59      ! [I: nat,J: nat,L: list_rat,X2: rat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.33/0.59       => ( ( ord_less_nat @ I @ J )
% 0.33/0.59         => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 0.33/0.59           => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 0.33/0.59             => ( ( ord_less_eq_rat @ ( nth_rat @ L @ I ) @ X2 )
% 0.33/0.59               => ( ( ord_less_rat @ X2 @ ( nth_rat @ L @ J ) )
% 0.33/0.59                 => ~ ! [K3: nat] :
% 0.33/0.59                        ( ( ord_less_eq_nat @ I @ K3 )
% 0.33/0.59                       => ( ( ord_less_nat @ K3 @ J )
% 0.33/0.59                         => ( ( ord_less_eq_rat @ ( nth_rat @ L @ K3 ) @ X2 )
% 0.33/0.59                           => ~ ( ord_less_rat @ X2 @ ( nth_rat @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_in_between
% 0.33/0.59  thf(fact_4496_sorted__in__between,axiom,
% 0.33/0.59      ! [I: nat,J: nat,L: list_num,X2: num] :
% 0.33/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.33/0.59       => ( ( ord_less_nat @ I @ J )
% 0.33/0.59         => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 0.33/0.59           => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 0.33/0.59             => ( ( ord_less_eq_num @ ( nth_num @ L @ I ) @ X2 )
% 0.33/0.59               => ( ( ord_less_num @ X2 @ ( nth_num @ L @ J ) )
% 0.33/0.59                 => ~ ! [K3: nat] :
% 0.33/0.59                        ( ( ord_less_eq_nat @ I @ K3 )
% 0.33/0.59                       => ( ( ord_less_nat @ K3 @ J )
% 0.33/0.59                         => ( ( ord_less_eq_num @ ( nth_num @ L @ K3 ) @ X2 )
% 0.33/0.59                           => ~ ( ord_less_num @ X2 @ ( nth_num @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_in_between
% 0.33/0.59  thf(fact_4497_sorted__in__between,axiom,
% 0.33/0.59      ! [I: nat,J: nat,L: list_nat,X2: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.33/0.59       => ( ( ord_less_nat @ I @ J )
% 0.33/0.59         => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 0.33/0.59           => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 0.33/0.59             => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I ) @ X2 )
% 0.33/0.59               => ( ( ord_less_nat @ X2 @ ( nth_nat @ L @ J ) )
% 0.33/0.59                 => ~ ! [K3: nat] :
% 0.33/0.59                        ( ( ord_less_eq_nat @ I @ K3 )
% 0.33/0.59                       => ( ( ord_less_nat @ K3 @ J )
% 0.33/0.59                         => ( ( ord_less_eq_nat @ ( nth_nat @ L @ K3 ) @ X2 )
% 0.33/0.59                           => ~ ( ord_less_nat @ X2 @ ( nth_nat @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_in_between
% 0.33/0.59  thf(fact_4498_sorted__in__between,axiom,
% 0.33/0.59      ! [I: nat,J: nat,L: list_int,X2: int] :
% 0.33/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.33/0.59       => ( ( ord_less_nat @ I @ J )
% 0.33/0.59         => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 0.33/0.59           => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 0.33/0.59             => ( ( ord_less_eq_int @ ( nth_int @ L @ I ) @ X2 )
% 0.33/0.59               => ( ( ord_less_int @ X2 @ ( nth_int @ L @ J ) )
% 0.33/0.59                 => ~ ! [K3: nat] :
% 0.33/0.59                        ( ( ord_less_eq_nat @ I @ K3 )
% 0.33/0.59                       => ( ( ord_less_nat @ K3 @ J )
% 0.33/0.59                         => ( ( ord_less_eq_int @ ( nth_int @ L @ K3 ) @ X2 )
% 0.33/0.59                           => ~ ( ord_less_int @ X2 @ ( nth_int @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_in_between
% 0.33/0.59  thf(fact_4499_diff__numeral__special_I6_J,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.59        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % diff_numeral_special(6)
% 0.33/0.59  thf(fact_4500_diff__numeral__special_I6_J,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.59        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % diff_numeral_special(6)
% 0.33/0.59  thf(fact_4501_diff__numeral__special_I6_J,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.59        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % diff_numeral_special(6)
% 0.33/0.59  thf(fact_4502_diff__numeral__special_I5_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % diff_numeral_special(5)
% 0.33/0.59  thf(fact_4503_diff__numeral__special_I5_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 0.33/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % diff_numeral_special(5)
% 0.33/0.59  thf(fact_4504_diff__numeral__special_I5_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 0.33/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % diff_numeral_special(5)
% 0.33/0.59  thf(fact_4505_add__neg__numeral__special_I5_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_neg_numeral_special(5)
% 0.33/0.59  thf(fact_4506_add__neg__numeral__special_I5_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.33/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_neg_numeral_special(5)
% 0.33/0.59  thf(fact_4507_add__neg__numeral__special_I5_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.33/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_neg_numeral_special(5)
% 0.33/0.59  thf(fact_4508_add__neg__numeral__special_I6_J,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_neg_numeral_special(6)
% 0.33/0.59  thf(fact_4509_add__neg__numeral__special_I6_J,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.33/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_neg_numeral_special(6)
% 0.33/0.59  thf(fact_4510_add__neg__numeral__special_I6_J,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_neg_numeral_special(6)
% 0.33/0.59  thf(fact_4511_nth__rotate,axiom,
% 0.33/0.59      ! [N: nat,Xs: list_nat,M: nat] :
% 0.33/0.59        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.33/0.59       => ( ( nth_nat @ ( rotate_nat @ M @ Xs ) @ N )
% 0.33/0.59          = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( plus_plus_nat @ M @ N ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_rotate
% 0.33/0.59  thf(fact_4512_nth__rotate,axiom,
% 0.33/0.59      ! [N: nat,Xs: list_int,M: nat] :
% 0.33/0.59        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.33/0.59       => ( ( nth_int @ ( rotate_int @ M @ Xs ) @ N )
% 0.33/0.59          = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( plus_plus_nat @ M @ N ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_rotate
% 0.33/0.59  thf(fact_4513_nth__rotate,axiom,
% 0.33/0.59      ! [N: nat,Xs: list_o,M: nat] :
% 0.33/0.59        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.33/0.59       => ( ( nth_o @ ( rotate_o @ M @ Xs ) @ N )
% 0.33/0.59          = ( nth_o @ Xs @ ( modulo_modulo_nat @ ( plus_plus_nat @ M @ N ) @ ( size_size_list_o @ Xs ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_rotate
% 0.33/0.59  thf(fact_4514_nth__Cons__pos,axiom,
% 0.33/0.59      ! [N: nat,X2: int,Xs: list_int] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59       => ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ N )
% 0.33/0.59          = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_Cons_pos
% 0.33/0.59  thf(fact_4515_nth__Cons__pos,axiom,
% 0.33/0.59      ! [N: nat,X2: nat,Xs: list_nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59       => ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ N )
% 0.33/0.59          = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_Cons_pos
% 0.33/0.59  thf(fact_4516_nth__Cons__pos,axiom,
% 0.33/0.59      ! [N: nat,X2: char,Xs: list_char] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59       => ( ( nth_char @ ( cons_char @ X2 @ Xs ) @ N )
% 0.33/0.59          = ( nth_char @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_Cons_pos
% 0.33/0.59  thf(fact_4517_length__rotate,axiom,
% 0.33/0.59      ! [N: nat,Xs: list_nat] :
% 0.33/0.59        ( ( size_size_list_nat @ ( rotate_nat @ N @ Xs ) )
% 0.33/0.59        = ( size_size_list_nat @ Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % length_rotate
% 0.33/0.59  thf(fact_4518_length__rotate,axiom,
% 0.33/0.59      ! [N: nat,Xs: list_int] :
% 0.33/0.59        ( ( size_size_list_int @ ( rotate_int @ N @ Xs ) )
% 0.33/0.59        = ( size_size_list_int @ Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % length_rotate
% 0.33/0.59  thf(fact_4519_length__rotate,axiom,
% 0.33/0.59      ! [N: nat,Xs: list_o] :
% 0.33/0.59        ( ( size_size_list_o @ ( rotate_o @ N @ Xs ) )
% 0.33/0.59        = ( size_size_list_o @ Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % length_rotate
% 0.33/0.59  thf(fact_4520_nth__Cons__0,axiom,
% 0.33/0.59      ! [X2: int,Xs: list_int] :
% 0.33/0.59        ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ zero_zero_nat )
% 0.33/0.59        = X2 ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_Cons_0
% 0.33/0.59  thf(fact_4521_nth__Cons__0,axiom,
% 0.33/0.59      ! [X2: nat,Xs: list_nat] :
% 0.33/0.59        ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ zero_zero_nat )
% 0.33/0.59        = X2 ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_Cons_0
% 0.33/0.59  thf(fact_4522_nth__Cons__0,axiom,
% 0.33/0.59      ! [X2: char,Xs: list_char] :
% 0.33/0.59        ( ( nth_char @ ( cons_char @ X2 @ Xs ) @ zero_zero_nat )
% 0.33/0.59        = X2 ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_Cons_0
% 0.33/0.59  thf(fact_4523_rotate__length01,axiom,
% 0.33/0.59      ! [Xs: list_nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 0.33/0.59       => ( ( rotate_nat @ N @ Xs )
% 0.33/0.59          = Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % rotate_length01
% 0.33/0.59  thf(fact_4524_rotate__length01,axiom,
% 0.33/0.59      ! [Xs: list_int,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 0.33/0.59       => ( ( rotate_int @ N @ Xs )
% 0.33/0.59          = Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % rotate_length01
% 0.33/0.59  thf(fact_4525_rotate__length01,axiom,
% 0.33/0.59      ! [Xs: list_o,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 0.33/0.59       => ( ( rotate_o @ N @ Xs )
% 0.33/0.59          = Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % rotate_length01
% 0.33/0.59  thf(fact_4526_rotate__id,axiom,
% 0.33/0.59      ! [N: nat,Xs: list_nat] :
% 0.33/0.59        ( ( ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.33/0.59          = zero_zero_nat )
% 0.33/0.59       => ( ( rotate_nat @ N @ Xs )
% 0.33/0.59          = Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % rotate_id
% 0.33/0.59  thf(fact_4527_rotate__id,axiom,
% 0.33/0.59      ! [N: nat,Xs: list_int] :
% 0.33/0.59        ( ( ( modulo_modulo_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.33/0.59          = zero_zero_nat )
% 0.33/0.59       => ( ( rotate_int @ N @ Xs )
% 0.33/0.59          = Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % rotate_id
% 0.33/0.59  thf(fact_4528_rotate__id,axiom,
% 0.33/0.59      ! [N: nat,Xs: list_o] :
% 0.33/0.59        ( ( ( modulo_modulo_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.33/0.59          = zero_zero_nat )
% 0.33/0.59       => ( ( rotate_o @ N @ Xs )
% 0.33/0.59          = Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % rotate_id
% 0.33/0.59  thf(fact_4529_nth__Cons__numeral,axiom,
% 0.33/0.59      ! [X2: int,Xs: list_int,V: num] :
% 0.33/0.59        ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ ( numeral_numeral_nat @ V ) )
% 0.33/0.59        = ( nth_int @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_Cons_numeral
% 0.33/0.59  thf(fact_4530_nth__Cons__numeral,axiom,
% 0.33/0.59      ! [X2: nat,Xs: list_nat,V: num] :
% 0.33/0.59        ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ ( numeral_numeral_nat @ V ) )
% 0.33/0.59        = ( nth_nat @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_Cons_numeral
% 0.33/0.59  thf(fact_4531_nth__Cons__numeral,axiom,
% 0.33/0.59      ! [X2: char,Xs: list_char,V: num] :
% 0.33/0.59        ( ( nth_char @ ( cons_char @ X2 @ Xs ) @ ( numeral_numeral_nat @ V ) )
% 0.33/0.59        = ( nth_char @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_Cons_numeral
% 0.33/0.59  thf(fact_4532_mult__inc,axiom,
% 0.33/0.59      ! [X2: num,Y: num] :
% 0.33/0.59        ( ( times_times_num @ X2 @ ( inc @ Y ) )
% 0.33/0.59        = ( plus_plus_num @ ( times_times_num @ X2 @ Y ) @ X2 ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mult_inc
% 0.33/0.59  thf(fact_4533_sorted2,axiom,
% 0.33/0.59      ! [X2: rat,Y: rat,Zs: list_rat] :
% 0.33/0.59        ( ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ X2 @ ( cons_rat @ Y @ Zs ) ) )
% 0.33/0.59        = ( ( ord_less_eq_rat @ X2 @ Y )
% 0.33/0.59          & ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ Y @ Zs ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted2
% 0.33/0.59  thf(fact_4534_sorted2,axiom,
% 0.33/0.59      ! [X2: num,Y: num,Zs: list_num] :
% 0.33/0.59        ( ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ X2 @ ( cons_num @ Y @ Zs ) ) )
% 0.33/0.59        = ( ( ord_less_eq_num @ X2 @ Y )
% 0.33/0.59          & ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ Y @ Zs ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted2
% 0.33/0.59  thf(fact_4535_sorted2,axiom,
% 0.33/0.59      ! [X2: nat,Y: nat,Zs: list_nat] :
% 0.33/0.59        ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X2 @ ( cons_nat @ Y @ Zs ) ) )
% 0.33/0.59        = ( ( ord_less_eq_nat @ X2 @ Y )
% 0.33/0.59          & ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ Y @ Zs ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted2
% 0.33/0.59  thf(fact_4536_sorted2,axiom,
% 0.33/0.59      ! [X2: int,Y: int,Zs: list_int] :
% 0.33/0.59        ( ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X2 @ ( cons_int @ Y @ Zs ) ) )
% 0.33/0.59        = ( ( ord_less_eq_int @ X2 @ Y )
% 0.33/0.59          & ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ Y @ Zs ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted2
% 0.33/0.59  thf(fact_4537_add__inc,axiom,
% 0.33/0.59      ! [X2: num,Y: num] :
% 0.33/0.59        ( ( plus_plus_num @ X2 @ ( inc @ Y ) )
% 0.33/0.59        = ( inc @ ( plus_plus_num @ X2 @ Y ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_inc
% 0.33/0.59  thf(fact_4538_list__tail__coinc,axiom,
% 0.33/0.59      ! [N1: int,R1: list_int,N22: int,R22: list_int] :
% 0.33/0.59        ( ( ( cons_int @ N1 @ R1 )
% 0.33/0.59          = ( cons_int @ N22 @ R22 ) )
% 0.33/0.59       => ( ( N1 = N22 )
% 0.33/0.59          & ( R1 = R22 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_tail_coinc
% 0.33/0.59  thf(fact_4539_list__tail__coinc,axiom,
% 0.33/0.59      ! [N1: nat,R1: list_nat,N22: nat,R22: list_nat] :
% 0.33/0.59        ( ( ( cons_nat @ N1 @ R1 )
% 0.33/0.59          = ( cons_nat @ N22 @ R22 ) )
% 0.33/0.59       => ( ( N1 = N22 )
% 0.33/0.59          & ( R1 = R22 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_tail_coinc
% 0.33/0.59  thf(fact_4540_list__tail__coinc,axiom,
% 0.33/0.59      ! [N1: char,R1: list_char,N22: char,R22: list_char] :
% 0.33/0.59        ( ( ( cons_char @ N1 @ R1 )
% 0.33/0.59          = ( cons_char @ N22 @ R22 ) )
% 0.33/0.59       => ( ( N1 = N22 )
% 0.33/0.59          & ( R1 = R22 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_tail_coinc
% 0.33/0.59  thf(fact_4541_sorted__wrt__true,axiom,
% 0.33/0.59      ! [Xs: list_nat] :
% 0.33/0.59        ( sorted_wrt_nat
% 0.33/0.59        @ ^ [Uu: nat,Uv: nat] : $true
% 0.33/0.59        @ Xs ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_wrt_true
% 0.33/0.59  thf(fact_4542_sorted__wrt__true,axiom,
% 0.33/0.59      ! [Xs: list_int] :
% 0.33/0.59        ( sorted_wrt_int
% 0.33/0.59        @ ^ [Uu: int,Uv: int] : $true
% 0.33/0.59        @ Xs ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_wrt_true
% 0.33/0.59  thf(fact_4543_sorted1,axiom,
% 0.33/0.59      ! [X2: rat] : ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ X2 @ nil_rat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted1
% 0.33/0.59  thf(fact_4544_sorted1,axiom,
% 0.33/0.59      ! [X2: num] : ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ X2 @ nil_num ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted1
% 0.33/0.59  thf(fact_4545_sorted1,axiom,
% 0.33/0.59      ! [X2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X2 @ nil_nat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted1
% 0.33/0.59  thf(fact_4546_sorted1,axiom,
% 0.33/0.59      ! [X2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X2 @ nil_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted1
% 0.33/0.59  thf(fact_4547_mergesort__by__rel__merge__induct,axiom,
% 0.33/0.59      ! [P: list_int > list_int > $o,R3: int > int > $o,Xs: list_int,Ys: list_int] :
% 0.33/0.59        ( ! [Xs2: list_int] : ( P @ Xs2 @ nil_int )
% 0.33/0.59       => ( ! [X_12: list_int] : ( P @ nil_int @ X_12 )
% 0.33/0.59         => ( ! [X3: int,Xs2: list_int,Y2: int,Ys4: list_int] :
% 0.33/0.59                ( ( R3 @ X3 @ Y2 )
% 0.33/0.59               => ( ( P @ Xs2 @ ( cons_int @ Y2 @ Ys4 ) )
% 0.33/0.59                 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59           => ( ! [X3: int,Xs2: list_int,Y2: int,Ys4: list_int] :
% 0.33/0.59                  ( ~ ( R3 @ X3 @ Y2 )
% 0.33/0.59                 => ( ( P @ ( cons_int @ X3 @ Xs2 ) @ Ys4 )
% 0.33/0.59                   => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mergesort_by_rel_merge_induct
% 0.33/0.59  thf(fact_4548_mergesort__by__rel__merge__induct,axiom,
% 0.33/0.59      ! [P: list_nat > list_int > $o,R3: nat > int > $o,Xs: list_nat,Ys: list_int] :
% 0.33/0.59        ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_int )
% 0.33/0.59       => ( ! [X_12: list_int] : ( P @ nil_nat @ X_12 )
% 0.33/0.59         => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int] :
% 0.33/0.59                ( ( R3 @ X3 @ Y2 )
% 0.33/0.59               => ( ( P @ Xs2 @ ( cons_int @ Y2 @ Ys4 ) )
% 0.33/0.59                 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59           => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int] :
% 0.33/0.59                  ( ~ ( R3 @ X3 @ Y2 )
% 0.33/0.59                 => ( ( P @ ( cons_nat @ X3 @ Xs2 ) @ Ys4 )
% 0.33/0.59                   => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mergesort_by_rel_merge_induct
% 0.33/0.59  thf(fact_4549_mergesort__by__rel__merge__induct,axiom,
% 0.33/0.59      ! [P: list_char > list_int > $o,R3: char > int > $o,Xs: list_char,Ys: list_int] :
% 0.33/0.59        ( ! [Xs2: list_char] : ( P @ Xs2 @ nil_int )
% 0.33/0.59       => ( ! [X_12: list_int] : ( P @ nil_char @ X_12 )
% 0.33/0.59         => ( ! [X3: char,Xs2: list_char,Y2: int,Ys4: list_int] :
% 0.33/0.59                ( ( R3 @ X3 @ Y2 )
% 0.33/0.59               => ( ( P @ Xs2 @ ( cons_int @ Y2 @ Ys4 ) )
% 0.33/0.59                 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59           => ( ! [X3: char,Xs2: list_char,Y2: int,Ys4: list_int] :
% 0.33/0.59                  ( ~ ( R3 @ X3 @ Y2 )
% 0.33/0.59                 => ( ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys4 )
% 0.33/0.59                   => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mergesort_by_rel_merge_induct
% 0.33/0.59  thf(fact_4550_mergesort__by__rel__merge__induct,axiom,
% 0.33/0.59      ! [P: list_int > list_nat > $o,R3: int > nat > $o,Xs: list_int,Ys: list_nat] :
% 0.33/0.59        ( ! [Xs2: list_int] : ( P @ Xs2 @ nil_nat )
% 0.33/0.59       => ( ! [X_12: list_nat] : ( P @ nil_int @ X_12 )
% 0.33/0.59         => ( ! [X3: int,Xs2: list_int,Y2: nat,Ys4: list_nat] :
% 0.33/0.59                ( ( R3 @ X3 @ Y2 )
% 0.33/0.59               => ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys4 ) )
% 0.33/0.59                 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59           => ( ! [X3: int,Xs2: list_int,Y2: nat,Ys4: list_nat] :
% 0.33/0.59                  ( ~ ( R3 @ X3 @ Y2 )
% 0.33/0.59                 => ( ( P @ ( cons_int @ X3 @ Xs2 ) @ Ys4 )
% 0.33/0.59                   => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mergesort_by_rel_merge_induct
% 0.33/0.59  thf(fact_4551_mergesort__by__rel__merge__induct,axiom,
% 0.33/0.59      ! [P: list_nat > list_nat > $o,R3: nat > nat > $o,Xs: list_nat,Ys: list_nat] :
% 0.33/0.59        ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_nat )
% 0.33/0.59       => ( ! [X_12: list_nat] : ( P @ nil_nat @ X_12 )
% 0.33/0.59         => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys4: list_nat] :
% 0.33/0.59                ( ( R3 @ X3 @ Y2 )
% 0.33/0.59               => ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys4 ) )
% 0.33/0.59                 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59           => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys4: list_nat] :
% 0.33/0.59                  ( ~ ( R3 @ X3 @ Y2 )
% 0.33/0.59                 => ( ( P @ ( cons_nat @ X3 @ Xs2 ) @ Ys4 )
% 0.33/0.59                   => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mergesort_by_rel_merge_induct
% 0.33/0.59  thf(fact_4552_mergesort__by__rel__merge__induct,axiom,
% 0.33/0.59      ! [P: list_char > list_nat > $o,R3: char > nat > $o,Xs: list_char,Ys: list_nat] :
% 0.33/0.59        ( ! [Xs2: list_char] : ( P @ Xs2 @ nil_nat )
% 0.33/0.59       => ( ! [X_12: list_nat] : ( P @ nil_char @ X_12 )
% 0.33/0.59         => ( ! [X3: char,Xs2: list_char,Y2: nat,Ys4: list_nat] :
% 0.33/0.59                ( ( R3 @ X3 @ Y2 )
% 0.33/0.59               => ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys4 ) )
% 0.33/0.59                 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59           => ( ! [X3: char,Xs2: list_char,Y2: nat,Ys4: list_nat] :
% 0.33/0.59                  ( ~ ( R3 @ X3 @ Y2 )
% 0.33/0.59                 => ( ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys4 )
% 0.33/0.59                   => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mergesort_by_rel_merge_induct
% 0.33/0.59  thf(fact_4553_mergesort__by__rel__merge__induct,axiom,
% 0.33/0.59      ! [P: list_int > list_char > $o,R3: int > char > $o,Xs: list_int,Ys: list_char] :
% 0.33/0.59        ( ! [Xs2: list_int] : ( P @ Xs2 @ nil_char )
% 0.33/0.59       => ( ! [X_12: list_char] : ( P @ nil_int @ X_12 )
% 0.33/0.59         => ( ! [X3: int,Xs2: list_int,Y2: char,Ys4: list_char] :
% 0.33/0.59                ( ( R3 @ X3 @ Y2 )
% 0.33/0.59               => ( ( P @ Xs2 @ ( cons_char @ Y2 @ Ys4 ) )
% 0.33/0.59                 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59           => ( ! [X3: int,Xs2: list_int,Y2: char,Ys4: list_char] :
% 0.33/0.59                  ( ~ ( R3 @ X3 @ Y2 )
% 0.33/0.59                 => ( ( P @ ( cons_int @ X3 @ Xs2 ) @ Ys4 )
% 0.33/0.59                   => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mergesort_by_rel_merge_induct
% 0.33/0.59  thf(fact_4554_mergesort__by__rel__merge__induct,axiom,
% 0.33/0.59      ! [P: list_nat > list_char > $o,R3: nat > char > $o,Xs: list_nat,Ys: list_char] :
% 0.33/0.59        ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_char )
% 0.33/0.59       => ( ! [X_12: list_char] : ( P @ nil_nat @ X_12 )
% 0.33/0.59         => ( ! [X3: nat,Xs2: list_nat,Y2: char,Ys4: list_char] :
% 0.33/0.59                ( ( R3 @ X3 @ Y2 )
% 0.33/0.59               => ( ( P @ Xs2 @ ( cons_char @ Y2 @ Ys4 ) )
% 0.33/0.59                 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59           => ( ! [X3: nat,Xs2: list_nat,Y2: char,Ys4: list_char] :
% 0.33/0.59                  ( ~ ( R3 @ X3 @ Y2 )
% 0.33/0.59                 => ( ( P @ ( cons_nat @ X3 @ Xs2 ) @ Ys4 )
% 0.33/0.59                   => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mergesort_by_rel_merge_induct
% 0.33/0.59  thf(fact_4555_mergesort__by__rel__merge__induct,axiom,
% 0.33/0.59      ! [P: list_char > list_char > $o,R3: char > char > $o,Xs: list_char,Ys: list_char] :
% 0.33/0.59        ( ! [Xs2: list_char] : ( P @ Xs2 @ nil_char )
% 0.33/0.59       => ( ! [X_12: list_char] : ( P @ nil_char @ X_12 )
% 0.33/0.59         => ( ! [X3: char,Xs2: list_char,Y2: char,Ys4: list_char] :
% 0.33/0.59                ( ( R3 @ X3 @ Y2 )
% 0.33/0.59               => ( ( P @ Xs2 @ ( cons_char @ Y2 @ Ys4 ) )
% 0.33/0.59                 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59           => ( ! [X3: char,Xs2: list_char,Y2: char,Ys4: list_char] :
% 0.33/0.59                  ( ~ ( R3 @ X3 @ Y2 )
% 0.33/0.59                 => ( ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys4 )
% 0.33/0.59                   => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 0.33/0.59             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mergesort_by_rel_merge_induct
% 0.33/0.59  thf(fact_4556_list__induct__first2,axiom,
% 0.33/0.59      ! [P: list_int > $o,Xs: list_int] :
% 0.33/0.59        ( ( P @ nil_int )
% 0.33/0.59       => ( ! [X3: int] : ( P @ ( cons_int @ X3 @ nil_int ) )
% 0.33/0.59         => ( ! [X1: int,X23: int,Xs2: list_int] :
% 0.33/0.59                ( ( P @ Xs2 )
% 0.33/0.59               => ( P @ ( cons_int @ X1 @ ( cons_int @ X23 @ Xs2 ) ) ) )
% 0.33/0.59           => ( P @ Xs ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct_first2
% 0.33/0.59  thf(fact_4557_list__induct__first2,axiom,
% 0.33/0.59      ! [P: list_nat > $o,Xs: list_nat] :
% 0.33/0.59        ( ( P @ nil_nat )
% 0.33/0.59       => ( ! [X3: nat] : ( P @ ( cons_nat @ X3 @ nil_nat ) )
% 0.33/0.59         => ( ! [X1: nat,X23: nat,Xs2: list_nat] :
% 0.33/0.59                ( ( P @ Xs2 )
% 0.33/0.59               => ( P @ ( cons_nat @ X1 @ ( cons_nat @ X23 @ Xs2 ) ) ) )
% 0.33/0.59           => ( P @ Xs ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct_first2
% 0.33/0.59  thf(fact_4558_list__induct__first2,axiom,
% 0.33/0.59      ! [P: list_char > $o,Xs: list_char] :
% 0.33/0.59        ( ( P @ nil_char )
% 0.33/0.59       => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 0.33/0.59         => ( ! [X1: char,X23: char,Xs2: list_char] :
% 0.33/0.59                ( ( P @ Xs2 )
% 0.33/0.59               => ( P @ ( cons_char @ X1 @ ( cons_char @ X23 @ Xs2 ) ) ) )
% 0.33/0.59           => ( P @ Xs ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct_first2
% 0.33/0.59  thf(fact_4559_list__2pre__induct,axiom,
% 0.33/0.59      ! [P: list_int > list_int > $o,W1: list_int,W22: list_int] :
% 0.33/0.59        ( ( P @ nil_int @ nil_int )
% 0.33/0.59       => ( ! [E3: int,W12: list_int,W23: list_int] :
% 0.33/0.59              ( ( P @ W12 @ W23 )
% 0.33/0.59             => ( P @ ( cons_int @ E3 @ W12 ) @ W23 ) )
% 0.33/0.59         => ( ! [E3: int,W13: list_int,W24: list_int] :
% 0.33/0.59                ( ( P @ W13 @ W24 )
% 0.33/0.59               => ( P @ W13 @ ( cons_int @ E3 @ W24 ) ) )
% 0.33/0.59           => ( P @ W1 @ W22 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_2pre_induct
% 0.33/0.59  thf(fact_4560_list__2pre__induct,axiom,
% 0.33/0.59      ! [P: list_int > list_nat > $o,W1: list_int,W22: list_nat] :
% 0.33/0.59        ( ( P @ nil_int @ nil_nat )
% 0.33/0.59       => ( ! [E3: int,W12: list_int,W23: list_nat] :
% 0.33/0.59              ( ( P @ W12 @ W23 )
% 0.33/0.59             => ( P @ ( cons_int @ E3 @ W12 ) @ W23 ) )
% 0.33/0.59         => ( ! [E3: nat,W13: list_int,W24: list_nat] :
% 0.33/0.59                ( ( P @ W13 @ W24 )
% 0.33/0.59               => ( P @ W13 @ ( cons_nat @ E3 @ W24 ) ) )
% 0.33/0.59           => ( P @ W1 @ W22 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_2pre_induct
% 0.33/0.59  thf(fact_4561_list__2pre__induct,axiom,
% 0.33/0.59      ! [P: list_int > list_char > $o,W1: list_int,W22: list_char] :
% 0.33/0.59        ( ( P @ nil_int @ nil_char )
% 0.33/0.59       => ( ! [E3: int,W12: list_int,W23: list_char] :
% 0.33/0.59              ( ( P @ W12 @ W23 )
% 0.33/0.59             => ( P @ ( cons_int @ E3 @ W12 ) @ W23 ) )
% 0.33/0.59         => ( ! [E3: char,W13: list_int,W24: list_char] :
% 0.33/0.59                ( ( P @ W13 @ W24 )
% 0.33/0.59               => ( P @ W13 @ ( cons_char @ E3 @ W24 ) ) )
% 0.33/0.59           => ( P @ W1 @ W22 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_2pre_induct
% 0.33/0.59  thf(fact_4562_list__2pre__induct,axiom,
% 0.33/0.59      ! [P: list_nat > list_int > $o,W1: list_nat,W22: list_int] :
% 0.33/0.59        ( ( P @ nil_nat @ nil_int )
% 0.33/0.59       => ( ! [E3: nat,W12: list_nat,W23: list_int] :
% 0.33/0.59              ( ( P @ W12 @ W23 )
% 0.33/0.59             => ( P @ ( cons_nat @ E3 @ W12 ) @ W23 ) )
% 0.33/0.59         => ( ! [E3: int,W13: list_nat,W24: list_int] :
% 0.33/0.59                ( ( P @ W13 @ W24 )
% 0.33/0.59               => ( P @ W13 @ ( cons_int @ E3 @ W24 ) ) )
% 0.33/0.59           => ( P @ W1 @ W22 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_2pre_induct
% 0.33/0.59  thf(fact_4563_list__2pre__induct,axiom,
% 0.33/0.59      ! [P: list_nat > list_nat > $o,W1: list_nat,W22: list_nat] :
% 0.33/0.59        ( ( P @ nil_nat @ nil_nat )
% 0.33/0.59       => ( ! [E3: nat,W12: list_nat,W23: list_nat] :
% 0.33/0.59              ( ( P @ W12 @ W23 )
% 0.33/0.59             => ( P @ ( cons_nat @ E3 @ W12 ) @ W23 ) )
% 0.33/0.59         => ( ! [E3: nat,W13: list_nat,W24: list_nat] :
% 0.33/0.59                ( ( P @ W13 @ W24 )
% 0.33/0.59               => ( P @ W13 @ ( cons_nat @ E3 @ W24 ) ) )
% 0.33/0.59           => ( P @ W1 @ W22 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_2pre_induct
% 0.33/0.59  thf(fact_4564_list__2pre__induct,axiom,
% 0.33/0.59      ! [P: list_nat > list_char > $o,W1: list_nat,W22: list_char] :
% 0.33/0.59        ( ( P @ nil_nat @ nil_char )
% 0.33/0.59       => ( ! [E3: nat,W12: list_nat,W23: list_char] :
% 0.33/0.59              ( ( P @ W12 @ W23 )
% 0.33/0.59             => ( P @ ( cons_nat @ E3 @ W12 ) @ W23 ) )
% 0.33/0.59         => ( ! [E3: char,W13: list_nat,W24: list_char] :
% 0.33/0.59                ( ( P @ W13 @ W24 )
% 0.33/0.59               => ( P @ W13 @ ( cons_char @ E3 @ W24 ) ) )
% 0.33/0.59           => ( P @ W1 @ W22 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_2pre_induct
% 0.33/0.59  thf(fact_4565_list__2pre__induct,axiom,
% 0.33/0.59      ! [P: list_char > list_int > $o,W1: list_char,W22: list_int] :
% 0.33/0.59        ( ( P @ nil_char @ nil_int )
% 0.33/0.59       => ( ! [E3: char,W12: list_char,W23: list_int] :
% 0.33/0.59              ( ( P @ W12 @ W23 )
% 0.33/0.59             => ( P @ ( cons_char @ E3 @ W12 ) @ W23 ) )
% 0.33/0.59         => ( ! [E3: int,W13: list_char,W24: list_int] :
% 0.33/0.59                ( ( P @ W13 @ W24 )
% 0.33/0.59               => ( P @ W13 @ ( cons_int @ E3 @ W24 ) ) )
% 0.33/0.59           => ( P @ W1 @ W22 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_2pre_induct
% 0.33/0.59  thf(fact_4566_list__2pre__induct,axiom,
% 0.33/0.59      ! [P: list_char > list_nat > $o,W1: list_char,W22: list_nat] :
% 0.33/0.59        ( ( P @ nil_char @ nil_nat )
% 0.33/0.59       => ( ! [E3: char,W12: list_char,W23: list_nat] :
% 0.33/0.59              ( ( P @ W12 @ W23 )
% 0.33/0.59             => ( P @ ( cons_char @ E3 @ W12 ) @ W23 ) )
% 0.33/0.59         => ( ! [E3: nat,W13: list_char,W24: list_nat] :
% 0.33/0.59                ( ( P @ W13 @ W24 )
% 0.33/0.59               => ( P @ W13 @ ( cons_nat @ E3 @ W24 ) ) )
% 0.33/0.59           => ( P @ W1 @ W22 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_2pre_induct
% 0.33/0.59  thf(fact_4567_list__2pre__induct,axiom,
% 0.33/0.59      ! [P: list_char > list_char > $o,W1: list_char,W22: list_char] :
% 0.33/0.59        ( ( P @ nil_char @ nil_char )
% 0.33/0.59       => ( ! [E3: char,W12: list_char,W23: list_char] :
% 0.33/0.59              ( ( P @ W12 @ W23 )
% 0.33/0.59             => ( P @ ( cons_char @ E3 @ W12 ) @ W23 ) )
% 0.33/0.59         => ( ! [E3: char,W13: list_char,W24: list_char] :
% 0.33/0.59                ( ( P @ W13 @ W24 )
% 0.33/0.59               => ( P @ W13 @ ( cons_char @ E3 @ W24 ) ) )
% 0.33/0.59           => ( P @ W1 @ W22 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_2pre_induct
% 0.33/0.59  thf(fact_4568_neq__NilE,axiom,
% 0.33/0.59      ! [L: list_int] :
% 0.33/0.59        ( ( L != nil_int )
% 0.33/0.59       => ~ ! [X3: int,Xs2: list_int] :
% 0.33/0.59              ( L
% 0.33/0.59             != ( cons_int @ X3 @ Xs2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % neq_NilE
% 0.33/0.59  thf(fact_4569_neq__NilE,axiom,
% 0.33/0.59      ! [L: list_nat] :
% 0.33/0.59        ( ( L != nil_nat )
% 0.33/0.59       => ~ ! [X3: nat,Xs2: list_nat] :
% 0.33/0.59              ( L
% 0.33/0.59             != ( cons_nat @ X3 @ Xs2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % neq_NilE
% 0.33/0.59  thf(fact_4570_neq__NilE,axiom,
% 0.33/0.59      ! [L: list_char] :
% 0.33/0.59        ( ( L != nil_char )
% 0.33/0.59       => ~ ! [X3: char,Xs2: list_char] :
% 0.33/0.59              ( L
% 0.33/0.59             != ( cons_char @ X3 @ Xs2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % neq_NilE
% 0.33/0.59  thf(fact_4571_strict__sorted__imp__sorted,axiom,
% 0.33/0.59      ! [Xs: list_Code_integer] :
% 0.33/0.59        ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ Xs )
% 0.33/0.59       => ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % strict_sorted_imp_sorted
% 0.33/0.59  thf(fact_4572_strict__sorted__imp__sorted,axiom,
% 0.33/0.59      ! [Xs: list_rat] :
% 0.33/0.59        ( ( sorted_wrt_rat @ ord_less_rat @ Xs )
% 0.33/0.59       => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % strict_sorted_imp_sorted
% 0.33/0.59  thf(fact_4573_strict__sorted__imp__sorted,axiom,
% 0.33/0.59      ! [Xs: list_num] :
% 0.33/0.59        ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 0.33/0.59       => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % strict_sorted_imp_sorted
% 0.33/0.59  thf(fact_4574_strict__sorted__imp__sorted,axiom,
% 0.33/0.59      ! [Xs: list_nat] :
% 0.33/0.59        ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 0.33/0.59       => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % strict_sorted_imp_sorted
% 0.33/0.59  thf(fact_4575_strict__sorted__imp__sorted,axiom,
% 0.33/0.59      ! [Xs: list_int] :
% 0.33/0.59        ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 0.33/0.59       => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 0.33/0.59  
% 0.33/0.59  % strict_sorted_imp_sorted
% 0.33/0.59  thf(fact_4576_sorted0,axiom,
% 0.33/0.59      sorted_wrt_rat @ ord_less_eq_rat @ nil_rat ).
% 0.33/0.59  
% 0.33/0.59  % sorted0
% 0.33/0.59  thf(fact_4577_sorted0,axiom,
% 0.33/0.59      sorted_wrt_num @ ord_less_eq_num @ nil_num ).
% 0.33/0.59  
% 0.33/0.59  % sorted0
% 0.33/0.59  thf(fact_4578_sorted0,axiom,
% 0.33/0.59      sorted_wrt_nat @ ord_less_eq_nat @ nil_nat ).
% 0.33/0.59  
% 0.33/0.59  % sorted0
% 0.33/0.59  thf(fact_4579_sorted0,axiom,
% 0.33/0.59      sorted_wrt_int @ ord_less_eq_int @ nil_int ).
% 0.33/0.59  
% 0.33/0.59  % sorted0
% 0.33/0.59  thf(fact_4580_sorted__wrt__less__idx,axiom,
% 0.33/0.59      ! [Ns: list_nat,I: nat] :
% 0.33/0.59        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 0.33/0.59       => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 0.33/0.59         => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_wrt_less_idx
% 0.33/0.59  thf(fact_4581_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_char,Ws: list_char,P: list_nat > list_int > list_char > list_char > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_char @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_char @ Zs )
% 0.33/0.59              = ( size_size_list_char @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_char @ nil_char )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: char,Zs2: list_char,W3: char,Ws2: list_char] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_char @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_char @ Zs2 )
% 0.33/0.59                          = ( size_size_list_char @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_char @ Z4 @ Zs2 ) @ ( cons_char @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4582_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_char,Ws: list_nat,P: list_nat > list_int > list_char > list_nat > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_char @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_char @ Zs )
% 0.33/0.59              = ( size_size_list_nat @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_char @ nil_nat )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: char,Zs2: list_char,W3: nat,Ws2: list_nat] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_char @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_char @ Zs2 )
% 0.33/0.59                          = ( size_size_list_nat @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_char @ Z4 @ Zs2 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4583_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_char,Ws: list_int,P: list_nat > list_int > list_char > list_int > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_char @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_char @ Zs )
% 0.33/0.59              = ( size_size_list_int @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_char @ nil_int )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: char,Zs2: list_char,W3: int,Ws2: list_int] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_char @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_char @ Zs2 )
% 0.33/0.59                          = ( size_size_list_int @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_char @ Z4 @ Zs2 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4584_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_char,Ws: list_o,P: list_nat > list_int > list_char > list_o > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_char @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_char @ Zs )
% 0.33/0.59              = ( size_size_list_o @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_char @ nil_o )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: char,Zs2: list_char,W3: $o,Ws2: list_o] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_char @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_char @ Zs2 )
% 0.33/0.59                          = ( size_size_list_o @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_char @ Z4 @ Zs2 ) @ ( cons_o @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4585_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_nat,Ws: list_char,P: list_nat > list_int > list_nat > list_char > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_nat @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_nat @ Zs )
% 0.33/0.59              = ( size_size_list_char @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_nat @ nil_char )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: nat,Zs2: list_nat,W3: char,Ws2: list_char] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_nat @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_nat @ Zs2 )
% 0.33/0.59                          = ( size_size_list_char @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_nat @ Z4 @ Zs2 ) @ ( cons_char @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4586_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_nat,Ws: list_nat,P: list_nat > list_int > list_nat > list_nat > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_nat @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_nat @ Zs )
% 0.33/0.59              = ( size_size_list_nat @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_nat @ nil_nat )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: nat,Zs2: list_nat,W3: nat,Ws2: list_nat] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_nat @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_nat @ Zs2 )
% 0.33/0.59                          = ( size_size_list_nat @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_nat @ Z4 @ Zs2 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4587_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_nat,Ws: list_int,P: list_nat > list_int > list_nat > list_int > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_nat @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_nat @ Zs )
% 0.33/0.59              = ( size_size_list_int @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_nat @ nil_int )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: nat,Zs2: list_nat,W3: int,Ws2: list_int] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_nat @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_nat @ Zs2 )
% 0.33/0.59                          = ( size_size_list_int @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_nat @ Z4 @ Zs2 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4588_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_nat,Ws: list_o,P: list_nat > list_int > list_nat > list_o > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_nat @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_nat @ Zs )
% 0.33/0.59              = ( size_size_list_o @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_nat @ nil_o )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: nat,Zs2: list_nat,W3: $o,Ws2: list_o] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_nat @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_nat @ Zs2 )
% 0.33/0.59                          = ( size_size_list_o @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_nat @ Z4 @ Zs2 ) @ ( cons_o @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4589_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_int,Ws: list_char,P: list_nat > list_int > list_int > list_char > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_int @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_int @ Zs )
% 0.33/0.59              = ( size_size_list_char @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_int @ nil_char )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: int,Zs2: list_int,W3: char,Ws2: list_char] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_int @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_int @ Zs2 )
% 0.33/0.59                          = ( size_size_list_char @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_int @ Z4 @ Zs2 ) @ ( cons_char @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4590_list__induct4,axiom,
% 0.33/0.59      ! [Xs: list_nat,Ys: list_int,Zs: list_int,Ws: list_nat,P: list_nat > list_int > list_int > list_nat > $o] :
% 0.33/0.59        ( ( ( size_size_list_nat @ Xs )
% 0.33/0.59          = ( size_size_list_int @ Ys ) )
% 0.33/0.59       => ( ( ( size_size_list_int @ Ys )
% 0.33/0.59            = ( size_size_list_int @ Zs ) )
% 0.33/0.59         => ( ( ( size_size_list_int @ Zs )
% 0.33/0.59              = ( size_size_list_nat @ Ws ) )
% 0.33/0.59           => ( ( P @ nil_nat @ nil_int @ nil_int @ nil_nat )
% 0.33/0.59             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: int,Zs2: list_int,W3: nat,Ws2: list_nat] :
% 0.33/0.59                    ( ( ( size_size_list_nat @ Xs2 )
% 0.33/0.59                      = ( size_size_list_int @ Ys4 ) )
% 0.33/0.59                   => ( ( ( size_size_list_int @ Ys4 )
% 0.33/0.59                        = ( size_size_list_int @ Zs2 ) )
% 0.33/0.59                     => ( ( ( size_size_list_int @ Zs2 )
% 0.33/0.59                          = ( size_size_list_nat @ Ws2 ) )
% 0.33/0.59                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 0.33/0.59                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_int @ Z4 @ Zs2 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 0.33/0.59               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % list_induct4
% 0.33/0.59  thf(fact_4591_upto__aux__rec,axiom,
% 0.33/0.59      ( upto_aux
% 0.33/0.59      = ( ^ [I2: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I2 ) @ Js @ ( upto_aux @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % upto_aux_rec
% 0.33/0.59  thf(fact_4592_upto__rec__numeral_I4_J,axiom,
% 0.33/0.59      ! [M: num,N: num] :
% 0.33/0.59        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.59         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.59            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.33/0.59        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.59         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.59            = nil_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % upto_rec_numeral(4)
% 0.33/0.59  thf(fact_4593_upto__rec__numeral_I3_J,axiom,
% 0.33/0.59      ! [M: num,N: num] :
% 0.33/0.59        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.59         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.59            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.33/0.59        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.59         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.59            = nil_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % upto_rec_numeral(3)
% 0.33/0.59  thf(fact_4594_upto__rec__numeral_I2_J,axiom,
% 0.33/0.59      ! [M: num,N: num] :
% 0.33/0.59        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.59         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.59            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.33/0.59        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.59         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.59            = nil_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % upto_rec_numeral(2)
% 0.33/0.59  thf(fact_4595_Suc__numeral,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( suc @ ( numeral_numeral_nat @ N ) )
% 0.33/0.59        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_numeral
% 0.33/0.59  thf(fact_4596_nth__upto,axiom,
% 0.33/0.59      ! [I: int,K: nat,J: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 0.33/0.59       => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 0.33/0.59          = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nth_upto
% 0.33/0.59  thf(fact_4597_length__upto,axiom,
% 0.33/0.59      ! [I: int,J: int] :
% 0.33/0.59        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 0.33/0.59        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % length_upto
% 0.33/0.59  thf(fact_4598_upto__rec__numeral_I1_J,axiom,
% 0.33/0.59      ! [M: num,N: num] :
% 0.33/0.59        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.59         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.59            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.33/0.59        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.59         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.59            = nil_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % upto_rec_numeral(1)
% 0.33/0.59  thf(fact_4599_num_Osize_I4_J,axiom,
% 0.33/0.59      ( ( size_size_num @ one )
% 0.33/0.59      = zero_zero_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % num.size(4)
% 0.33/0.59  thf(fact_4600_sorted__upto,axiom,
% 0.33/0.59      ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sorted_upto
% 0.33/0.59  thf(fact_4601_add__One__commute,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( plus_plus_num @ one @ N )
% 0.33/0.59        = ( plus_plus_num @ N @ one ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_One_commute
% 0.33/0.59  thf(fact_4602_num__induct,axiom,
% 0.33/0.59      ! [P: num > $o,X2: num] :
% 0.33/0.59        ( ( P @ one )
% 0.33/0.59       => ( ! [X3: num] :
% 0.33/0.59              ( ( P @ X3 )
% 0.33/0.59             => ( P @ ( inc @ X3 ) ) )
% 0.33/0.59         => ( P @ X2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % num_induct
% 0.33/0.59  thf(fact_4603_le__num__One__iff,axiom,
% 0.33/0.59      ! [X2: num] :
% 0.33/0.59        ( ( ord_less_eq_num @ X2 @ one )
% 0.33/0.59        = ( X2 = one ) ) ).
% 0.33/0.59  
% 0.33/0.59  % le_num_One_iff
% 0.33/0.59  thf(fact_4604_numerals_I1_J,axiom,
% 0.33/0.59      ( ( numeral_numeral_nat @ one )
% 0.33/0.59      = one_one_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % numerals(1)
% 0.33/0.59  thf(fact_4605_add__One,axiom,
% 0.33/0.59      ! [X2: num] :
% 0.33/0.59        ( ( plus_plus_num @ X2 @ one )
% 0.33/0.59        = ( inc @ X2 ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_One
% 0.33/0.59  thf(fact_4606_numeral__1__eq__Suc__0,axiom,
% 0.33/0.59      ( ( numeral_numeral_nat @ one )
% 0.33/0.59      = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % numeral_1_eq_Suc_0
% 0.33/0.59  thf(fact_4607_upto__rec1,axiom,
% 0.33/0.59      ! [I: int,J: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ I @ J )
% 0.33/0.59       => ( ( upto @ I @ J )
% 0.33/0.59          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % upto_rec1
% 0.33/0.59  thf(fact_4608_upto_Osimps,axiom,
% 0.33/0.59      ( upto
% 0.33/0.59      = ( ^ [I2: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I2 @ J3 ) @ ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % upto.simps
% 0.33/0.59  thf(fact_4609_upto_Oelims,axiom,
% 0.33/0.59      ! [X2: int,Xa: int,Y: list_int] :
% 0.33/0.59        ( ( ( upto @ X2 @ Xa )
% 0.33/0.59          = Y )
% 0.33/0.59       => ( ( ( ord_less_eq_int @ X2 @ Xa )
% 0.33/0.59           => ( Y
% 0.33/0.59              = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa ) ) ) )
% 0.33/0.59          & ( ~ ( ord_less_eq_int @ X2 @ Xa )
% 0.33/0.59           => ( Y = nil_int ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % upto.elims
% 0.33/0.59  thf(fact_4610_Suc__nat__number__of__add,axiom,
% 0.33/0.59      ! [V: num,N: nat] :
% 0.33/0.59        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 0.33/0.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_nat_number_of_add
% 0.33/0.59  thf(fact_4611_neg__zmod__mult__2,axiom,
% 0.33/0.59      ! [A: int,B: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.33/0.59       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.59          = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % neg_zmod_mult_2
% 0.33/0.59  thf(fact_4612_verit__eq__simplify_I8_J,axiom,
% 0.33/0.59      ! [X22: num,Y22: num] :
% 0.33/0.59        ( ( ( bit0 @ X22 )
% 0.33/0.59          = ( bit0 @ Y22 ) )
% 0.33/0.59        = ( X22 = Y22 ) ) ).
% 0.33/0.59  
% 0.33/0.59  % verit_eq_simplify(8)
% 0.33/0.59  thf(fact_4613_semiring__norm_I6_J,axiom,
% 0.33/0.59      ! [M: num,N: num] :
% 0.33/0.59        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.33/0.59        = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(6)
% 0.33/0.59  thf(fact_4614_semiring__norm_I2_J,axiom,
% 0.33/0.59      ( ( plus_plus_num @ one @ one )
% 0.33/0.59      = ( bit0 @ one ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(2)
% 0.33/0.59  thf(fact_4615_num__double,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( times_times_num @ ( bit0 @ one ) @ N )
% 0.33/0.59        = ( bit0 @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % num_double
% 0.33/0.59  thf(fact_4616_add__2__eq__Suc_H,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59        = ( suc @ ( suc @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_2_eq_Suc'
% 0.33/0.59  thf(fact_4617_add__2__eq__Suc,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.33/0.59        = ( suc @ ( suc @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % add_2_eq_Suc
% 0.33/0.59  thf(fact_4618_Suc__1,axiom,
% 0.33/0.59      ( ( suc @ one_one_nat )
% 0.33/0.59      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_1
% 0.33/0.59  thf(fact_4619_add__self__div__2,axiom,
% 0.33/0.59      ! [M: nat] :
% 0.33/0.59        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59        = M ) ).
% 0.33/0.59  
% 0.33/0.59  % add_self_div_2
% 0.33/0.59  thf(fact_4620_not__mod2__eq__Suc__0__eq__0,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59         != ( suc @ zero_zero_nat ) )
% 0.33/0.59        = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59          = zero_zero_nat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % not_mod2_eq_Suc_0_eq_0
% 0.33/0.59  thf(fact_4621_add__self__mod__2,axiom,
% 0.33/0.59      ! [M: nat] :
% 0.33/0.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59        = zero_zero_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % add_self_mod_2
% 0.33/0.59  thf(fact_4622_half__nonnegative__int__iff,axiom,
% 0.33/0.59      ! [K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.33/0.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % half_nonnegative_int_iff
% 0.33/0.59  thf(fact_4623_half__negative__int__iff,axiom,
% 0.33/0.59      ! [K: int] :
% 0.33/0.59        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.33/0.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % half_negative_int_iff
% 0.33/0.59  thf(fact_4624_mod2__gr__0,axiom,
% 0.33/0.59      ! [M: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.33/0.59        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59          = one_one_nat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod2_gr_0
% 0.33/0.59  thf(fact_4625_verit__eq__simplify_I10_J,axiom,
% 0.33/0.59      ! [X22: num] :
% 0.33/0.59        ( one
% 0.33/0.59       != ( bit0 @ X22 ) ) ).
% 0.33/0.59  
% 0.33/0.59  % verit_eq_simplify(10)
% 0.33/0.59  thf(fact_4626_inc_Osimps_I1_J,axiom,
% 0.33/0.59      ( ( inc @ one )
% 0.33/0.59      = ( bit0 @ one ) ) ).
% 0.33/0.59  
% 0.33/0.59  % inc.simps(1)
% 0.33/0.59  thf(fact_4627_num_Osize_I5_J,axiom,
% 0.33/0.59      ! [X22: num] :
% 0.33/0.59        ( ( size_size_num @ ( bit0 @ X22 ) )
% 0.33/0.59        = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % num.size(5)
% 0.33/0.59  thf(fact_4628_numeral__2__eq__2,axiom,
% 0.33/0.59      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.33/0.59      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % numeral_2_eq_2
% 0.33/0.59  thf(fact_4629_nat__1__add__1,axiom,
% 0.33/0.59      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.33/0.59      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_1_add_1
% 0.33/0.59  thf(fact_4630_power2__nat__le__imp__le,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 0.33/0.59       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % power2_nat_le_imp_le
% 0.33/0.59  thf(fact_4631_power2__nat__le__eq__le,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.33/0.59        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % power2_nat_le_eq_le
% 0.33/0.59  thf(fact_4632_self__le__ge2__pow,axiom,
% 0.33/0.59      ! [K: nat,M: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.33/0.59       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % self_le_ge2_pow
% 0.33/0.59  thf(fact_4633_less__2__cases__iff,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59        = ( ( N = zero_zero_nat )
% 0.33/0.59          | ( N
% 0.33/0.59            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % less_2_cases_iff
% 0.33/0.59  thf(fact_4634_less__2__cases,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59       => ( ( N = zero_zero_nat )
% 0.33/0.59          | ( N
% 0.33/0.59            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % less_2_cases
% 0.33/0.59  thf(fact_4635_nat__induct2,axiom,
% 0.33/0.59      ! [P: nat > $o,N: nat] :
% 0.33/0.59        ( ( P @ zero_zero_nat )
% 0.33/0.59       => ( ( P @ one_one_nat )
% 0.33/0.59         => ( ! [N2: nat] :
% 0.33/0.59                ( ( P @ N2 )
% 0.33/0.59               => ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.33/0.59           => ( P @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_induct2
% 0.33/0.59  thf(fact_4636_nat__2,axiom,
% 0.33/0.59      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.59      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_2
% 0.33/0.59  thf(fact_4637_diff__le__diff__pow,axiom,
% 0.33/0.59      ! [K: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.33/0.59       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % diff_le_diff_pow
% 0.33/0.59  thf(fact_4638_not__exp__less__eq__0__int,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 0.33/0.59  
% 0.33/0.59  % not_exp_less_eq_0_int
% 0.33/0.59  thf(fact_4639_nat__bit__induct,axiom,
% 0.33/0.59      ! [P: nat > $o,N: nat] :
% 0.33/0.59        ( ( P @ zero_zero_nat )
% 0.33/0.59       => ( ! [N2: nat] :
% 0.33/0.59              ( ( P @ N2 )
% 0.33/0.59             => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.59               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.59         => ( ! [N2: nat] :
% 0.33/0.59                ( ( P @ N2 )
% 0.33/0.59               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.33/0.59           => ( P @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_bit_induct
% 0.33/0.59  thf(fact_4640_div__2__gt__zero,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.59       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % div_2_gt_zero
% 0.33/0.59  thf(fact_4641_Suc__n__div__2__gt__zero,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_n_div_2_gt_zero
% 0.33/0.59  thf(fact_4642_minus__1__div__exp__eq__int,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.33/0.59        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % minus_1_div_exp_eq_int
% 0.33/0.59  thf(fact_4643_ex__power__ivl2,axiom,
% 0.33/0.59      ! [B: nat,K: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.33/0.59       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.33/0.59         => ? [N2: nat] :
% 0.33/0.59              ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.33/0.59              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % ex_power_ivl2
% 0.33/0.59  thf(fact_4644_ex__power__ivl1,axiom,
% 0.33/0.59      ! [B: nat,K: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.33/0.59       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 0.33/0.59         => ? [N2: nat] :
% 0.33/0.59              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.33/0.59              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % ex_power_ivl1
% 0.33/0.59  thf(fact_4645_int__bit__induct,axiom,
% 0.33/0.59      ! [P: int > $o,K: int] :
% 0.33/0.59        ( ( P @ zero_zero_int )
% 0.33/0.59       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.59         => ( ! [K3: int] :
% 0.33/0.59                ( ( P @ K3 )
% 0.33/0.59               => ( ( K3 != zero_zero_int )
% 0.33/0.59                 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 0.33/0.59           => ( ! [K3: int] :
% 0.33/0.59                  ( ( P @ K3 )
% 0.33/0.59                 => ( ( K3
% 0.33/0.59                     != ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.59                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 0.33/0.59             => ( P @ K ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % int_bit_induct
% 0.33/0.59  thf(fact_4646_pos__zdiv__mult__2,axiom,
% 0.33/0.59      ! [A: int,B: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.59       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.59          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % pos_zdiv_mult_2
% 0.33/0.59  thf(fact_4647_neg__zdiv__mult__2,axiom,
% 0.33/0.59      ! [A: int,B: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.33/0.59       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.59          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % neg_zdiv_mult_2
% 0.33/0.59  thf(fact_4648_pos__zmod__mult__2,axiom,
% 0.33/0.59      ! [A: int,B: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.33/0.59       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.33/0.59          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % pos_zmod_mult_2
% 0.33/0.59  thf(fact_4649_unset__bit__nonnegative__int__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 0.33/0.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % unset_bit_nonnegative_int_iff
% 0.33/0.59  thf(fact_4650_set__bit__nonnegative__int__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 0.33/0.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % set_bit_nonnegative_int_iff
% 0.33/0.59  thf(fact_4651_flip__bit__nonnegative__int__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 0.33/0.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % flip_bit_nonnegative_int_iff
% 0.33/0.59  thf(fact_4652_unset__bit__negative__int__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 0.33/0.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % unset_bit_negative_int_iff
% 0.33/0.59  thf(fact_4653_set__bit__negative__int__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 0.33/0.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % set_bit_negative_int_iff
% 0.33/0.59  thf(fact_4654_flip__bit__negative__int__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 0.33/0.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % flip_bit_negative_int_iff
% 0.33/0.59  thf(fact_4655_signed__take__bit__add,axiom,
% 0.33/0.59      ! [N: nat,K: int,L: int] :
% 0.33/0.59        ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 0.33/0.59        = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_add
% 0.33/0.59  thf(fact_4656_unset__bit__nat__def,axiom,
% 0.33/0.59      ( bit_se4205575877204974255it_nat
% 0.33/0.59      = ( ^ [M2: nat,N3: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M2 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % unset_bit_nat_def
% 0.33/0.59  thf(fact_4657_unset__bit__less__eq,axiom,
% 0.33/0.59      ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 0.33/0.59  
% 0.33/0.59  % unset_bit_less_eq
% 0.33/0.59  thf(fact_4658_set__bit__greater__eq,axiom,
% 0.33/0.59      ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % set_bit_greater_eq
% 0.33/0.59  thf(fact_4659_signed__take__bit__int__greater__eq__self__iff,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.33/0.59        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_int_greater_eq_self_iff
% 0.33/0.59  thf(fact_4660_signed__take__bit__int__less__self__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.33/0.59        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_int_less_self_iff
% 0.33/0.59  thf(fact_4661_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 0.33/0.59      ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_int_greater_eq_minus_exp
% 0.33/0.59  thf(fact_4662_signed__take__bit__int__less__eq__self__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.33/0.59        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_int_less_eq_self_iff
% 0.33/0.59  thf(fact_4663_signed__take__bit__int__less__eq,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.33/0.59       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_int_less_eq
% 0.33/0.59  thf(fact_4664_signed__take__bit__int__eq__self__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.33/0.59          = K )
% 0.33/0.59        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.33/0.59          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_int_eq_self_iff
% 0.33/0.59  thf(fact_4665_signed__take__bit__int__eq__self,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.33/0.59       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.33/0.59         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.33/0.59            = K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_int_eq_self
% 0.33/0.59  thf(fact_4666_signed__take__bit__int__greater__eq,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.33/0.59       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_int_greater_eq
% 0.33/0.59  thf(fact_4667_binomial__code,axiom,
% 0.33/0.59      ( binomial
% 0.33/0.59      = ( ^ [N3: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N3 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N3 @ ( minus_minus_nat @ N3 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N3 @ K2 ) @ one_one_nat ) @ N3 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_code
% 0.33/0.59  thf(fact_4668_signed__take__bit__Suc__minus__bit1,axiom,
% 0.33/0.59      ! [N: nat,K: num] :
% 0.33/0.59        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.33/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_Suc_minus_bit1
% 0.33/0.59  thf(fact_4669_concat__bit__Suc,axiom,
% 0.33/0.59      ! [N: nat,K: int,L: int] :
% 0.33/0.59        ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 0.33/0.59        = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % concat_bit_Suc
% 0.33/0.59  thf(fact_4670_verit__eq__simplify_I9_J,axiom,
% 0.33/0.59      ! [X32: num,Y32: num] :
% 0.33/0.59        ( ( ( bit1 @ X32 )
% 0.33/0.59          = ( bit1 @ Y32 ) )
% 0.33/0.59        = ( X32 = Y32 ) ) ).
% 0.33/0.59  
% 0.33/0.59  % verit_eq_simplify(9)
% 0.33/0.59  thf(fact_4671_nat__dvd__1__iff__1,axiom,
% 0.33/0.59      ! [M: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.33/0.59        = ( M = one_one_nat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_dvd_1_iff_1
% 0.33/0.59  thf(fact_4672_int__dvd__int__iff,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.33/0.59        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % int_dvd_int_iff
% 0.33/0.59  thf(fact_4673_dvd__1__iff__1,axiom,
% 0.33/0.59      ! [M: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.33/0.59        = ( M
% 0.33/0.59          = ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_1_iff_1
% 0.33/0.59  thf(fact_4674_dvd__1__left,axiom,
% 0.33/0.59      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_1_left
% 0.33/0.59  thf(fact_4675_nat__mult__dvd__cancel__disj,axiom,
% 0.33/0.59      ! [K: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.33/0.59        = ( ( K = zero_zero_nat )
% 0.33/0.59          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_mult_dvd_cancel_disj
% 0.33/0.59  thf(fact_4676_zdvd1__eq,axiom,
% 0.33/0.59      ! [X2: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ X2 @ one_one_int )
% 0.33/0.59        = ( ( abs_abs_int @ X2 )
% 0.33/0.59          = one_one_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd1_eq
% 0.33/0.59  thf(fact_4677_binomial__n__n,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( binomial @ N @ N )
% 0.33/0.59        = one_one_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_n_n
% 0.33/0.59  thf(fact_4678_concat__bit__0,axiom,
% 0.33/0.59      ! [K: int,L: int] :
% 0.33/0.59        ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 0.33/0.59        = L ) ).
% 0.33/0.59  
% 0.33/0.59  % concat_bit_0
% 0.33/0.59  thf(fact_4679_concat__bit__of__zero__2,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 0.33/0.59        = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % concat_bit_of_zero_2
% 0.33/0.59  thf(fact_4680_binomial__1,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 0.33/0.59        = N ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_1
% 0.33/0.59  thf(fact_4681_binomial__0__Suc,axiom,
% 0.33/0.59      ! [K: nat] :
% 0.33/0.59        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 0.33/0.59        = zero_zero_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_0_Suc
% 0.33/0.59  thf(fact_4682_binomial__eq__0__iff,axiom,
% 0.33/0.59      ! [N: nat,K: nat] :
% 0.33/0.59        ( ( ( binomial @ N @ K )
% 0.33/0.59          = zero_zero_nat )
% 0.33/0.59        = ( ord_less_nat @ N @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_eq_0_iff
% 0.33/0.59  thf(fact_4683_binomial__Suc__Suc,axiom,
% 0.33/0.59      ! [N: nat,K: nat] :
% 0.33/0.59        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 0.33/0.59        = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_Suc_Suc
% 0.33/0.59  thf(fact_4684_semiring__norm_I7_J,axiom,
% 0.33/0.59      ! [M: num,N: num] :
% 0.33/0.59        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.33/0.59        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(7)
% 0.33/0.59  thf(fact_4685_semiring__norm_I9_J,axiom,
% 0.33/0.59      ! [M: num,N: num] :
% 0.33/0.59        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.33/0.59        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(9)
% 0.33/0.59  thf(fact_4686_binomial__n__0,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( binomial @ N @ zero_zero_nat )
% 0.33/0.59        = one_one_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_n_0
% 0.33/0.59  thf(fact_4687_dvd__nat__abs__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( dvd_dvd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 0.33/0.59        = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_nat_abs_iff
% 0.33/0.59  thf(fact_4688_nat__abs__dvd__iff,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 0.33/0.59        = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_abs_dvd_iff
% 0.33/0.59  thf(fact_4689_concat__bit__nonnegative__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int,L: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 0.33/0.59        = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 0.33/0.59  
% 0.33/0.59  % concat_bit_nonnegative_iff
% 0.33/0.59  thf(fact_4690_concat__bit__negative__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int,L: int] :
% 0.33/0.59        ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 0.33/0.59        = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % concat_bit_negative_iff
% 0.33/0.59  thf(fact_4691_zero__less__binomial__iff,axiom,
% 0.33/0.59      ! [N: nat,K: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 0.33/0.59        = ( ord_less_eq_nat @ K @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zero_less_binomial_iff
% 0.33/0.59  thf(fact_4692_semiring__norm_I3_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 0.33/0.59        = ( bit1 @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(3)
% 0.33/0.59  thf(fact_4693_semiring__norm_I4_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 0.33/0.59        = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(4)
% 0.33/0.59  thf(fact_4694_semiring__norm_I5_J,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 0.33/0.59        = ( bit1 @ M ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(5)
% 0.33/0.59  thf(fact_4695_semiring__norm_I8_J,axiom,
% 0.33/0.59      ! [M: num] :
% 0.33/0.59        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 0.33/0.59        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(8)
% 0.33/0.59  thf(fact_4696_semiring__norm_I10_J,axiom,
% 0.33/0.59      ! [M: num,N: num] :
% 0.33/0.59        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.33/0.59        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(10)
% 0.33/0.59  thf(fact_4697_semiring__norm_I16_J,axiom,
% 0.33/0.59      ! [M: num,N: num] :
% 0.33/0.59        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.33/0.59        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % semiring_norm(16)
% 0.33/0.59  thf(fact_4698_odd__Suc__minus__one,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.33/0.59       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.33/0.59          = N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % odd_Suc_minus_one
% 0.33/0.59  thf(fact_4699_even__diff__nat,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 0.33/0.59        = ( ( ord_less_nat @ M @ N )
% 0.33/0.59          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % even_diff_nat
% 0.33/0.59  thf(fact_4700_Suc__mod__eq__add3__mod__numeral,axiom,
% 0.33/0.59      ! [M: nat,V: num] :
% 0.33/0.59        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.33/0.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_mod_eq_add3_mod_numeral
% 0.33/0.59  thf(fact_4701_mod__Suc__eq__mod__add3,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.33/0.59        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_Suc_eq_mod_add3
% 0.33/0.59  thf(fact_4702_Suc__div__eq__add3__div__numeral,axiom,
% 0.33/0.59      ! [M: nat,V: num] :
% 0.33/0.59        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.33/0.59        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_div_eq_add3_div_numeral
% 0.33/0.59  thf(fact_4703_div__Suc__eq__div__add3,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.33/0.59        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % div_Suc_eq_div_add3
% 0.33/0.59  thf(fact_4704_odd__two__times__div__two__nat,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.33/0.59       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.33/0.59          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % odd_two_times_div_two_nat
% 0.33/0.59  thf(fact_4705_zmod__numeral__Bit1,axiom,
% 0.33/0.59      ! [V: num,W2: num] :
% 0.33/0.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 0.33/0.59        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W2 ) ) ) @ one_one_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zmod_numeral_Bit1
% 0.33/0.59  thf(fact_4706_signed__take__bit__Suc__bit1,axiom,
% 0.33/0.59      ! [N: nat,K: num] :
% 0.33/0.59        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.33/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_Suc_bit1
% 0.33/0.59  thf(fact_4707_take__bit__nat__less__eq__self,axiom,
% 0.33/0.59      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_nat_less_eq_self
% 0.33/0.59  thf(fact_4708_take__bit__tightened__less__eq__nat,axiom,
% 0.33/0.59      ! [M: nat,N: nat,Q2: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.59       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_tightened_less_eq_nat
% 0.33/0.59  thf(fact_4709_choose__one,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( binomial @ N @ one_one_nat )
% 0.33/0.59        = N ) ).
% 0.33/0.59  
% 0.33/0.59  % choose_one
% 0.33/0.59  thf(fact_4710_verit__eq__simplify_I14_J,axiom,
% 0.33/0.59      ! [X22: num,X32: num] :
% 0.33/0.59        ( ( bit0 @ X22 )
% 0.33/0.59       != ( bit1 @ X32 ) ) ).
% 0.33/0.59  
% 0.33/0.59  % verit_eq_simplify(14)
% 0.33/0.59  thf(fact_4711_verit__eq__simplify_I12_J,axiom,
% 0.33/0.59      ! [X32: num] :
% 0.33/0.59        ( one
% 0.33/0.59       != ( bit1 @ X32 ) ) ).
% 0.33/0.59  
% 0.33/0.59  % verit_eq_simplify(12)
% 0.33/0.59  thf(fact_4712_gcd__nat_Oextremum,axiom,
% 0.33/0.59      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.extremum
% 0.33/0.59  thf(fact_4713_gcd__nat_Oextremum__strict,axiom,
% 0.33/0.59      ! [A: nat] :
% 0.33/0.59        ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.33/0.59          & ( zero_zero_nat != A ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.extremum_strict
% 0.33/0.59  thf(fact_4714_gcd__nat_Oextremum__unique,axiom,
% 0.33/0.59      ! [A: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.33/0.59        = ( A = zero_zero_nat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.extremum_unique
% 0.33/0.59  thf(fact_4715_gcd__nat_Onot__eq__extremum,axiom,
% 0.33/0.59      ! [A: nat] :
% 0.33/0.59        ( ( A != zero_zero_nat )
% 0.33/0.59        = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 0.33/0.59          & ( A != zero_zero_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.not_eq_extremum
% 0.33/0.59  thf(fact_4716_gcd__nat_Oextremum__uniqueI,axiom,
% 0.33/0.59      ! [A: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.33/0.59       => ( A = zero_zero_nat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.extremum_uniqueI
% 0.33/0.59  thf(fact_4717_dvd__diff__nat,axiom,
% 0.33/0.59      ! [K: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ K @ M )
% 0.33/0.59       => ( ( dvd_dvd_nat @ K @ N )
% 0.33/0.59         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_diff_nat
% 0.33/0.59  thf(fact_4718_uminus__dvd__conv_I2_J,axiom,
% 0.33/0.59      ( dvd_dvd_int
% 0.33/0.59      = ( ^ [D4: int,T2: int] : ( dvd_dvd_int @ D4 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % uminus_dvd_conv(2)
% 0.33/0.59  thf(fact_4719_uminus__dvd__conv_I1_J,axiom,
% 0.33/0.59      ( dvd_dvd_int
% 0.33/0.59      = ( ^ [D4: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D4 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % uminus_dvd_conv(1)
% 0.33/0.59  thf(fact_4720_zdvd__zdiffD,axiom,
% 0.33/0.59      ! [K: int,M: int,N: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 0.33/0.59       => ( ( dvd_dvd_int @ K @ N )
% 0.33/0.59         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_zdiffD
% 0.33/0.59  thf(fact_4721_zdvd__antisym__abs,axiom,
% 0.33/0.59      ! [A: int,B: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ A @ B )
% 0.33/0.59       => ( ( dvd_dvd_int @ B @ A )
% 0.33/0.59         => ( ( abs_abs_int @ A )
% 0.33/0.59            = ( abs_abs_int @ B ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_antisym_abs
% 0.33/0.59  thf(fact_4722_take__bit__nat__eq,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.59       => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 0.33/0.59          = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_nat_eq
% 0.33/0.59  thf(fact_4723_nat__take__bit__eq,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.59       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.33/0.59          = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_take_bit_eq
% 0.33/0.59  thf(fact_4724_concat__bit__assoc,axiom,
% 0.33/0.59      ! [N: nat,K: int,M: nat,L: int,R: int] :
% 0.33/0.59        ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R ) )
% 0.33/0.59        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R ) ) ).
% 0.33/0.59  
% 0.33/0.59  % concat_bit_assoc
% 0.33/0.59  thf(fact_4725_binomial__eq__0,axiom,
% 0.33/0.59      ! [N: nat,K: nat] :
% 0.33/0.59        ( ( ord_less_nat @ N @ K )
% 0.33/0.59       => ( ( binomial @ N @ K )
% 0.33/0.59          = zero_zero_nat ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_eq_0
% 0.33/0.59  thf(fact_4726_binomial__symmetric,axiom,
% 0.33/0.59      ! [K: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.59       => ( ( binomial @ N @ K )
% 0.33/0.59          = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_symmetric
% 0.33/0.59  thf(fact_4727_take__bit__tightened__less__eq__int,axiom,
% 0.33/0.59      ! [M: nat,N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.59       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_tightened_less_eq_int
% 0.33/0.59  thf(fact_4728_take__bit__int__less__eq__self__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.33/0.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_int_less_eq_self_iff
% 0.33/0.59  thf(fact_4729_take__bit__nonnegative,axiom,
% 0.33/0.59      ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_nonnegative
% 0.33/0.59  thf(fact_4730_not__take__bit__negative,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 0.33/0.59  
% 0.33/0.59  % not_take_bit_negative
% 0.33/0.59  thf(fact_4731_take__bit__int__greater__self__iff,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.33/0.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_int_greater_self_iff
% 0.33/0.59  thf(fact_4732_choose__mult__lemma,axiom,
% 0.33/0.59      ! [M: nat,R: nat,K: nat] :
% 0.33/0.59        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 0.33/0.59        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % choose_mult_lemma
% 0.33/0.59  thf(fact_4733_num_Oexhaust,axiom,
% 0.33/0.59      ! [Y: num] :
% 0.33/0.59        ( ( Y != one )
% 0.33/0.59       => ( ! [X23: num] :
% 0.33/0.59              ( Y
% 0.33/0.59             != ( bit0 @ X23 ) )
% 0.33/0.59         => ~ ! [X33: num] :
% 0.33/0.59                ( Y
% 0.33/0.59               != ( bit1 @ X33 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % num.exhaust
% 0.33/0.59  thf(fact_4734_binomial__le__pow,axiom,
% 0.33/0.59      ! [R: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ R @ N )
% 0.33/0.59       => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_le_pow
% 0.33/0.59  thf(fact_4735_dvd__pos__nat,axiom,
% 0.33/0.59      ! [N: nat,M: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59       => ( ( dvd_dvd_nat @ M @ N )
% 0.33/0.59         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_pos_nat
% 0.33/0.59  thf(fact_4736_nat__dvd__not__less,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.33/0.59       => ( ( ord_less_nat @ M @ N )
% 0.33/0.59         => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_dvd_not_less
% 0.33/0.59  thf(fact_4737_dvd__minus__self,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 0.33/0.59        = ( ( ord_less_nat @ N @ M )
% 0.33/0.59          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_minus_self
% 0.33/0.59  thf(fact_4738_zdvd__antisym__nonneg,axiom,
% 0.33/0.59      ! [M: int,N: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.33/0.59       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.33/0.59         => ( ( dvd_dvd_int @ M @ N )
% 0.33/0.59           => ( ( dvd_dvd_int @ N @ M )
% 0.33/0.59             => ( M = N ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_antisym_nonneg
% 0.33/0.59  thf(fact_4739_zdvd__not__zless,axiom,
% 0.33/0.59      ! [M: int,N: int] :
% 0.33/0.59        ( ( ord_less_int @ zero_zero_int @ M )
% 0.33/0.59       => ( ( ord_less_int @ M @ N )
% 0.33/0.59         => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_not_zless
% 0.33/0.59  thf(fact_4740_less__eq__dvd__minus,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.59       => ( ( dvd_dvd_nat @ M @ N )
% 0.33/0.59          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % less_eq_dvd_minus
% 0.33/0.59  thf(fact_4741_dvd__diffD1,axiom,
% 0.33/0.59      ! [K: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.33/0.59       => ( ( dvd_dvd_nat @ K @ M )
% 0.33/0.59         => ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.59           => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_diffD1
% 0.33/0.59  thf(fact_4742_dvd__diffD,axiom,
% 0.33/0.59      ! [K: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.33/0.59       => ( ( dvd_dvd_nat @ K @ N )
% 0.33/0.59         => ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.59           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_diffD
% 0.33/0.59  thf(fact_4743_zdvd__mult__cancel,axiom,
% 0.33/0.59      ! [K: int,M: int,N: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 0.33/0.59       => ( ( K != zero_zero_int )
% 0.33/0.59         => ( dvd_dvd_int @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_mult_cancel
% 0.33/0.59  thf(fact_4744_zdvd__mono,axiom,
% 0.33/0.59      ! [K: int,M: int,T: int] :
% 0.33/0.59        ( ( K != zero_zero_int )
% 0.33/0.59       => ( ( dvd_dvd_int @ M @ T )
% 0.33/0.59          = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_mono
% 0.33/0.59  thf(fact_4745_bezout__add__nat,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59      ? [D5: nat,X3: nat,Y2: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ D5 @ A )
% 0.33/0.59        & ( dvd_dvd_nat @ D5 @ B )
% 0.33/0.59        & ( ( ( times_times_nat @ A @ X3 )
% 0.33/0.59            = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D5 ) )
% 0.33/0.59          | ( ( times_times_nat @ B @ X3 )
% 0.33/0.59            = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D5 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % bezout_add_nat
% 0.33/0.59  thf(fact_4746_bezout__lemma__nat,axiom,
% 0.33/0.59      ! [D: nat,A: nat,B: nat,X2: nat,Y: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ D @ A )
% 0.33/0.59       => ( ( dvd_dvd_nat @ D @ B )
% 0.33/0.59         => ( ( ( ( times_times_nat @ A @ X2 )
% 0.33/0.59                = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 0.33/0.59              | ( ( times_times_nat @ B @ X2 )
% 0.33/0.59                = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 0.33/0.59           => ? [X3: nat,Y2: nat] :
% 0.33/0.59                ( ( dvd_dvd_nat @ D @ A )
% 0.33/0.59                & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 0.33/0.59                & ( ( ( times_times_nat @ A @ X3 )
% 0.33/0.59                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y2 ) @ D ) )
% 0.33/0.59                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 0.33/0.59                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % bezout_lemma_nat
% 0.33/0.59  thf(fact_4747_bezout1__nat,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59      ? [D5: nat,X3: nat,Y2: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ D5 @ A )
% 0.33/0.59        & ( dvd_dvd_nat @ D5 @ B )
% 0.33/0.59        & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y2 ) )
% 0.33/0.59            = D5 )
% 0.33/0.59          | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y2 ) )
% 0.33/0.59            = D5 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % bezout1_nat
% 0.33/0.59  thf(fact_4748_zdvd__reduce,axiom,
% 0.33/0.59      ! [K: int,N: int,M: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 0.33/0.59        = ( dvd_dvd_int @ K @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_reduce
% 0.33/0.59  thf(fact_4749_zdvd__period,axiom,
% 0.33/0.59      ! [A: int,D: int,X2: int,T: int,C: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ A @ D )
% 0.33/0.59       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X2 @ T ) )
% 0.33/0.59          = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X2 @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_period
% 0.33/0.59  thf(fact_4750_inc_Osimps_I3_J,axiom,
% 0.33/0.59      ! [X2: num] :
% 0.33/0.59        ( ( inc @ ( bit1 @ X2 ) )
% 0.33/0.59        = ( bit0 @ ( inc @ X2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % inc.simps(3)
% 0.33/0.59  thf(fact_4751_inc_Osimps_I2_J,axiom,
% 0.33/0.59      ! [X2: num] :
% 0.33/0.59        ( ( inc @ ( bit0 @ X2 ) )
% 0.33/0.59        = ( bit1 @ X2 ) ) ).
% 0.33/0.59  
% 0.33/0.59  % inc.simps(2)
% 0.33/0.59  thf(fact_4752_nat__dvd__iff,axiom,
% 0.33/0.59      ! [Z2: int,M: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ ( nat2 @ Z2 ) @ M )
% 0.33/0.59        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.33/0.59           => ( dvd_dvd_int @ Z2 @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.33/0.59          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.33/0.59           => ( M = zero_zero_nat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_dvd_iff
% 0.33/0.59  thf(fact_4753_zero__less__binomial,axiom,
% 0.33/0.59      ! [K: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.59       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zero_less_binomial
% 0.33/0.59  thf(fact_4754_Suc__times__binomial__add,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 0.33/0.59        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_times_binomial_add
% 0.33/0.59  thf(fact_4755_choose__mult,axiom,
% 0.33/0.59      ! [K: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ K @ M )
% 0.33/0.59       => ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.59         => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 0.33/0.59            = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % choose_mult
% 0.33/0.59  thf(fact_4756_binomial__absorb__comp,axiom,
% 0.33/0.59      ! [N: nat,K: nat] :
% 0.33/0.59        ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 0.33/0.59        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_absorb_comp
% 0.33/0.59  thf(fact_4757_take__bit__decr__eq,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.33/0.59         != zero_zero_int )
% 0.33/0.59       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 0.33/0.59          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_decr_eq
% 0.33/0.59  thf(fact_4758_eval__nat__numeral_I3_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.33/0.59        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % eval_nat_numeral(3)
% 0.33/0.59  thf(fact_4759_dvd__imp__le,axiom,
% 0.33/0.59      ! [K: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ K @ N )
% 0.33/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59         => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_imp_le
% 0.33/0.59  thf(fact_4760_dvd__mult__cancel,axiom,
% 0.33/0.59      ! [K: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.33/0.59       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.59         => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_mult_cancel
% 0.33/0.59  thf(fact_4761_nat__mult__dvd__cancel1,axiom,
% 0.33/0.59      ! [K: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.33/0.59          = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_mult_dvd_cancel1
% 0.33/0.59  thf(fact_4762_bezout__add__strong__nat,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59        ( ( A != zero_zero_nat )
% 0.33/0.59       => ? [D5: nat,X3: nat,Y2: nat] :
% 0.33/0.59            ( ( dvd_dvd_nat @ D5 @ A )
% 0.33/0.59            & ( dvd_dvd_nat @ D5 @ B )
% 0.33/0.59            & ( ( times_times_nat @ A @ X3 )
% 0.33/0.59              = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D5 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % bezout_add_strong_nat
% 0.33/0.59  thf(fact_4763_zdvd__imp__le,axiom,
% 0.33/0.59      ! [Z2: int,N: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ Z2 @ N )
% 0.33/0.59       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.33/0.59         => ( ord_less_eq_int @ Z2 @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_imp_le
% 0.33/0.59  thf(fact_4764_mod__greater__zero__iff__not__dvd,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 0.33/0.59        = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_greater_zero_iff_not_dvd
% 0.33/0.59  thf(fact_4765_dvd__imp__le__int,axiom,
% 0.33/0.59      ! [I: int,D: int] :
% 0.33/0.59        ( ( I != zero_zero_int )
% 0.33/0.59       => ( ( dvd_dvd_int @ D @ I )
% 0.33/0.59         => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_imp_le_int
% 0.33/0.59  thf(fact_4766_mod__eq__dvd__iff__nat,axiom,
% 0.33/0.59      ! [N: nat,M: nat,Q2: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.59       => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.33/0.59            = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.33/0.59          = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_eq_dvd_iff_nat
% 0.33/0.59  thf(fact_4767_dvd__fact,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.33/0.59       => ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.59         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_fact
% 0.33/0.59  thf(fact_4768_even__nat__iff,axiom,
% 0.33/0.59      ! [K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.59       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 0.33/0.59          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % even_nat_iff
% 0.33/0.59  thf(fact_4769_gcd__nat_Oordering__top__axioms,axiom,
% 0.33/0.59      ( ordering_top_nat @ dvd_dvd_nat
% 0.33/0.59      @ ^ [M2: nat,N3: nat] :
% 0.33/0.59          ( ( dvd_dvd_nat @ M2 @ N3 )
% 0.33/0.59          & ( M2 != N3 ) )
% 0.33/0.59      @ zero_zero_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.ordering_top_axioms
% 0.33/0.59  thf(fact_4770_binomial__absorption,axiom,
% 0.33/0.59      ! [K: nat,N: nat] :
% 0.33/0.59        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 0.33/0.59        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_absorption
% 0.33/0.59  thf(fact_4771_odd__mod__4__div__2,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.33/0.59          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.33/0.59       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % odd_mod_4_div_2
% 0.33/0.59  thf(fact_4772_numeral__3__eq__3,axiom,
% 0.33/0.59      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.33/0.59      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % numeral_3_eq_3
% 0.33/0.59  thf(fact_4773_Suc3__eq__add__3,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( suc @ ( suc @ ( suc @ N ) ) )
% 0.33/0.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc3_eq_add_3
% 0.33/0.59  thf(fact_4774_binomial__fact__lemma,axiom,
% 0.33/0.59      ! [K: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.59       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 0.33/0.59          = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_fact_lemma
% 0.33/0.59  thf(fact_4775_dvd__mult__cancel2,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.33/0.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 0.33/0.59          = ( N = one_one_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_mult_cancel2
% 0.33/0.59  thf(fact_4776_dvd__mult__cancel1,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.33/0.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 0.33/0.59          = ( N = one_one_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_mult_cancel1
% 0.33/0.59  thf(fact_4777_even__even__mod__4__iff,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.33/0.59        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % even_even_mod_4_iff
% 0.33/0.59  thf(fact_4778_dvd__minus__add,axiom,
% 0.33/0.59      ! [Q2: nat,N: nat,R: nat,M: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ Q2 @ N )
% 0.33/0.59       => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 0.33/0.59         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 0.33/0.59            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_minus_add
% 0.33/0.59  thf(fact_4779_mod__nat__eqI,axiom,
% 0.33/0.59      ! [R: nat,N: nat,M: nat] :
% 0.33/0.59        ( ( ord_less_nat @ R @ N )
% 0.33/0.59       => ( ( ord_less_eq_nat @ R @ M )
% 0.33/0.59         => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 0.33/0.59           => ( ( modulo_modulo_nat @ M @ N )
% 0.33/0.59              = R ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_nat_eqI
% 0.33/0.59  thf(fact_4780_zdvd__mult__cancel1,axiom,
% 0.33/0.59      ! [M: int,N: int] :
% 0.33/0.59        ( ( M != zero_zero_int )
% 0.33/0.59       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 0.33/0.59          = ( ( abs_abs_int @ N )
% 0.33/0.59            = one_one_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zdvd_mult_cancel1
% 0.33/0.59  thf(fact_4781_mod__int__pos__iff,axiom,
% 0.33/0.59      ! [K: int,L: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 0.33/0.59        = ( ( dvd_dvd_int @ L @ K )
% 0.33/0.59          | ( ( L = zero_zero_int )
% 0.33/0.59            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 0.33/0.59          | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mod_int_pos_iff
% 0.33/0.59  thf(fact_4782_power__dvd__imp__le,axiom,
% 0.33/0.59      ! [I: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 0.33/0.59       => ( ( ord_less_nat @ one_one_nat @ I )
% 0.33/0.59         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % power_dvd_imp_le
% 0.33/0.59  thf(fact_4783_take__bit__Suc__minus__bit1,axiom,
% 0.33/0.59      ! [N: nat,K: num] :
% 0.33/0.59        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.33/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_Suc_minus_bit1
% 0.33/0.59  thf(fact_4784_num_Osize_I6_J,axiom,
% 0.33/0.59      ! [X32: num] :
% 0.33/0.59        ( ( size_size_num @ ( bit1 @ X32 ) )
% 0.33/0.59        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % num.size(6)
% 0.33/0.59  thf(fact_4785_choose__reduce__nat,axiom,
% 0.33/0.59      ! [N: nat,K: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.59         => ( ( binomial @ N @ K )
% 0.33/0.59            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % choose_reduce_nat
% 0.33/0.59  thf(fact_4786_times__binomial__minus1__eq,axiom,
% 0.33/0.59      ! [K: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.33/0.59       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 0.33/0.59          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % times_binomial_minus1_eq
% 0.33/0.59  thf(fact_4787_binomial__le__pow2,axiom,
% 0.33/0.59      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_le_pow2
% 0.33/0.59  thf(fact_4788_odd__pos,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.33/0.59       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % odd_pos
% 0.33/0.59  thf(fact_4789_binomial__altdef__nat,axiom,
% 0.33/0.59      ! [K: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ K @ N )
% 0.33/0.59       => ( ( binomial @ N @ K )
% 0.33/0.59          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_altdef_nat
% 0.33/0.59  thf(fact_4790_Suc__mod__eq__add3__mod,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.33/0.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_mod_eq_add3_mod
% 0.33/0.59  thf(fact_4791_Suc__div__eq__add3__div,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.33/0.59        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_div_eq_add3_div
% 0.33/0.59  thf(fact_4792_even__diff__iff,axiom,
% 0.33/0.59      ! [K: int,L: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 0.33/0.59        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % even_diff_iff
% 0.33/0.59  thf(fact_4793_even__add__abs__iff,axiom,
% 0.33/0.59      ! [K: int,L: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 0.33/0.59        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % even_add_abs_iff
% 0.33/0.59  thf(fact_4794_even__abs__add__iff,axiom,
% 0.33/0.59      ! [K: int,L: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 0.33/0.59        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % even_abs_add_iff
% 0.33/0.59  thf(fact_4795_dvd__power__iff__le,axiom,
% 0.33/0.59      ! [K: nat,M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.33/0.59       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 0.33/0.59          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_power_iff_le
% 0.33/0.59  thf(fact_4796_take__bit__nat__less__self__iff,axiom,
% 0.33/0.59      ! [N: nat,M: nat] :
% 0.33/0.59        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 0.33/0.59        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_nat_less_self_iff
% 0.33/0.59  thf(fact_4797_binomial__addition__formula,axiom,
% 0.33/0.59      ! [N: nat,K: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59       => ( ( binomial @ N @ ( suc @ K ) )
% 0.33/0.59          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % binomial_addition_formula
% 0.33/0.59  thf(fact_4798_take__bit__int__less__self__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.33/0.59        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_int_less_self_iff
% 0.33/0.59  thf(fact_4799_take__bit__int__greater__eq__self__iff,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.33/0.59        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_int_greater_eq_self_iff
% 0.33/0.59  thf(fact_4800_choose__two,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.59        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % choose_two
% 0.33/0.59  thf(fact_4801_take__bit__int__eq__self__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.33/0.59          = K )
% 0.33/0.59        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.59          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_int_eq_self_iff
% 0.33/0.59  thf(fact_4802_take__bit__int__eq__self,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.59       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.33/0.59         => ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.33/0.59            = K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_int_eq_self
% 0.33/0.59  thf(fact_4803_signed__take__bit__eq__take__bit__shift,axiom,
% 0.33/0.59      ( bit_ri631733984087533419it_int
% 0.33/0.59      = ( ^ [N3: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_eq_take_bit_shift
% 0.33/0.59  thf(fact_4804_take__bit__incr__eq,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.33/0.59         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.33/0.59       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.33/0.59          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_incr_eq
% 0.33/0.59  thf(fact_4805_take__bit__int__less__eq,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.33/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.59         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_int_less_eq
% 0.33/0.59  thf(fact_4806_take__bit__int__greater__eq,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.59       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_int_greater_eq
% 0.33/0.59  thf(fact_4807_even__mod__4__div__2,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.33/0.59          = ( suc @ zero_zero_nat ) )
% 0.33/0.59       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % even_mod_4_div_2
% 0.33/0.59  thf(fact_4808_take__bit__minus__small__eq,axiom,
% 0.33/0.59      ! [K: int,N: nat] :
% 0.33/0.59        ( ( ord_less_int @ zero_zero_int @ K )
% 0.33/0.59       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.33/0.59         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 0.33/0.59            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_minus_small_eq
% 0.33/0.59  thf(fact_4809_signed__take__bit__numeral__minus__bit1,axiom,
% 0.33/0.59      ! [L: num,K: num] :
% 0.33/0.59        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.33/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_numeral_minus_bit1
% 0.33/0.59  thf(fact_4810_signed__take__bit__numeral__bit1,axiom,
% 0.33/0.59      ! [L: num,K: num] :
% 0.33/0.59        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.33/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % signed_take_bit_numeral_bit1
% 0.33/0.59  thf(fact_4811_take__bit__numeral__minus__bit1,axiom,
% 0.33/0.59      ! [L: num,K: num] :
% 0.33/0.59        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.33/0.59        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_numeral_minus_bit1
% 0.33/0.59  thf(fact_4812_num_Osize__gen_I3_J,axiom,
% 0.33/0.59      ! [X32: num] :
% 0.33/0.59        ( ( size_num @ ( bit1 @ X32 ) )
% 0.33/0.59        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % num.size_gen(3)
% 0.33/0.59  thf(fact_4813_num_Osize__gen_I2_J,axiom,
% 0.33/0.59      ! [X22: num] :
% 0.33/0.59        ( ( size_num @ ( bit0 @ X22 ) )
% 0.33/0.59        = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % num.size_gen(2)
% 0.33/0.59  thf(fact_4814_nat__of__bool,axiom,
% 0.33/0.59      ! [P: $o] :
% 0.33/0.59        ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.33/0.59        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.33/0.59  
% 0.33/0.59  % nat_of_bool
% 0.33/0.59  thf(fact_4815_Suc__0__mod__eq,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.59        = ( zero_n2687167440665602831ol_nat
% 0.33/0.59          @ ( N
% 0.33/0.59           != ( suc @ zero_zero_nat ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_0_mod_eq
% 0.33/0.59  thf(fact_4816_pred__numeral__simps_I1_J,axiom,
% 0.33/0.59      ( ( pred_numeral @ one )
% 0.33/0.59      = zero_zero_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % pred_numeral_simps(1)
% 0.33/0.59  thf(fact_4817_eq__numeral__Suc,axiom,
% 0.33/0.59      ! [K: num,N: nat] :
% 0.33/0.59        ( ( ( numeral_numeral_nat @ K )
% 0.33/0.59          = ( suc @ N ) )
% 0.33/0.59        = ( ( pred_numeral @ K )
% 0.33/0.59          = N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % eq_numeral_Suc
% 0.33/0.59  thf(fact_4818_Suc__eq__numeral,axiom,
% 0.33/0.59      ! [N: nat,K: num] :
% 0.33/0.59        ( ( ( suc @ N )
% 0.33/0.59          = ( numeral_numeral_nat @ K ) )
% 0.33/0.59        = ( N
% 0.33/0.59          = ( pred_numeral @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % Suc_eq_numeral
% 0.33/0.59  thf(fact_4819_pred__numeral__inc,axiom,
% 0.33/0.59      ! [K: num] :
% 0.33/0.59        ( ( pred_numeral @ ( inc @ K ) )
% 0.33/0.59        = ( numeral_numeral_nat @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % pred_numeral_inc
% 0.33/0.59  thf(fact_4820_less__numeral__Suc,axiom,
% 0.33/0.59      ! [K: num,N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.33/0.59        = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % less_numeral_Suc
% 0.33/0.59  thf(fact_4821_less__Suc__numeral,axiom,
% 0.33/0.59      ! [N: nat,K: num] :
% 0.33/0.59        ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.33/0.59        = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % less_Suc_numeral
% 0.33/0.59  thf(fact_4822_pred__numeral__simps_I3_J,axiom,
% 0.33/0.59      ! [K: num] :
% 0.33/0.59        ( ( pred_numeral @ ( bit1 @ K ) )
% 0.33/0.59        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % pred_numeral_simps(3)
% 0.33/0.59  thf(fact_4823_le__numeral__Suc,axiom,
% 0.33/0.59      ! [K: num,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.33/0.59        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % le_numeral_Suc
% 0.33/0.59  thf(fact_4824_le__Suc__numeral,axiom,
% 0.33/0.59      ! [N: nat,K: num] :
% 0.33/0.59        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.33/0.59        = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % le_Suc_numeral
% 0.33/0.59  thf(fact_4825_diff__numeral__Suc,axiom,
% 0.33/0.59      ! [K: num,N: nat] :
% 0.33/0.59        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.33/0.59        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % diff_numeral_Suc
% 0.33/0.59  thf(fact_4826_diff__Suc__numeral,axiom,
% 0.33/0.59      ! [N: nat,K: num] :
% 0.33/0.59        ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.33/0.59        = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % diff_Suc_numeral
% 0.33/0.59  thf(fact_4827_take__bit__of__Suc__0,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.33/0.59        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_of_Suc_0
% 0.33/0.59  thf(fact_4828_dvd__antisym,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ M @ N )
% 0.33/0.59       => ( ( dvd_dvd_nat @ N @ M )
% 0.33/0.59         => ( M = N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_antisym
% 0.33/0.59  thf(fact_4829_gcd__nat_Onot__eq__order__implies__strict,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59        ( ( A != B )
% 0.33/0.59       => ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59         => ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59            & ( A != B ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.not_eq_order_implies_strict
% 0.33/0.59  thf(fact_4830_gcd__nat_Ostrict__implies__not__eq,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59        ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59          & ( A != B ) )
% 0.33/0.59       => ( A != B ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.strict_implies_not_eq
% 0.33/0.59  thf(fact_4831_gcd__nat_Ostrict__implies__order,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59        ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59          & ( A != B ) )
% 0.33/0.59       => ( dvd_dvd_nat @ A @ B ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.strict_implies_order
% 0.33/0.59  thf(fact_4832_gcd__nat_Ostrict__iff__order,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59        ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59          & ( A != B ) )
% 0.33/0.59        = ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59          & ( A != B ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.strict_iff_order
% 0.33/0.59  thf(fact_4833_gcd__nat_Oorder__iff__strict,axiom,
% 0.33/0.59      ( dvd_dvd_nat
% 0.33/0.59      = ( ^ [A2: nat,B2: nat] :
% 0.33/0.59            ( ( ( dvd_dvd_nat @ A2 @ B2 )
% 0.33/0.59              & ( A2 != B2 ) )
% 0.33/0.59            | ( A2 = B2 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.order_iff_strict
% 0.33/0.59  thf(fact_4834_gcd__nat_Ostrict__iff__not,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59        ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59          & ( A != B ) )
% 0.33/0.59        = ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.strict_iff_not
% 0.33/0.59  thf(fact_4835_gcd__nat_Ostrict__trans2,axiom,
% 0.33/0.59      ! [A: nat,B: nat,C: nat] :
% 0.33/0.59        ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59          & ( A != B ) )
% 0.33/0.59       => ( ( dvd_dvd_nat @ B @ C )
% 0.33/0.59         => ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.59            & ( A != C ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.strict_trans2
% 0.33/0.59  thf(fact_4836_gcd__nat_Ostrict__trans1,axiom,
% 0.33/0.59      ! [A: nat,B: nat,C: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59       => ( ( ( dvd_dvd_nat @ B @ C )
% 0.33/0.59            & ( B != C ) )
% 0.33/0.59         => ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.59            & ( A != C ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.strict_trans1
% 0.33/0.59  thf(fact_4837_gcd__nat_Ostrict__trans,axiom,
% 0.33/0.59      ! [A: nat,B: nat,C: nat] :
% 0.33/0.59        ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59          & ( A != B ) )
% 0.33/0.59       => ( ( ( dvd_dvd_nat @ B @ C )
% 0.33/0.59            & ( B != C ) )
% 0.33/0.59         => ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.59            & ( A != C ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.strict_trans
% 0.33/0.59  thf(fact_4838_gcd__nat_Oantisym,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59       => ( ( dvd_dvd_nat @ B @ A )
% 0.33/0.59         => ( A = B ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.antisym
% 0.33/0.59  thf(fact_4839_gcd__nat_Oirrefl,axiom,
% 0.33/0.59      ! [A: nat] :
% 0.33/0.59        ~ ( ( dvd_dvd_nat @ A @ A )
% 0.33/0.59          & ( A != A ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.irrefl
% 0.33/0.59  thf(fact_4840_gcd__nat_Oeq__iff,axiom,
% 0.33/0.59      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.59      = ( ^ [A2: nat,B2: nat] :
% 0.33/0.59            ( ( dvd_dvd_nat @ A2 @ B2 )
% 0.33/0.59            & ( dvd_dvd_nat @ B2 @ A2 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.eq_iff
% 0.33/0.59  thf(fact_4841_gcd__nat_Otrans,axiom,
% 0.33/0.59      ! [A: nat,B: nat,C: nat] :
% 0.33/0.59        ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59       => ( ( dvd_dvd_nat @ B @ C )
% 0.33/0.59         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.trans
% 0.33/0.59  thf(fact_4842_gcd__nat_Orefl,axiom,
% 0.33/0.59      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.refl
% 0.33/0.59  thf(fact_4843_gcd__nat_Oasym,axiom,
% 0.33/0.59      ! [A: nat,B: nat] :
% 0.33/0.59        ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.59          & ( A != B ) )
% 0.33/0.59       => ~ ( ( dvd_dvd_nat @ B @ A )
% 0.33/0.59            & ( B != A ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % gcd_nat.asym
% 0.33/0.59  thf(fact_4844_numeral__eq__Suc,axiom,
% 0.33/0.59      ( numeral_numeral_nat
% 0.33/0.59      = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % numeral_eq_Suc
% 0.33/0.59  thf(fact_4845_pred__numeral__def,axiom,
% 0.33/0.59      ( pred_numeral
% 0.33/0.59      = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % pred_numeral_def
% 0.33/0.59  thf(fact_4846_num_Osize__gen_I1_J,axiom,
% 0.33/0.59      ( ( size_num @ one )
% 0.33/0.59      = zero_zero_nat ) ).
% 0.33/0.59  
% 0.33/0.59  % num.size_gen(1)
% 0.33/0.59  thf(fact_4847_set__decode__0,axiom,
% 0.33/0.59      ! [X2: nat] :
% 0.33/0.59        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X2 ) )
% 0.33/0.59        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % set_decode_0
% 0.33/0.59  thf(fact_4848_set__decode__def,axiom,
% 0.33/0.59      ( nat_set_decode
% 0.33/0.59      = ( ^ [X: nat] :
% 0.33/0.59            ( collect_nat
% 0.33/0.59            @ ^ [N3: nat] :
% 0.33/0.59                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % set_decode_def
% 0.33/0.59  thf(fact_4849_and__int__unfold,axiom,
% 0.33/0.59      ( bit_se725231765392027082nd_int
% 0.33/0.59      = ( ^ [K2: int,L2: int] :
% 0.33/0.59            ( if_int
% 0.33/0.59            @ ( ( K2 = zero_zero_int )
% 0.33/0.59              | ( L2 = zero_zero_int ) )
% 0.33/0.59            @ zero_zero_int
% 0.33/0.59            @ ( if_int
% 0.33/0.59              @ ( K2
% 0.33/0.59                = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.59              @ L2
% 0.33/0.59              @ ( if_int
% 0.33/0.59                @ ( L2
% 0.33/0.59                  = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.59                @ K2
% 0.33/0.59                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % and_int_unfold
% 0.33/0.59  thf(fact_4850_take__bit__eq__mask__iff__exp__dvd,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.33/0.59          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.33/0.59        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_eq_mask_iff_exp_dvd
% 0.33/0.59  thf(fact_4851_modulo__int__def,axiom,
% 0.33/0.59      ( modulo_modulo_int
% 0.33/0.59      = ( ^ [K2: int,L2: int] :
% 0.33/0.59            ( if_int @ ( L2 = zero_zero_int ) @ K2
% 0.33/0.59            @ ( if_int
% 0.33/0.59              @ ( ( sgn_sgn_int @ K2 )
% 0.33/0.59                = ( sgn_sgn_int @ L2 ) )
% 0.33/0.59              @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 0.33/0.59              @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 0.33/0.59                @ ( minus_minus_int
% 0.33/0.59                  @ ( times_times_int @ ( abs_abs_int @ L2 )
% 0.33/0.59                    @ ( zero_n2684676970156552555ol_int
% 0.33/0.59                      @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) )
% 0.33/0.59                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % modulo_int_def
% 0.33/0.59  thf(fact_4852_mask__nat__positive__iff,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.33/0.59        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mask_nat_positive_iff
% 0.33/0.59  thf(fact_4853_and__nonnegative__int__iff,axiom,
% 0.33/0.59      ! [K: int,L: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 0.33/0.59        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.59          | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % and_nonnegative_int_iff
% 0.33/0.59  thf(fact_4854_and__negative__int__iff,axiom,
% 0.33/0.59      ! [K: int,L: int] :
% 0.33/0.59        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 0.33/0.59        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.59          & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % and_negative_int_iff
% 0.33/0.59  thf(fact_4855_sgn__mult__dvd__iff,axiom,
% 0.33/0.59      ! [R: int,L: int,K: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R ) @ L ) @ K )
% 0.33/0.59        = ( ( dvd_dvd_int @ L @ K )
% 0.33/0.59          & ( ( R = zero_zero_int )
% 0.33/0.59           => ( K = zero_zero_int ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sgn_mult_dvd_iff
% 0.33/0.59  thf(fact_4856_mult__sgn__dvd__iff,axiom,
% 0.33/0.59      ! [L: int,R: int,K: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R ) ) @ K )
% 0.33/0.59        = ( ( dvd_dvd_int @ L @ K )
% 0.33/0.59          & ( ( R = zero_zero_int )
% 0.33/0.59           => ( K = zero_zero_int ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mult_sgn_dvd_iff
% 0.33/0.59  thf(fact_4857_dvd__sgn__mult__iff,axiom,
% 0.33/0.59      ! [L: int,R: int,K: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R ) @ K ) )
% 0.33/0.59        = ( ( dvd_dvd_int @ L @ K )
% 0.33/0.59          | ( R = zero_zero_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_sgn_mult_iff
% 0.33/0.59  thf(fact_4858_dvd__mult__sgn__iff,axiom,
% 0.33/0.59      ! [L: int,K: int,R: int] :
% 0.33/0.59        ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R ) ) )
% 0.33/0.59        = ( ( dvd_dvd_int @ L @ K )
% 0.33/0.59          | ( R = zero_zero_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % dvd_mult_sgn_iff
% 0.33/0.59  thf(fact_4859_and__minus__numerals_I2_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.33/0.59        = one_one_int ) ).
% 0.33/0.59  
% 0.33/0.59  % and_minus_numerals(2)
% 0.33/0.59  thf(fact_4860_and__minus__numerals_I6_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.33/0.59        = one_one_int ) ).
% 0.33/0.59  
% 0.33/0.59  % and_minus_numerals(6)
% 0.33/0.59  thf(fact_4861_and__minus__numerals_I5_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.33/0.59        = zero_zero_int ) ).
% 0.33/0.59  
% 0.33/0.59  % and_minus_numerals(5)
% 0.33/0.59  thf(fact_4862_and__minus__numerals_I1_J,axiom,
% 0.33/0.59      ! [N: num] :
% 0.33/0.59        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.33/0.59        = zero_zero_int ) ).
% 0.33/0.59  
% 0.33/0.59  % and_minus_numerals(1)
% 0.33/0.59  thf(fact_4863_less__eq__mask,axiom,
% 0.33/0.59      ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % less_eq_mask
% 0.33/0.59  thf(fact_4864_subset__decode__imp__le,axiom,
% 0.33/0.59      ! [M: nat,N: nat] :
% 0.33/0.59        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 0.33/0.59       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % subset_decode_imp_le
% 0.33/0.59  thf(fact_4865_AND__upper2_H,axiom,
% 0.33/0.59      ! [Y: int,Z2: int,X2: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.59       => ( ( ord_less_eq_int @ Y @ Z2 )
% 0.33/0.59         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Z2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % AND_upper2'
% 0.33/0.59  thf(fact_4866_AND__upper1_H,axiom,
% 0.33/0.59      ! [Y: int,Z2: int,Ya: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.59       => ( ( ord_less_eq_int @ Y @ Z2 )
% 0.33/0.59         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % AND_upper1'
% 0.33/0.59  thf(fact_4867_AND__upper2,axiom,
% 0.33/0.59      ! [Y: int,X2: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.59       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Y ) ) ).
% 0.33/0.59  
% 0.33/0.59  % AND_upper2
% 0.33/0.59  thf(fact_4868_AND__upper1,axiom,
% 0.33/0.59      ! [X2: int,Y: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.33/0.59       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ X2 ) ) ).
% 0.33/0.59  
% 0.33/0.59  % AND_upper1
% 0.33/0.59  thf(fact_4869_AND__lower,axiom,
% 0.33/0.59      ! [X2: int,Y: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.33/0.59       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % AND_lower
% 0.33/0.59  thf(fact_4870_int__sgnE,axiom,
% 0.33/0.59      ! [K: int] :
% 0.33/0.59        ~ ! [N2: nat,L3: int] :
% 0.33/0.59            ( K
% 0.33/0.59           != ( times_times_int @ ( sgn_sgn_int @ L3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % int_sgnE
% 0.33/0.59  thf(fact_4871_mask__nonnegative__int,axiom,
% 0.33/0.59      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mask_nonnegative_int
% 0.33/0.59  thf(fact_4872_not__mask__negative__int,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 0.33/0.59  
% 0.33/0.59  % not_mask_negative_int
% 0.33/0.59  thf(fact_4873_AND__upper2_H_H,axiom,
% 0.33/0.59      ! [Y: int,Z2: int,X2: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.59       => ( ( ord_less_int @ Y @ Z2 )
% 0.33/0.59         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Z2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % AND_upper2''
% 0.33/0.59  thf(fact_4874_AND__upper1_H_H,axiom,
% 0.33/0.59      ! [Y: int,Z2: int,Ya: int] :
% 0.33/0.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.59       => ( ( ord_less_int @ Y @ Z2 )
% 0.33/0.59         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z2 ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % AND_upper1''
% 0.33/0.59  thf(fact_4875_and__less__eq,axiom,
% 0.33/0.59      ! [L: int,K: int] :
% 0.33/0.59        ( ( ord_less_int @ L @ zero_zero_int )
% 0.33/0.59       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 0.33/0.59  
% 0.33/0.59  % and_less_eq
% 0.33/0.59  thf(fact_4876_sgn__mod,axiom,
% 0.33/0.59      ! [L: int,K: int] :
% 0.33/0.59        ( ( L != zero_zero_int )
% 0.33/0.59       => ( ~ ( dvd_dvd_int @ L @ K )
% 0.33/0.59         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 0.33/0.59            = ( sgn_sgn_int @ L ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % sgn_mod
% 0.33/0.59  thf(fact_4877_less__mask,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.59       => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % less_mask
% 0.33/0.59  thf(fact_4878_zsgn__def,axiom,
% 0.33/0.59      ( sgn_sgn_int
% 0.33/0.59      = ( ^ [I2: int] : ( if_int @ ( I2 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % zsgn_def
% 0.33/0.59  thf(fact_4879_div__sgn__abs__cancel,axiom,
% 0.33/0.59      ! [V: int,K: int,L: int] :
% 0.33/0.59        ( ( V != zero_zero_int )
% 0.33/0.59       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 0.33/0.59          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % div_sgn_abs_cancel
% 0.33/0.59  thf(fact_4880_take__bit__eq__mask__iff,axiom,
% 0.33/0.59      ! [N: nat,K: int] :
% 0.33/0.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.33/0.59          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.33/0.59        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.33/0.59          = zero_zero_int ) ) ).
% 0.33/0.59  
% 0.33/0.59  % take_bit_eq_mask_iff
% 0.33/0.59  thf(fact_4881_div__noneq__sgn__abs,axiom,
% 0.33/0.59      ! [L: int,K: int] :
% 0.33/0.59        ( ( L != zero_zero_int )
% 0.33/0.59       => ( ( ( sgn_sgn_int @ K )
% 0.33/0.59           != ( sgn_sgn_int @ L ) )
% 0.33/0.59         => ( ( divide_divide_int @ K @ L )
% 0.33/0.59            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 0.33/0.59              @ ( zero_n2684676970156552555ol_int
% 0.33/0.59                @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % div_noneq_sgn_abs
% 0.33/0.59  thf(fact_4882_and__int__rec,axiom,
% 0.33/0.59      ( bit_se725231765392027082nd_int
% 0.33/0.59      = ( ^ [K2: int,L2: int] :
% 0.33/0.59            ( plus_plus_int
% 0.33/0.59            @ ( zero_n2684676970156552555ol_int
% 0.33/0.59              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.33/0.59                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.33/0.59            @ ( 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 ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % and_int_rec
% 0.33/0.59  thf(fact_4883_mask__half__int,axiom,
% 0.33/0.59      ! [N: nat] :
% 0.33/0.59        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.59        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mask_half_int
% 0.33/0.59  thf(fact_4884_mask__nat__def,axiom,
% 0.33/0.59      ( bit_se2002935070580805687sk_nat
% 0.33/0.59      = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mask_nat_def
% 0.33/0.59  thf(fact_4885_mask__int__def,axiom,
% 0.33/0.59      ( bit_se2000444600071755411sk_int
% 0.33/0.59      = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % mask_int_def
% 0.33/0.59  thf(fact_4886_divide__int__unfold,axiom,
% 0.33/0.59      ! [L: int,K: int,N: nat,M: nat] :
% 0.33/0.59        ( ( ( ( ( sgn_sgn_int @ L )
% 0.33/0.59              = zero_zero_int )
% 0.33/0.59            | ( ( sgn_sgn_int @ K )
% 0.33/0.59              = zero_zero_int )
% 0.33/0.59            | ( N = zero_zero_nat ) )
% 0.33/0.59         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.33/0.59            = zero_zero_int ) )
% 0.33/0.59        & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.33/0.59                = zero_zero_int )
% 0.33/0.59              | ( ( sgn_sgn_int @ K )
% 0.33/0.59                = zero_zero_int )
% 0.33/0.59              | ( N = zero_zero_nat ) )
% 0.33/0.59         => ( ( ( ( sgn_sgn_int @ K )
% 0.33/0.59                = ( sgn_sgn_int @ L ) )
% 0.33/0.59             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.33/0.59                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 0.33/0.59            & ( ( ( sgn_sgn_int @ K )
% 0.33/0.59               != ( sgn_sgn_int @ L ) )
% 0.33/0.59             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.33/0.59                = ( uminus_uminus_int
% 0.33/0.59                  @ ( semiri1314217659103216013at_int
% 0.33/0.59                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 0.33/0.59                      @ ( zero_n2687167440665602831ol_nat
% 0.33/0.59                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.59  
% 0.33/0.59  % divide_int_unfold
% 0.33/0.59  thf(fact_4887_modulo__int__unfold,axiom,
% 0.33/0.59      ! [L: int,K: int,N: nat,M: nat] :
% 0.33/0.59        ( ( ( ( ( sgn_sgn_int @ L )
% 0.33/0.59              = zero_zero_int )
% 0.33/0.59            | ( ( sgn_sgn_int @ K )
% 0.33/0.59              = zero_zero_int )
% 0.33/0.59            | ( N = zero_zero_nat ) )
% 0.33/0.59         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.33/0.59            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 0.33/0.59        & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.33/0.59                = zero_zero_int )
% 0.33/0.59              | ( ( sgn_sgn_int @ K )
% 0.33/0.59                = zero_zero_int )
% 0.33/0.59              | ( N = zero_zero_nat ) )
% 0.33/0.59         => ( ( ( ( sgn_sgn_int @ K )
% 0.33/0.59                = ( sgn_sgn_int @ L ) )
% 0.33/0.59             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.33/0.59                = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 0.33/0.59            & ( ( ( sgn_sgn_int @ K )
% 0.33/0.59               != ( sgn_sgn_int @ L ) )
% 0.33/0.59             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.33/0.59                = ( times_times_int @ ( sgn_sgn_int @ L )
% 0.33/0.59                  @ ( minus_minus_int
% 0.33/0.59                    @ ( semiri1314217659103216013at_int
% 0.33/0.59                      @ ( times_times_nat @ N
% 0.33/0.60                        @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60                          @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 0.33/0.60                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % modulo_int_unfold
% 0.33/0.60  thf(fact_4888_divide__int__def,axiom,
% 0.33/0.60      ( divide_divide_int
% 0.33/0.60      = ( ^ [K2: int,L2: int] :
% 0.33/0.60            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 0.33/0.60            @ ( if_int
% 0.33/0.60              @ ( ( sgn_sgn_int @ K2 )
% 0.33/0.60                = ( sgn_sgn_int @ L2 ) )
% 0.33/0.60              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 0.33/0.60              @ ( uminus_uminus_int
% 0.33/0.60                @ ( semiri1314217659103216013at_int
% 0.33/0.60                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 0.33/0.60                    @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60                      @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divide_int_def
% 0.33/0.60  thf(fact_4889_take__bit__Suc__from__most,axiom,
% 0.33/0.60      ! [N: nat,K: int] :
% 0.33/0.60        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 0.33/0.60        = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_Suc_from_most
% 0.33/0.60  thf(fact_4890_Suc__0__xor__eq,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.60        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.33/0.60          @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Suc_0_xor_eq
% 0.33/0.60  thf(fact_4891_xor__Suc__0__eq,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.33/0.60          @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_Suc_0_eq
% 0.33/0.60  thf(fact_4892_horner__sum__of__bool__2__less,axiom,
% 0.33/0.60      ! [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 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % horner_sum_of_bool_2_less
% 0.33/0.60  thf(fact_4893_xor__nonnegative__int__iff,axiom,
% 0.33/0.60      ! [K: int,L: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 0.33/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.60          = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_nonnegative_int_iff
% 0.33/0.60  thf(fact_4894_push__bit__nonnegative__int__iff,axiom,
% 0.33/0.60      ! [N: nat,K: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 0.33/0.60        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.33/0.60  
% 0.33/0.60  % push_bit_nonnegative_int_iff
% 0.33/0.60  thf(fact_4895_xor__negative__int__iff,axiom,
% 0.33/0.60      ! [K: int,L: int] :
% 0.33/0.60        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 0.33/0.60        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.60         != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_negative_int_iff
% 0.33/0.60  thf(fact_4896_push__bit__negative__int__iff,axiom,
% 0.33/0.60      ! [N: nat,K: int] :
% 0.33/0.60        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 0.33/0.60        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % push_bit_negative_int_iff
% 0.33/0.60  thf(fact_4897_concat__bit__of__zero__1,axiom,
% 0.33/0.60      ! [N: nat,L: int] :
% 0.33/0.60        ( ( bit_concat_bit @ N @ zero_zero_int @ L )
% 0.33/0.60        = ( bit_se545348938243370406it_int @ N @ L ) ) ).
% 0.33/0.60  
% 0.33/0.60  % concat_bit_of_zero_1
% 0.33/0.60  thf(fact_4898_signed__take__bit__nonnegative__iff,axiom,
% 0.33/0.60      ! [N: nat,K: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.33/0.60        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % signed_take_bit_nonnegative_iff
% 0.33/0.60  thf(fact_4899_signed__take__bit__negative__iff,axiom,
% 0.33/0.60      ! [N: nat,K: int] :
% 0.33/0.60        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 0.33/0.60        = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % signed_take_bit_negative_iff
% 0.33/0.60  thf(fact_4900_and__nat__numerals_I1_J,axiom,
% 0.33/0.60      ! [Y: num] :
% 0.33/0.60        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.33/0.60        = zero_zero_nat ) ).
% 0.33/0.60  
% 0.33/0.60  % and_nat_numerals(1)
% 0.33/0.60  thf(fact_4901_and__nat__numerals_I3_J,axiom,
% 0.33/0.60      ! [X2: num] :
% 0.33/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = zero_zero_nat ) ).
% 0.33/0.60  
% 0.33/0.60  % and_nat_numerals(3)
% 0.33/0.60  thf(fact_4902_push__bit__of__Suc__0,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % push_bit_of_Suc_0
% 0.33/0.60  thf(fact_4903_xor__nat__numerals_I4_J,axiom,
% 0.33/0.60      ! [X2: num] :
% 0.33/0.60        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_nat_numerals(4)
% 0.33/0.60  thf(fact_4904_xor__nat__numerals_I3_J,axiom,
% 0.33/0.60      ! [X2: num] :
% 0.33/0.60        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_nat_numerals(3)
% 0.33/0.60  thf(fact_4905_xor__nat__numerals_I2_J,axiom,
% 0.33/0.60      ! [Y: num] :
% 0.33/0.60        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.60        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_nat_numerals(2)
% 0.33/0.60  thf(fact_4906_xor__nat__numerals_I1_J,axiom,
% 0.33/0.60      ! [Y: num] :
% 0.33/0.60        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.33/0.60        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_nat_numerals(1)
% 0.33/0.60  thf(fact_4907_and__nat__numerals_I4_J,axiom,
% 0.33/0.60      ! [X2: num] :
% 0.33/0.60        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = one_one_nat ) ).
% 0.33/0.60  
% 0.33/0.60  % and_nat_numerals(4)
% 0.33/0.60  thf(fact_4908_and__nat__numerals_I2_J,axiom,
% 0.33/0.60      ! [Y: num] :
% 0.33/0.60        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.60        = one_one_nat ) ).
% 0.33/0.60  
% 0.33/0.60  % and_nat_numerals(2)
% 0.33/0.60  thf(fact_4909_and__Suc__0__eq,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_Suc_0_eq
% 0.33/0.60  thf(fact_4910_Suc__0__and__eq,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.60        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Suc_0_and_eq
% 0.33/0.60  thf(fact_4911_flip__bit__nat__def,axiom,
% 0.33/0.60      ( bit_se2161824704523386999it_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] : ( bit_se6528837805403552850or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % flip_bit_nat_def
% 0.33/0.60  thf(fact_4912_xor__nat__def,axiom,
% 0.33/0.60      ( bit_se6528837805403552850or_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_nat_def
% 0.33/0.60  thf(fact_4913_bit__push__bit__iff__int,axiom,
% 0.33/0.60      ! [M: nat,K: int,N: nat] :
% 0.33/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 0.33/0.60        = ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.60          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_push_bit_iff_int
% 0.33/0.60  thf(fact_4914_flip__bit__int__def,axiom,
% 0.33/0.60      ( bit_se2159334234014336723it_int
% 0.33/0.60      = ( ^ [N3: nat,K2: int] : ( bit_se6526347334894502574or_int @ K2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % flip_bit_int_def
% 0.33/0.60  thf(fact_4915_XOR__lower,axiom,
% 0.33/0.60      ! [X2: int,Y: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.33/0.60       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.60         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % XOR_lower
% 0.33/0.60  thf(fact_4916_bit__not__int__iff_H,axiom,
% 0.33/0.60      ! [K: int,N: nat] :
% 0.33/0.60        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 0.33/0.60        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_not_int_iff'
% 0.33/0.60  thf(fact_4917_and__nat__def,axiom,
% 0.33/0.60      ( bit_se727722235901077358nd_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_nat_def
% 0.33/0.60  thf(fact_4918_concat__bit__eq,axiom,
% 0.33/0.60      ( bit_concat_bit
% 0.33/0.60      = ( ^ [N3: nat,K2: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N3 @ K2 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % concat_bit_eq
% 0.33/0.60  thf(fact_4919_bit__imp__take__bit__positive,axiom,
% 0.33/0.60      ! [N: nat,M: nat,K: int] :
% 0.33/0.60        ( ( ord_less_nat @ N @ M )
% 0.33/0.60       => ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.33/0.60         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_imp_take_bit_positive
% 0.33/0.60  thf(fact_4920_bit__concat__bit__iff,axiom,
% 0.33/0.60      ! [M: nat,K: int,L: int,N: nat] :
% 0.33/0.60        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 0.33/0.60        = ( ( ( ord_less_nat @ N @ M )
% 0.33/0.60            & ( bit_se1146084159140164899it_int @ K @ N ) )
% 0.33/0.60          | ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.60            & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_concat_bit_iff
% 0.33/0.60  thf(fact_4921_int__bit__bound,axiom,
% 0.33/0.60      ! [K: int] :
% 0.33/0.60        ~ ! [N2: nat] :
% 0.33/0.60            ( ! [M6: nat] :
% 0.33/0.60                ( ( ord_less_eq_nat @ N2 @ M6 )
% 0.33/0.60               => ( ( bit_se1146084159140164899it_int @ K @ M6 )
% 0.33/0.60                  = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 0.33/0.60           => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.33/0.60               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.33/0.60                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_bit_bound
% 0.33/0.60  thf(fact_4922_push__bit__minus__one,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % push_bit_minus_one
% 0.33/0.60  thf(fact_4923_XOR__upper,axiom,
% 0.33/0.60      ! [X2: int,N: nat,Y: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.33/0.60       => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.33/0.60         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.33/0.60           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % XOR_upper
% 0.33/0.60  thf(fact_4924_and__nat__unfold,axiom,
% 0.33/0.60      ( bit_se727722235901077358nd_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] :
% 0.33/0.60            ( if_nat
% 0.33/0.60            @ ( ( M2 = zero_zero_nat )
% 0.33/0.60              | ( N3 = zero_zero_nat ) )
% 0.33/0.60            @ zero_zero_nat
% 0.33/0.60            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_nat_unfold
% 0.33/0.60  thf(fact_4925_and__nat__rec,axiom,
% 0.33/0.60      ( bit_se727722235901077358nd_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] :
% 0.33/0.60            ( plus_plus_nat
% 0.33/0.60            @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 0.33/0.60                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 0.33/0.60            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_nat_rec
% 0.33/0.60  thf(fact_4926_xor__nat__unfold,axiom,
% 0.33/0.60      ( bit_se6528837805403552850or_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_nat_unfold
% 0.33/0.60  thf(fact_4927_xor__int__rec,axiom,
% 0.33/0.60      ( bit_se6526347334894502574or_int
% 0.33/0.60      = ( ^ [K2: int,L2: int] :
% 0.33/0.60            ( plus_plus_int
% 0.33/0.60            @ ( zero_n2684676970156552555ol_int
% 0.33/0.60              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 0.33/0.60               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.33/0.60            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_int_rec
% 0.33/0.60  thf(fact_4928_xor__nat__rec,axiom,
% 0.33/0.60      ( bit_se6528837805403552850or_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] :
% 0.33/0.60            ( plus_plus_nat
% 0.33/0.60            @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.33/0.60               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.33/0.60            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_nat_rec
% 0.33/0.60  thf(fact_4929_set__bit__eq,axiom,
% 0.33/0.60      ( bit_se7879613467334960850it_int
% 0.33/0.60      = ( ^ [N3: nat,K2: int] :
% 0.33/0.60            ( plus_plus_int @ K2
% 0.33/0.60            @ ( times_times_int
% 0.33/0.60              @ ( zero_n2684676970156552555ol_int
% 0.33/0.60                @ ~ ( bit_se1146084159140164899it_int @ K2 @ N3 ) )
% 0.33/0.60              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % set_bit_eq
% 0.33/0.60  thf(fact_4930_xor__int__unfold,axiom,
% 0.33/0.60      ( bit_se6526347334894502574or_int
% 0.33/0.60      = ( ^ [K2: int,L2: int] :
% 0.33/0.60            ( if_int
% 0.33/0.60            @ ( K2
% 0.33/0.60              = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60            @ ( bit_ri7919022796975470100ot_int @ L2 )
% 0.33/0.60            @ ( if_int
% 0.33/0.60              @ ( L2
% 0.33/0.60                = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60              @ ( bit_ri7919022796975470100ot_int @ K2 )
% 0.33/0.60              @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_int_unfold
% 0.33/0.60  thf(fact_4931_mask__eq__sum__exp__nat,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.60          @ ( collect_nat
% 0.33/0.60            @ ^ [Q6: nat] : ( ord_less_nat @ Q6 @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % mask_eq_sum_exp_nat
% 0.33/0.60  thf(fact_4932_not__nonnegative__int__iff,axiom,
% 0.33/0.60      ! [K: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.33/0.60        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % not_nonnegative_int_iff
% 0.33/0.60  thf(fact_4933_not__negative__int__iff,axiom,
% 0.33/0.60      ! [K: int] :
% 0.33/0.60        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 0.33/0.60        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.33/0.60  
% 0.33/0.60  % not_negative_int_iff
% 0.33/0.60  thf(fact_4934_bit__Suc__0__iff,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.60        = ( N = zero_zero_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_Suc_0_iff
% 0.33/0.60  thf(fact_4935_not__bit__Suc__0__Suc,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % not_bit_Suc_0_Suc
% 0.33/0.60  thf(fact_4936_bit__push__bit__iff__nat,axiom,
% 0.33/0.60      ! [M: nat,Q2: nat,N: nat] :
% 0.33/0.60        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 0.33/0.60        = ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.60          & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_push_bit_iff_nat
% 0.33/0.60  thf(fact_4937_not__bit__Suc__0__numeral,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % not_bit_Suc_0_numeral
% 0.33/0.60  thf(fact_4938_not__int__def,axiom,
% 0.33/0.60      ( bit_ri7919022796975470100ot_int
% 0.33/0.60      = ( ^ [K2: int] : ( minus_minus_int @ ( uminus_uminus_int @ K2 ) @ one_one_int ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % not_int_def
% 0.33/0.60  thf(fact_4939_and__not__numerals_I1_J,axiom,
% 0.33/0.60      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.33/0.60      = zero_zero_int ) ).
% 0.33/0.60  
% 0.33/0.60  % and_not_numerals(1)
% 0.33/0.60  thf(fact_4940_unset__bit__int__def,axiom,
% 0.33/0.60      ( bit_se4203085406695923979it_int
% 0.33/0.60      = ( ^ [N3: nat,K2: int] : ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % unset_bit_int_def
% 0.33/0.60  thf(fact_4941_and__not__numerals_I2_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.33/0.60        = one_one_int ) ).
% 0.33/0.60  
% 0.33/0.60  % and_not_numerals(2)
% 0.33/0.60  thf(fact_4942_and__not__numerals_I4_J,axiom,
% 0.33/0.60      ! [M: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.33/0.60        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_not_numerals(4)
% 0.33/0.60  thf(fact_4943_bit__nat__iff,axiom,
% 0.33/0.60      ! [K: int,N: nat] :
% 0.33/0.60        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 0.33/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.60          & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_nat_iff
% 0.33/0.60  thf(fact_4944_bit__minus__int__iff,axiom,
% 0.33/0.60      ! [K: int,N: nat] :
% 0.33/0.60        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 0.33/0.60        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_minus_int_iff
% 0.33/0.60  thf(fact_4945_and__not__numerals_I7_J,axiom,
% 0.33/0.60      ! [M: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.33/0.60        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_not_numerals(7)
% 0.33/0.60  thf(fact_4946_and__not__numerals_I3_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.33/0.60        = zero_zero_int ) ).
% 0.33/0.60  
% 0.33/0.60  % and_not_numerals(3)
% 0.33/0.60  thf(fact_4947_and__not__numerals_I8_J,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.33/0.60        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_not_numerals(8)
% 0.33/0.60  thf(fact_4948_not__int__rec,axiom,
% 0.33/0.60      ( bit_ri7919022796975470100ot_int
% 0.33/0.60      = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % not_int_rec
% 0.33/0.60  thf(fact_4949_atMost__atLeast0,axiom,
% 0.33/0.60      ( set_ord_atMost_nat
% 0.33/0.60      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atMost_atLeast0
% 0.33/0.60  thf(fact_4950_all__nat__less,axiom,
% 0.33/0.60      ! [N: nat,P: nat > $o] :
% 0.33/0.60        ( ( ! [M2: nat] :
% 0.33/0.60              ( ( ord_less_eq_nat @ M2 @ N )
% 0.33/0.60             => ( P @ M2 ) ) )
% 0.33/0.60        = ( ! [X: nat] :
% 0.33/0.60              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.33/0.60             => ( P @ X ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % all_nat_less
% 0.33/0.60  thf(fact_4951_ex__nat__less,axiom,
% 0.33/0.60      ! [N: nat,P: nat > $o] :
% 0.33/0.60        ( ( ? [M2: nat] :
% 0.33/0.60              ( ( ord_less_eq_nat @ M2 @ N )
% 0.33/0.60              & ( P @ M2 ) ) )
% 0.33/0.60        = ( ? [X: nat] :
% 0.33/0.60              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.33/0.60              & ( P @ X ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % ex_nat_less
% 0.33/0.60  thf(fact_4952_sum__choose__upper,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [K2: nat] : ( binomial @ K2 @ M )
% 0.33/0.60          @ ( set_ord_atMost_nat @ N ) )
% 0.33/0.60        = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % sum_choose_upper
% 0.33/0.60  thf(fact_4953_sum__choose__lower,axiom,
% 0.33/0.60      ! [R: nat,N: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R @ K2 ) @ K2 )
% 0.33/0.60          @ ( set_ord_atMost_nat @ N ) )
% 0.33/0.60        = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % sum_choose_lower
% 0.33/0.60  thf(fact_4954_choose__rising__sum_I1_J,axiom,
% 0.33/0.60      ! [N: nat,M: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 0.33/0.60          @ ( set_ord_atMost_nat @ M ) )
% 0.33/0.60        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % choose_rising_sum(1)
% 0.33/0.60  thf(fact_4955_choose__rising__sum_I2_J,axiom,
% 0.33/0.60      ! [N: nat,M: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 0.33/0.60          @ ( set_ord_atMost_nat @ M ) )
% 0.33/0.60        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 0.33/0.60  
% 0.33/0.60  % choose_rising_sum(2)
% 0.33/0.60  thf(fact_4956_sum__choose__diagonal,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.60       => ( ( groups3542108847815614940at_nat
% 0.33/0.60            @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 0.33/0.60            @ ( set_ord_atMost_nat @ M ) )
% 0.33/0.60          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % sum_choose_diagonal
% 0.33/0.60  thf(fact_4957_vandermonde,axiom,
% 0.33/0.60      ! [M: nat,N: nat,R: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K2 ) ) )
% 0.33/0.60          @ ( set_ord_atMost_nat @ R ) )
% 0.33/0.60        = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 0.33/0.60  
% 0.33/0.60  % vandermonde
% 0.33/0.60  thf(fact_4958_choose__row__sum,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 0.33/0.60        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % choose_row_sum
% 0.33/0.60  thf(fact_4959_binomial,axiom,
% 0.33/0.60      ! [A: nat,B: nat,N: nat] :
% 0.33/0.60        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 0.33/0.60        = ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 0.33/0.60          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % binomial
% 0.33/0.60  thf(fact_4960_choose__square__sum,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.33/0.60          @ ( set_ord_atMost_nat @ N ) )
% 0.33/0.60        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % choose_square_sum
% 0.33/0.60  thf(fact_4961_gauss__sum__nat,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [X: nat] : X
% 0.33/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.33/0.60        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % gauss_sum_nat
% 0.33/0.60  thf(fact_4962_binomial__r__part__sum,axiom,
% 0.33/0.60      ! [M: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.33/0.60        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % binomial_r_part_sum
% 0.33/0.60  thf(fact_4963_choose__linear__sum,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [I2: nat] : ( times_times_nat @ I2 @ ( binomial @ N @ I2 ) )
% 0.33/0.60          @ ( set_ord_atMost_nat @ N ) )
% 0.33/0.60        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % choose_linear_sum
% 0.33/0.60  thf(fact_4964_arith__series__nat,axiom,
% 0.33/0.60      ! [A: nat,D: nat,N: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I2 @ D ) )
% 0.33/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.33/0.60        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % arith_series_nat
% 0.33/0.60  thf(fact_4965_Sum__Icc__nat,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [X: nat] : X
% 0.33/0.60          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.33/0.60        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Sum_Icc_nat
% 0.33/0.60  thf(fact_4966_Sum__Icc__int,axiom,
% 0.33/0.60      ! [M: int,N: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ M @ N )
% 0.33/0.60       => ( ( groups4538972089207619220nt_int
% 0.33/0.60            @ ^ [X: int] : X
% 0.33/0.60            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 0.33/0.60          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Sum_Icc_int
% 0.33/0.60  thf(fact_4967_Sum__Ico__nat,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [X: nat] : X
% 0.33/0.60          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.33/0.60        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Sum_Ico_nat
% 0.33/0.60  thf(fact_4968_sum__power2,axiom,
% 0.33/0.60      ! [K: nat] :
% 0.33/0.60        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 0.33/0.60        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % sum_power2
% 0.33/0.60  thf(fact_4969_prod__Suc__Suc__fact,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.33/0.60        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % prod_Suc_Suc_fact
% 0.33/0.60  thf(fact_4970_prod__Suc__fact,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.33/0.60        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % prod_Suc_fact
% 0.33/0.60  thf(fact_4971_all__nat__less__eq,axiom,
% 0.33/0.60      ! [N: nat,P: nat > $o] :
% 0.33/0.60        ( ( ! [M2: nat] :
% 0.33/0.60              ( ( ord_less_nat @ M2 @ N )
% 0.33/0.60             => ( P @ M2 ) ) )
% 0.33/0.60        = ( ! [X: nat] :
% 0.33/0.60              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.33/0.60             => ( P @ X ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % all_nat_less_eq
% 0.33/0.60  thf(fact_4972_ex__nat__less__eq,axiom,
% 0.33/0.60      ! [N: nat,P: nat > $o] :
% 0.33/0.60        ( ( ? [M2: nat] :
% 0.33/0.60              ( ( ord_less_nat @ M2 @ N )
% 0.33/0.60              & ( P @ M2 ) ) )
% 0.33/0.60        = ( ? [X: nat] :
% 0.33/0.60              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.33/0.60              & ( P @ X ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % ex_nat_less_eq
% 0.33/0.60  thf(fact_4973_atLeastLessThanSuc__atLeastAtMost,axiom,
% 0.33/0.60      ! [L: nat,U: nat] :
% 0.33/0.60        ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 0.33/0.60        = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastLessThanSuc_atLeastAtMost
% 0.33/0.60  thf(fact_4974_bset_I1_J,axiom,
% 0.33/0.60      ! [D3: int,B4: set_int,P: int > $o,Q: int > $o] :
% 0.33/0.60        ( ! [X3: int] :
% 0.33/0.60            ( ! [Xa2: int] :
% 0.33/0.60                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb2: int] :
% 0.33/0.60                    ( ( member_int @ Xb2 @ B4 )
% 0.33/0.60                   => ( X3
% 0.33/0.60                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60           => ( ( P @ X3 )
% 0.33/0.60             => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60       => ( ! [X3: int] :
% 0.33/0.60              ( ! [Xa2: int] :
% 0.33/0.60                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb2: int] :
% 0.33/0.60                      ( ( member_int @ Xb2 @ B4 )
% 0.33/0.60                     => ( X3
% 0.33/0.60                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60             => ( ( Q @ X3 )
% 0.33/0.60               => ( Q @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( ( P @ X4 )
% 0.33/0.60                  & ( Q @ X4 ) )
% 0.33/0.60               => ( ( P @ ( minus_minus_int @ X4 @ D3 ) )
% 0.33/0.60                  & ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(1)
% 0.33/0.60  thf(fact_4975_bset_I2_J,axiom,
% 0.33/0.60      ! [D3: int,B4: set_int,P: int > $o,Q: int > $o] :
% 0.33/0.60        ( ! [X3: int] :
% 0.33/0.60            ( ! [Xa2: int] :
% 0.33/0.60                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb2: int] :
% 0.33/0.60                    ( ( member_int @ Xb2 @ B4 )
% 0.33/0.60                   => ( X3
% 0.33/0.60                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60           => ( ( P @ X3 )
% 0.33/0.60             => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60       => ( ! [X3: int] :
% 0.33/0.60              ( ! [Xa2: int] :
% 0.33/0.60                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb2: int] :
% 0.33/0.60                      ( ( member_int @ Xb2 @ B4 )
% 0.33/0.60                     => ( X3
% 0.33/0.60                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60             => ( ( Q @ X3 )
% 0.33/0.60               => ( Q @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( ( P @ X4 )
% 0.33/0.60                  | ( Q @ X4 ) )
% 0.33/0.60               => ( ( P @ ( minus_minus_int @ X4 @ D3 ) )
% 0.33/0.60                  | ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(2)
% 0.33/0.60  thf(fact_4976_aset_I1_J,axiom,
% 0.33/0.60      ! [D3: int,A4: set_int,P: int > $o,Q: int > $o] :
% 0.33/0.60        ( ! [X3: int] :
% 0.33/0.60            ( ! [Xa2: int] :
% 0.33/0.60                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb2: int] :
% 0.33/0.60                    ( ( member_int @ Xb2 @ A4 )
% 0.33/0.60                   => ( X3
% 0.33/0.60                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60           => ( ( P @ X3 )
% 0.33/0.60             => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60       => ( ! [X3: int] :
% 0.33/0.60              ( ! [Xa2: int] :
% 0.33/0.60                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb2: int] :
% 0.33/0.60                      ( ( member_int @ Xb2 @ A4 )
% 0.33/0.60                     => ( X3
% 0.33/0.60                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60             => ( ( Q @ X3 )
% 0.33/0.60               => ( Q @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( ( P @ X4 )
% 0.33/0.60                  & ( Q @ X4 ) )
% 0.33/0.60               => ( ( P @ ( plus_plus_int @ X4 @ D3 ) )
% 0.33/0.60                  & ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(1)
% 0.33/0.60  thf(fact_4977_aset_I2_J,axiom,
% 0.33/0.60      ! [D3: int,A4: set_int,P: int > $o,Q: int > $o] :
% 0.33/0.60        ( ! [X3: int] :
% 0.33/0.60            ( ! [Xa2: int] :
% 0.33/0.60                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb2: int] :
% 0.33/0.60                    ( ( member_int @ Xb2 @ A4 )
% 0.33/0.60                   => ( X3
% 0.33/0.60                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60           => ( ( P @ X3 )
% 0.33/0.60             => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60       => ( ! [X3: int] :
% 0.33/0.60              ( ! [Xa2: int] :
% 0.33/0.60                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb2: int] :
% 0.33/0.60                      ( ( member_int @ Xb2 @ A4 )
% 0.33/0.60                     => ( X3
% 0.33/0.60                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60             => ( ( Q @ X3 )
% 0.33/0.60               => ( Q @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( ( P @ X4 )
% 0.33/0.60                  | ( Q @ X4 ) )
% 0.33/0.60               => ( ( P @ ( plus_plus_int @ X4 @ D3 ) )
% 0.33/0.60                  | ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(2)
% 0.33/0.60  thf(fact_4978_bset_I9_J,axiom,
% 0.33/0.60      ! [D: int,D3: int,B4: set_int,T: int] :
% 0.33/0.60        ( ( dvd_dvd_int @ D @ D3 )
% 0.33/0.60       => ! [X4: int] :
% 0.33/0.60            ( ! [Xa3: int] :
% 0.33/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb3: int] :
% 0.33/0.60                    ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                   => ( X4
% 0.33/0.60                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60           => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 0.33/0.60             => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(9)
% 0.33/0.60  thf(fact_4979_bset_I10_J,axiom,
% 0.33/0.60      ! [D: int,D3: int,B4: set_int,T: int] :
% 0.33/0.60        ( ( dvd_dvd_int @ D @ D3 )
% 0.33/0.60       => ! [X4: int] :
% 0.33/0.60            ( ! [Xa3: int] :
% 0.33/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb3: int] :
% 0.33/0.60                    ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                   => ( X4
% 0.33/0.60                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60           => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 0.33/0.60             => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(10)
% 0.33/0.60  thf(fact_4980_aset_I9_J,axiom,
% 0.33/0.60      ! [D: int,D3: int,A4: set_int,T: int] :
% 0.33/0.60        ( ( dvd_dvd_int @ D @ D3 )
% 0.33/0.60       => ! [X4: int] :
% 0.33/0.60            ( ! [Xa3: int] :
% 0.33/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb3: int] :
% 0.33/0.60                    ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                   => ( X4
% 0.33/0.60                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60           => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 0.33/0.60             => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(9)
% 0.33/0.60  thf(fact_4981_aset_I10_J,axiom,
% 0.33/0.60      ! [D: int,D3: int,A4: set_int,T: int] :
% 0.33/0.60        ( ( dvd_dvd_int @ D @ D3 )
% 0.33/0.60       => ! [X4: int] :
% 0.33/0.60            ( ! [Xa3: int] :
% 0.33/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb3: int] :
% 0.33/0.60                    ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                   => ( X4
% 0.33/0.60                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60           => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 0.33/0.60             => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(10)
% 0.33/0.60  thf(fact_4982_periodic__finite__ex,axiom,
% 0.33/0.60      ! [D: int,P: int > $o] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D )
% 0.33/0.60       => ( ! [X3: int,K3: int] :
% 0.33/0.60              ( ( P @ X3 )
% 0.33/0.60              = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D ) ) ) )
% 0.33/0.60         => ( ( ? [X5: int] : ( P @ X5 ) )
% 0.33/0.60            = ( ? [X: int] :
% 0.33/0.60                  ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 0.33/0.60                  & ( P @ X ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % periodic_finite_ex
% 0.33/0.60  thf(fact_4983_bset_I3_J,axiom,
% 0.33/0.60      ! [D3: int,T: int,B4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( X4 = T )
% 0.33/0.60               => ( ( minus_minus_int @ X4 @ D3 )
% 0.33/0.60                  = T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(3)
% 0.33/0.60  thf(fact_4984_bset_I4_J,axiom,
% 0.33/0.60      ! [D3: int,T: int,B4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ( member_int @ T @ B4 )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( X4 != T )
% 0.33/0.60               => ( ( minus_minus_int @ X4 @ D3 )
% 0.33/0.60                 != T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(4)
% 0.33/0.60  thf(fact_4985_bset_I5_J,axiom,
% 0.33/0.60      ! [D3: int,B4: set_int,T: int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ! [X4: int] :
% 0.33/0.60            ( ! [Xa3: int] :
% 0.33/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb3: int] :
% 0.33/0.60                    ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                   => ( X4
% 0.33/0.60                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60           => ( ( ord_less_int @ X4 @ T )
% 0.33/0.60             => ( ord_less_int @ ( minus_minus_int @ X4 @ D3 ) @ T ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(5)
% 0.33/0.60  thf(fact_4986_bset_I7_J,axiom,
% 0.33/0.60      ! [D3: int,T: int,B4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ( member_int @ T @ B4 )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( ord_less_int @ T @ X4 )
% 0.33/0.60               => ( ord_less_int @ T @ ( minus_minus_int @ X4 @ D3 ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(7)
% 0.33/0.60  thf(fact_4987_aset_I3_J,axiom,
% 0.33/0.60      ! [D3: int,T: int,A4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( X4 = T )
% 0.33/0.60               => ( ( plus_plus_int @ X4 @ D3 )
% 0.33/0.60                  = T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(3)
% 0.33/0.60  thf(fact_4988_aset_I4_J,axiom,
% 0.33/0.60      ! [D3: int,T: int,A4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ( member_int @ T @ A4 )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( X4 != T )
% 0.33/0.60               => ( ( plus_plus_int @ X4 @ D3 )
% 0.33/0.60                 != T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(4)
% 0.33/0.60  thf(fact_4989_aset_I5_J,axiom,
% 0.33/0.60      ! [D3: int,T: int,A4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ( member_int @ T @ A4 )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( ord_less_int @ X4 @ T )
% 0.33/0.60               => ( ord_less_int @ ( plus_plus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(5)
% 0.33/0.60  thf(fact_4990_aset_I7_J,axiom,
% 0.33/0.60      ! [D3: int,A4: set_int,T: int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ! [X4: int] :
% 0.33/0.60            ( ! [Xa3: int] :
% 0.33/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb3: int] :
% 0.33/0.60                    ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                   => ( X4
% 0.33/0.60                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60           => ( ( ord_less_int @ T @ X4 )
% 0.33/0.60             => ( ord_less_int @ T @ ( plus_plus_int @ X4 @ D3 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(7)
% 0.33/0.60  thf(fact_4991_fact__eq__fact__times,axiom,
% 0.33/0.60      ! [N: nat,M: nat] :
% 0.33/0.60        ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.60       => ( ( semiri1408675320244567234ct_nat @ M )
% 0.33/0.60          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 0.33/0.60            @ ( groups708209901874060359at_nat
% 0.33/0.60              @ ^ [X: nat] : X
% 0.33/0.60              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % fact_eq_fact_times
% 0.33/0.60  thf(fact_4992_bset_I6_J,axiom,
% 0.33/0.60      ! [D3: int,B4: set_int,T: int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ! [X4: int] :
% 0.33/0.60            ( ! [Xa3: int] :
% 0.33/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb3: int] :
% 0.33/0.60                    ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                   => ( X4
% 0.33/0.60                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60           => ( ( ord_less_eq_int @ X4 @ T )
% 0.33/0.60             => ( ord_less_eq_int @ ( minus_minus_int @ X4 @ D3 ) @ T ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(6)
% 0.33/0.60  thf(fact_4993_bset_I8_J,axiom,
% 0.33/0.60      ! [D3: int,T: int,B4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ B4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( ord_less_eq_int @ T @ X4 )
% 0.33/0.60               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X4 @ D3 ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bset(8)
% 0.33/0.60  thf(fact_4994_aset_I6_J,axiom,
% 0.33/0.60      ! [D3: int,T: int,A4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 0.33/0.60         => ! [X4: int] :
% 0.33/0.60              ( ! [Xa3: int] :
% 0.33/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                 => ! [Xb3: int] :
% 0.33/0.60                      ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                     => ( X4
% 0.33/0.60                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60             => ( ( ord_less_eq_int @ X4 @ T )
% 0.33/0.60               => ( ord_less_eq_int @ ( plus_plus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(6)
% 0.33/0.60  thf(fact_4995_aset_I8_J,axiom,
% 0.33/0.60      ! [D3: int,A4: set_int,T: int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ! [X4: int] :
% 0.33/0.60            ( ! [Xa3: int] :
% 0.33/0.60                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60               => ! [Xb3: int] :
% 0.33/0.60                    ( ( member_int @ Xb3 @ A4 )
% 0.33/0.60                   => ( X4
% 0.33/0.60                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.33/0.60           => ( ( ord_less_eq_int @ T @ X4 )
% 0.33/0.60             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X4 @ D3 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % aset(8)
% 0.33/0.60  thf(fact_4996_cppi,axiom,
% 0.33/0.60      ! [D3: int,P: int > $o,P2: int > $o,A4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ? [Z5: int] :
% 0.33/0.60            ! [X3: int] :
% 0.33/0.60              ( ( ord_less_int @ Z5 @ X3 )
% 0.33/0.60             => ( ( P @ X3 )
% 0.33/0.60                = ( P2 @ X3 ) ) )
% 0.33/0.60         => ( ! [X3: int] :
% 0.33/0.60                ( ! [Xa2: int] :
% 0.33/0.60                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                   => ! [Xb2: int] :
% 0.33/0.60                        ( ( member_int @ Xb2 @ A4 )
% 0.33/0.60                       => ( X3
% 0.33/0.60                         != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60               => ( ( P @ X3 )
% 0.33/0.60                 => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60           => ( ! [X3: int,K3: int] :
% 0.33/0.60                  ( ( P2 @ X3 )
% 0.33/0.60                  = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 0.33/0.60             => ( ( ? [X5: int] : ( P @ X5 ) )
% 0.33/0.60                = ( ? [X: int] :
% 0.33/0.60                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                      & ( P2 @ X ) )
% 0.33/0.60                  | ? [X: int] :
% 0.33/0.60                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                      & ? [Y4: int] :
% 0.33/0.60                          ( ( member_int @ Y4 @ A4 )
% 0.33/0.60                          & ( P @ ( minus_minus_int @ Y4 @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % cppi
% 0.33/0.60  thf(fact_4997_cpmi,axiom,
% 0.33/0.60      ! [D3: int,P: int > $o,P2: int > $o,B4: set_int] :
% 0.33/0.60        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.33/0.60       => ( ? [Z5: int] :
% 0.33/0.60            ! [X3: int] :
% 0.33/0.60              ( ( ord_less_int @ X3 @ Z5 )
% 0.33/0.60             => ( ( P @ X3 )
% 0.33/0.60                = ( P2 @ X3 ) ) )
% 0.33/0.60         => ( ! [X3: int] :
% 0.33/0.60                ( ! [Xa2: int] :
% 0.33/0.60                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                   => ! [Xb2: int] :
% 0.33/0.60                        ( ( member_int @ Xb2 @ B4 )
% 0.33/0.60                       => ( X3
% 0.33/0.60                         != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.33/0.60               => ( ( P @ X3 )
% 0.33/0.60                 => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 0.33/0.60           => ( ! [X3: int,K3: int] :
% 0.33/0.60                  ( ( P2 @ X3 )
% 0.33/0.60                  = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 0.33/0.60             => ( ( ? [X5: int] : ( P @ X5 ) )
% 0.33/0.60                = ( ? [X: int] :
% 0.33/0.60                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                      & ( P2 @ X ) )
% 0.33/0.60                  | ? [X: int] :
% 0.33/0.60                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.33/0.60                      & ? [Y4: int] :
% 0.33/0.60                          ( ( member_int @ Y4 @ B4 )
% 0.33/0.60                          & ( P @ ( plus_plus_int @ Y4 @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % cpmi
% 0.33/0.60  thf(fact_4998_fact__div__fact,axiom,
% 0.33/0.60      ! [N: nat,M: nat] :
% 0.33/0.60        ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.60       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.33/0.60          = ( groups708209901874060359at_nat
% 0.33/0.60            @ ^ [X: nat] : X
% 0.33/0.60            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % fact_div_fact
% 0.33/0.60  thf(fact_4999_integer__of__int__code,axiom,
% 0.33/0.60      ( code_integer_of_int
% 0.33/0.60      = ( ^ [K2: int] :
% 0.33/0.60            ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 0.33/0.60            @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.33/0.60              @ ( if_Code_integer
% 0.33/0.60                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.33/0.60                  = zero_zero_int )
% 0.33/0.60                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.33/0.60                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_of_int_code
% 0.33/0.60  thf(fact_5000_or__int__rec,axiom,
% 0.33/0.60      ( bit_se1409905431419307370or_int
% 0.33/0.60      = ( ^ [K2: int,L2: int] :
% 0.33/0.60            ( plus_plus_int
% 0.33/0.60            @ ( zero_n2684676970156552555ol_int
% 0.33/0.60              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.33/0.60                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.33/0.60            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_int_rec
% 0.33/0.60  thf(fact_5001_integer__of__int__eq__of__int,axiom,
% 0.33/0.60      code_integer_of_int = ring_18347121197199848620nteger ).
% 0.33/0.60  
% 0.33/0.60  % integer_of_int_eq_of_int
% 0.33/0.60  thf(fact_5002_finite__atLeastAtMost,axiom,
% 0.33/0.60      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_atLeastAtMost
% 0.33/0.60  thf(fact_5003_finite__atLeastLessThan,axiom,
% 0.33/0.60      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_atLeastLessThan
% 0.33/0.60  thf(fact_5004_finite__atMost,axiom,
% 0.33/0.60      ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_atMost
% 0.33/0.60  thf(fact_5005_or__nonnegative__int__iff,axiom,
% 0.33/0.60      ! [K: int,L: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 0.33/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.33/0.60          & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_nonnegative_int_iff
% 0.33/0.60  thf(fact_5006_or__negative__int__iff,axiom,
% 0.33/0.60      ! [K: int,L: int] :
% 0.33/0.60        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 0.33/0.60        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.33/0.60          | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_negative_int_iff
% 0.33/0.60  thf(fact_5007_or__nat__numerals_I4_J,axiom,
% 0.33/0.60      ! [X2: num] :
% 0.33/0.60        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_nat_numerals(4)
% 0.33/0.60  thf(fact_5008_or__nat__numerals_I2_J,axiom,
% 0.33/0.60      ! [Y: num] :
% 0.33/0.60        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.33/0.60        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_nat_numerals(2)
% 0.33/0.60  thf(fact_5009_or__nat__numerals_I1_J,axiom,
% 0.33/0.60      ! [Y: num] :
% 0.33/0.60        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.33/0.60        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_nat_numerals(1)
% 0.33/0.60  thf(fact_5010_or__nat__numerals_I3_J,axiom,
% 0.33/0.60      ! [X2: num] :
% 0.33/0.60        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_nat_numerals(3)
% 0.33/0.60  thf(fact_5011_or__minus__numerals_I2_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.33/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_minus_numerals(2)
% 0.33/0.60  thf(fact_5012_or__minus__numerals_I6_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.33/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_minus_numerals(6)
% 0.33/0.60  thf(fact_5013_and__minus__minus__numerals,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.60        = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_minus_minus_numerals
% 0.33/0.60  thf(fact_5014_or__minus__minus__numerals,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.60        = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_minus_minus_numerals
% 0.33/0.60  thf(fact_5015_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 0.33/0.60      ! [L: code_integer,U: code_integer] :
% 0.33/0.60        ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 0.33/0.60        = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastLessThanPlusOne_atLeastAtMost_integer
% 0.33/0.60  thf(fact_5016_or__nat__def,axiom,
% 0.33/0.60      ( bit_se1412395901928357646or_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_nat_def
% 0.33/0.60  thf(fact_5017_less__eq__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( ord_less_eq_int @ Xa @ X2 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % less_eq_integer.abs_eq
% 0.33/0.60  thf(fact_5018_less__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( ord_less_int @ Xa @ X2 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % less_integer.abs_eq
% 0.33/0.60  thf(fact_5019_one__integer__def,axiom,
% 0.33/0.60      ( one_one_Code_integer
% 0.33/0.60      = ( code_integer_of_int @ one_one_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % one_integer_def
% 0.33/0.60  thf(fact_5020_times__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( times_times_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % times_integer.abs_eq
% 0.33/0.60  thf(fact_5021_uminus__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [X2: int] :
% 0.33/0.60        ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( uminus_uminus_int @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % uminus_integer.abs_eq
% 0.33/0.60  thf(fact_5022_zero__integer__def,axiom,
% 0.33/0.60      ( zero_z3403309356797280102nteger
% 0.33/0.60      = ( code_integer_of_int @ zero_zero_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % zero_integer_def
% 0.33/0.60  thf(fact_5023_sgn__integer__code,axiom,
% 0.33/0.60      ( sgn_sgn_Code_integer
% 0.33/0.60      = ( ^ [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 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % sgn_integer_code
% 0.33/0.60  thf(fact_5024_abs__integer__code,axiom,
% 0.33/0.60      ( abs_abs_Code_integer
% 0.33/0.60      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % abs_integer_code
% 0.33/0.60  thf(fact_5025_less__integer__code_I1_J,axiom,
% 0.33/0.60      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 0.33/0.60  
% 0.33/0.60  % less_integer_code(1)
% 0.33/0.60  thf(fact_5026_minus__integer__code_I2_J,axiom,
% 0.33/0.60      ! [L: code_integer] :
% 0.33/0.60        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 0.33/0.60        = ( uminus1351360451143612070nteger @ L ) ) ).
% 0.33/0.60  
% 0.33/0.60  % minus_integer_code(2)
% 0.33/0.60  thf(fact_5027_minus__integer__code_I1_J,axiom,
% 0.33/0.60      ! [K: code_integer] :
% 0.33/0.60        ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 0.33/0.60        = K ) ).
% 0.33/0.60  
% 0.33/0.60  % minus_integer_code(1)
% 0.33/0.60  thf(fact_5028_uminus__integer__code_I1_J,axiom,
% 0.33/0.60      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.33/0.60      = zero_z3403309356797280102nteger ) ).
% 0.33/0.60  
% 0.33/0.60  % uminus_integer_code(1)
% 0.33/0.60  thf(fact_5029_or__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( bit_se1080825931792720795nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_se1409905431419307370or_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_integer.abs_eq
% 0.33/0.60  thf(fact_5030_plus__integer__code_I2_J,axiom,
% 0.33/0.60      ! [L: code_integer] :
% 0.33/0.60        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 0.33/0.60        = L ) ).
% 0.33/0.60  
% 0.33/0.60  % plus_integer_code(2)
% 0.33/0.60  thf(fact_5031_plus__integer__code_I1_J,axiom,
% 0.33/0.60      ! [K: code_integer] :
% 0.33/0.60        ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 0.33/0.60        = K ) ).
% 0.33/0.60  
% 0.33/0.60  % plus_integer_code(1)
% 0.33/0.60  thf(fact_5032_times__integer__code_I1_J,axiom,
% 0.33/0.60      ! [K: code_integer] :
% 0.33/0.60        ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 0.33/0.60        = zero_z3403309356797280102nteger ) ).
% 0.33/0.60  
% 0.33/0.60  % times_integer_code(1)
% 0.33/0.60  thf(fact_5033_times__integer__code_I2_J,axiom,
% 0.33/0.60      ! [L: code_integer] :
% 0.33/0.60        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 0.33/0.60        = zero_z3403309356797280102nteger ) ).
% 0.33/0.60  
% 0.33/0.60  % times_integer_code(2)
% 0.33/0.60  thf(fact_5034_plus__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( plus_plus_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % plus_integer.abs_eq
% 0.33/0.60  thf(fact_5035_minus__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( minus_minus_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % minus_integer.abs_eq
% 0.33/0.60  thf(fact_5036_abs__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [X2: int] :
% 0.33/0.60        ( ( abs_abs_Code_integer @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( abs_abs_int @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % abs_integer.abs_eq
% 0.33/0.60  thf(fact_5037_divide__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( divide_divide_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divide_integer.abs_eq
% 0.33/0.60  thf(fact_5038_modulo__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( modulo_modulo_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % modulo_integer.abs_eq
% 0.33/0.60  thf(fact_5039_take__bit__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: nat,X2: int] :
% 0.33/0.60        ( ( bit_se1745604003318907178nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_se2923211474154528505it_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_integer.abs_eq
% 0.33/0.60  thf(fact_5040_not__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [X2: int] :
% 0.33/0.60        ( ( bit_ri7632146776885996613nteger @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_ri7919022796975470100ot_int @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % not_integer.abs_eq
% 0.33/0.60  thf(fact_5041_and__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( bit_se3949692690581998587nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_se725231765392027082nd_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_integer.abs_eq
% 0.33/0.60  thf(fact_5042_bounded__nat__set__is__finite,axiom,
% 0.33/0.60      ! [N4: set_nat,N: nat] :
% 0.33/0.60        ( ! [X3: nat] :
% 0.33/0.60            ( ( member_nat @ X3 @ N4 )
% 0.33/0.60           => ( ord_less_nat @ X3 @ N ) )
% 0.33/0.60       => ( finite_finite_nat @ N4 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bounded_nat_set_is_finite
% 0.33/0.60  thf(fact_5043_finite__nat__set__iff__bounded,axiom,
% 0.33/0.60      ( finite_finite_nat
% 0.33/0.60      = ( ^ [N8: set_nat] :
% 0.33/0.60          ? [M2: nat] :
% 0.33/0.60          ! [X: nat] :
% 0.33/0.60            ( ( member_nat @ X @ N8 )
% 0.33/0.60           => ( ord_less_nat @ X @ M2 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_nat_set_iff_bounded
% 0.33/0.60  thf(fact_5044_sgn__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [X2: int] :
% 0.33/0.60        ( ( sgn_sgn_Code_integer @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( sgn_sgn_int @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % sgn_integer.abs_eq
% 0.33/0.60  thf(fact_5045_finite__nat__set__iff__bounded__le,axiom,
% 0.33/0.60      ( finite_finite_nat
% 0.33/0.60      = ( ^ [N8: set_nat] :
% 0.33/0.60          ? [M2: nat] :
% 0.33/0.60          ! [X: nat] :
% 0.33/0.60            ( ( member_nat @ X @ N8 )
% 0.33/0.60           => ( ord_less_eq_nat @ X @ M2 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_nat_set_iff_bounded_le
% 0.33/0.60  thf(fact_5046_bit__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [X2: int] :
% 0.33/0.60        ( ( bit_se9216721137139052372nteger @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( bit_se1146084159140164899it_int @ X2 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_integer.abs_eq
% 0.33/0.60  thf(fact_5047_xor__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: int,X2: int] :
% 0.33/0.60        ( ( bit_se3222712562003087583nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_se6526347334894502574or_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_integer.abs_eq
% 0.33/0.60  thf(fact_5048_push__bit__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: nat,X2: int] :
% 0.33/0.60        ( ( bit_se7788150548672797655nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_se545348938243370406it_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % push_bit_integer.abs_eq
% 0.33/0.60  thf(fact_5049_mask__integer_Oabs__eq,axiom,
% 0.33/0.60      ( bit_se2119862282449309892nteger
% 0.33/0.60      = ( ^ [X: nat] : ( code_integer_of_int @ ( bit_se2000444600071755411sk_int @ X ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % mask_integer.abs_eq
% 0.33/0.60  thf(fact_5050_unset__bit__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: nat,X2: int] :
% 0.33/0.60        ( ( bit_se8260200283734997820nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_se4203085406695923979it_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % unset_bit_integer.abs_eq
% 0.33/0.60  thf(fact_5051_set__bit__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: nat,X2: int] :
% 0.33/0.60        ( ( bit_se2793503036327961859nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_se7879613467334960850it_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % set_bit_integer.abs_eq
% 0.33/0.60  thf(fact_5052_flip__bit__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: nat,X2: int] :
% 0.33/0.60        ( ( bit_se1345352211410354436nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_se2159334234014336723it_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % flip_bit_integer.abs_eq
% 0.33/0.60  thf(fact_5053_finite__M__bounded__by__nat,axiom,
% 0.33/0.60      ! [P: nat > $o,I: nat] :
% 0.33/0.60        ( finite_finite_nat
% 0.33/0.60        @ ( collect_nat
% 0.33/0.60          @ ^ [K2: nat] :
% 0.33/0.60              ( ( P @ K2 )
% 0.33/0.60              & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_M_bounded_by_nat
% 0.33/0.60  thf(fact_5054_finite__less__ub,axiom,
% 0.33/0.60      ! [F: nat > nat,U: nat] :
% 0.33/0.60        ( ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( F @ N2 ) )
% 0.33/0.60       => ( finite_finite_nat
% 0.33/0.60          @ ( collect_nat
% 0.33/0.60            @ ^ [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ U ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_less_ub
% 0.33/0.60  thf(fact_5055_or__greater__eq,axiom,
% 0.33/0.60      ! [L: int,K: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.33/0.60       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_greater_eq
% 0.33/0.60  thf(fact_5056_OR__lower,axiom,
% 0.33/0.60      ! [X2: int,Y: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.33/0.60       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.60         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X2 @ Y ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % OR_lower
% 0.33/0.60  thf(fact_5057_plus__and__or,axiom,
% 0.33/0.60      ! [X2: int,Y: int] :
% 0.33/0.60        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ ( bit_se1409905431419307370or_int @ X2 @ Y ) )
% 0.33/0.60        = ( plus_plus_int @ X2 @ Y ) ) ).
% 0.33/0.60  
% 0.33/0.60  % plus_and_or
% 0.33/0.60  thf(fact_5058_nat_Odisc__eq__case_I1_J,axiom,
% 0.33/0.60      ! [Nat: nat] :
% 0.33/0.60        ( ( Nat = zero_zero_nat )
% 0.33/0.60        = ( case_nat_o @ $true
% 0.33/0.60          @ ^ [Uu: nat] : $false
% 0.33/0.60          @ Nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat.disc_eq_case(1)
% 0.33/0.60  thf(fact_5059_nat_Odisc__eq__case_I2_J,axiom,
% 0.33/0.60      ! [Nat: nat] :
% 0.33/0.60        ( ( Nat != zero_zero_nat )
% 0.33/0.60        = ( case_nat_o @ $false
% 0.33/0.60          @ ^ [Uu: nat] : $true
% 0.33/0.60          @ Nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat.disc_eq_case(2)
% 0.33/0.60  thf(fact_5060_set__bit__nat__def,axiom,
% 0.33/0.60      ( bit_se7882103937844011126it_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] : ( bit_se1412395901928357646or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % set_bit_nat_def
% 0.33/0.60  thf(fact_5061_or__not__numerals_I1_J,axiom,
% 0.33/0.60      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.33/0.60      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_not_numerals(1)
% 0.33/0.60  thf(fact_5062_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 0.33/0.60      ! [L: int,U: int] :
% 0.33/0.60        ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 0.33/0.60        = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastLessThanPlusOne_atLeastAtMost_int
% 0.33/0.60  thf(fact_5063_prod__int__eq,axiom,
% 0.33/0.60      ! [I: nat,J: nat] :
% 0.33/0.60        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.33/0.60        = ( groups1705073143266064639nt_int
% 0.33/0.60          @ ^ [X: int] : X
% 0.33/0.60          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % prod_int_eq
% 0.33/0.60  thf(fact_5064_set__bit__int__def,axiom,
% 0.33/0.60      ( bit_se7879613467334960850it_int
% 0.33/0.60      = ( ^ [N3: nat,K2: int] : ( bit_se1409905431419307370or_int @ K2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % set_bit_int_def
% 0.33/0.60  thf(fact_5065_less__eq__nat_Osimps_I2_J,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.33/0.60        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % less_eq_nat.simps(2)
% 0.33/0.60  thf(fact_5066_finite__divisors__nat,axiom,
% 0.33/0.60      ! [M: nat] :
% 0.33/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.33/0.60       => ( finite_finite_nat
% 0.33/0.60          @ ( collect_nat
% 0.33/0.60            @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_divisors_nat
% 0.33/0.60  thf(fact_5067_subset__eq__atLeast0__atMost__finite,axiom,
% 0.33/0.60      ! [N4: set_nat,N: nat] :
% 0.33/0.60        ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.33/0.60       => ( finite_finite_nat @ N4 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % subset_eq_atLeast0_atMost_finite
% 0.33/0.60  thf(fact_5068_subset__eq__atLeast0__lessThan__finite,axiom,
% 0.33/0.60      ! [N4: set_nat,N: nat] :
% 0.33/0.60        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.33/0.60       => ( finite_finite_nat @ N4 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % subset_eq_atLeast0_lessThan_finite
% 0.33/0.60  thf(fact_5069_or__not__numerals_I2_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.33/0.60        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_not_numerals(2)
% 0.33/0.60  thf(fact_5070_or__not__numerals_I4_J,axiom,
% 0.33/0.60      ! [M: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.33/0.60        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_not_numerals(4)
% 0.33/0.60  thf(fact_5071_prod__int__plus__eq,axiom,
% 0.33/0.60      ! [I: nat,J: nat] :
% 0.33/0.60        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 0.33/0.60        = ( groups1705073143266064639nt_int
% 0.33/0.60          @ ^ [X: int] : X
% 0.33/0.60          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % prod_int_plus_eq
% 0.33/0.60  thf(fact_5072_diff__Suc,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.33/0.60        = ( case_nat_nat @ zero_zero_nat
% 0.33/0.60          @ ^ [K2: nat] : K2
% 0.33/0.60          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % diff_Suc
% 0.33/0.60  thf(fact_5073_or__not__numerals_I3_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.33/0.60        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_not_numerals(3)
% 0.33/0.60  thf(fact_5074_or__not__numerals_I7_J,axiom,
% 0.33/0.60      ! [M: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.33/0.60        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_not_numerals(7)
% 0.33/0.60  thf(fact_5075_OR__upper,axiom,
% 0.33/0.60      ! [X2: int,N: nat,Y: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.33/0.60       => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.33/0.60         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.33/0.60           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X2 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % OR_upper
% 0.33/0.60  thf(fact_5076_or__not__numerals_I5_J,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.33/0.60        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_not_numerals(5)
% 0.33/0.60  thf(fact_5077_or__Suc__0__eq,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_Suc_0_eq
% 0.33/0.60  thf(fact_5078_Suc__0__or__eq,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.60        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Suc_0_or_eq
% 0.33/0.60  thf(fact_5079_or__not__numerals_I9_J,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.33/0.60        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_not_numerals(9)
% 0.33/0.60  thf(fact_5080_or__not__numerals_I8_J,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.33/0.60        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_not_numerals(8)
% 0.33/0.60  thf(fact_5081_or__nat__rec,axiom,
% 0.33/0.60      ( bit_se1412395901928357646or_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] :
% 0.33/0.60            ( plus_plus_nat
% 0.33/0.60            @ ( zero_n2687167440665602831ol_nat
% 0.33/0.60              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 0.33/0.60                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 0.33/0.60            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_nat_rec
% 0.33/0.60  thf(fact_5082_finite__Collect__le__nat,axiom,
% 0.33/0.60      ! [K: nat] :
% 0.33/0.60        ( finite_finite_nat
% 0.33/0.60        @ ( collect_nat
% 0.33/0.60          @ ^ [N3: nat] : ( ord_less_eq_nat @ N3 @ K ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_Collect_le_nat
% 0.33/0.60  thf(fact_5083_finite__Collect__less__nat,axiom,
% 0.33/0.60      ! [K: nat] :
% 0.33/0.60        ( finite_finite_nat
% 0.33/0.60        @ ( collect_nat
% 0.33/0.60          @ ^ [N3: nat] : ( ord_less_nat @ N3 @ K ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_Collect_less_nat
% 0.33/0.60  thf(fact_5084_finite__atLeastAtMost__int,axiom,
% 0.33/0.60      ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_atLeastAtMost_int
% 0.33/0.60  thf(fact_5085_finite__atLeastLessThan__int,axiom,
% 0.33/0.60      ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_atLeastLessThan_int
% 0.33/0.60  thf(fact_5086_finite__interval__int1,axiom,
% 0.33/0.60      ! [A: int,B: int] :
% 0.33/0.60        ( finite_finite_int
% 0.33/0.60        @ ( collect_int
% 0.33/0.60          @ ^ [I2: int] :
% 0.33/0.60              ( ( ord_less_eq_int @ A @ I2 )
% 0.33/0.60              & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_interval_int1
% 0.33/0.60  thf(fact_5087_finite__interval__int4,axiom,
% 0.33/0.60      ! [A: int,B: int] :
% 0.33/0.60        ( finite_finite_int
% 0.33/0.60        @ ( collect_int
% 0.33/0.60          @ ^ [I2: int] :
% 0.33/0.60              ( ( ord_less_int @ A @ I2 )
% 0.33/0.60              & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_interval_int4
% 0.33/0.60  thf(fact_5088_finite__atLeastLessThan__integer,axiom,
% 0.33/0.60      ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_atLeastLessThan_integer
% 0.33/0.60  thf(fact_5089_finite__atLeastAtMost__integer,axiom,
% 0.33/0.60      ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_atLeastAtMost_integer
% 0.33/0.60  thf(fact_5090_finite__interval__int3,axiom,
% 0.33/0.60      ! [A: int,B: int] :
% 0.33/0.60        ( finite_finite_int
% 0.33/0.60        @ ( collect_int
% 0.33/0.60          @ ^ [I2: int] :
% 0.33/0.60              ( ( ord_less_int @ A @ I2 )
% 0.33/0.60              & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_interval_int3
% 0.33/0.60  thf(fact_5091_finite__interval__int2,axiom,
% 0.33/0.60      ! [A: int,B: int] :
% 0.33/0.60        ( finite_finite_int
% 0.33/0.60        @ ( collect_int
% 0.33/0.60          @ ^ [I2: int] :
% 0.33/0.60              ( ( ord_less_eq_int @ A @ I2 )
% 0.33/0.60              & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_interval_int2
% 0.33/0.60  thf(fact_5092_finite__atLeastZeroLessThan__int,axiom,
% 0.33/0.60      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_atLeastZeroLessThan_int
% 0.33/0.60  thf(fact_5093_finite__atLeastZeroLessThan__integer,axiom,
% 0.33/0.60      ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_atLeastZeroLessThan_integer
% 0.33/0.60  thf(fact_5094_finite__divisors__int,axiom,
% 0.33/0.60      ! [I: int] :
% 0.33/0.60        ( ( I != zero_zero_int )
% 0.33/0.60       => ( finite_finite_int
% 0.33/0.60          @ ( collect_int
% 0.33/0.60            @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_divisors_int
% 0.33/0.60  thf(fact_5095_or__int__unfold,axiom,
% 0.33/0.60      ( bit_se1409905431419307370or_int
% 0.33/0.60      = ( ^ [K2: int,L2: int] :
% 0.33/0.60            ( if_int
% 0.33/0.60            @ ( ( K2
% 0.33/0.60                = ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60              | ( L2
% 0.33/0.60                = ( uminus_uminus_int @ one_one_int ) ) )
% 0.33/0.60            @ ( uminus_uminus_int @ one_one_int )
% 0.33/0.60            @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_int_unfold
% 0.33/0.60  thf(fact_5096_even__set__encode__iff,axiom,
% 0.33/0.60      ! [A4: set_nat] :
% 0.33/0.60        ( ( finite_finite_nat @ A4 )
% 0.33/0.60       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A4 ) )
% 0.33/0.60          = ( ~ ( member_nat @ zero_zero_nat @ A4 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % even_set_encode_iff
% 0.33/0.60  thf(fact_5097_Code__Numeral_Opositive__def,axiom,
% 0.33/0.60      code_positive = numera6620942414471956472nteger ).
% 0.33/0.60  
% 0.33/0.60  % Code_Numeral.positive_def
% 0.33/0.60  thf(fact_5098_or__nat__unfold,axiom,
% 0.33/0.60      ( bit_se1412395901928357646or_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_nat_unfold
% 0.33/0.60  thf(fact_5099_max__0R,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( ord_max_nat @ N @ zero_zero_nat )
% 0.33/0.60        = N ) ).
% 0.33/0.60  
% 0.33/0.60  % max_0R
% 0.33/0.60  thf(fact_5100_max__0L,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( ord_max_nat @ zero_zero_nat @ N )
% 0.33/0.60        = N ) ).
% 0.33/0.60  
% 0.33/0.60  % max_0L
% 0.33/0.60  thf(fact_5101_max__nat_Oright__neutral,axiom,
% 0.33/0.60      ! [A: nat] :
% 0.33/0.60        ( ( ord_max_nat @ A @ zero_zero_nat )
% 0.33/0.60        = A ) ).
% 0.33/0.60  
% 0.33/0.60  % max_nat.right_neutral
% 0.33/0.60  thf(fact_5102_max__nat_Oneutr__eq__iff,axiom,
% 0.33/0.60      ! [A: nat,B: nat] :
% 0.33/0.60        ( ( zero_zero_nat
% 0.33/0.60          = ( ord_max_nat @ A @ B ) )
% 0.33/0.60        = ( ( A = zero_zero_nat )
% 0.33/0.60          & ( B = zero_zero_nat ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % max_nat.neutr_eq_iff
% 0.33/0.60  thf(fact_5103_max__nat_Oleft__neutral,axiom,
% 0.33/0.60      ! [A: nat] :
% 0.33/0.60        ( ( ord_max_nat @ zero_zero_nat @ A )
% 0.33/0.60        = A ) ).
% 0.33/0.60  
% 0.33/0.60  % max_nat.left_neutral
% 0.33/0.60  thf(fact_5104_max__nat_Oeq__neutr__iff,axiom,
% 0.33/0.60      ! [A: nat,B: nat] :
% 0.33/0.60        ( ( ( ord_max_nat @ A @ B )
% 0.33/0.60          = zero_zero_nat )
% 0.33/0.60        = ( ( A = zero_zero_nat )
% 0.33/0.60          & ( B = zero_zero_nat ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % max_nat.eq_neutr_iff
% 0.33/0.60  thf(fact_5105_max__Suc__Suc,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.33/0.60        = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % max_Suc_Suc
% 0.33/0.60  thf(fact_5106_max__numeral__Suc,axiom,
% 0.33/0.60      ! [K: num,N: nat] :
% 0.33/0.60        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.33/0.60        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % max_numeral_Suc
% 0.33/0.60  thf(fact_5107_max__Suc__numeral,axiom,
% 0.33/0.60      ! [N: nat,K: num] :
% 0.33/0.60        ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.33/0.60        = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % max_Suc_numeral
% 0.33/0.60  thf(fact_5108_nat__mult__max__right,axiom,
% 0.33/0.60      ! [M: nat,N: nat,Q2: nat] :
% 0.33/0.60        ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 0.33/0.60        = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_mult_max_right
% 0.33/0.60  thf(fact_5109_nat__mult__max__left,axiom,
% 0.33/0.60      ! [M: nat,N: nat,Q2: nat] :
% 0.33/0.60        ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 0.33/0.60        = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_mult_max_left
% 0.33/0.60  thf(fact_5110_nat__add__max__left,axiom,
% 0.33/0.60      ! [M: nat,N: nat,Q2: nat] :
% 0.33/0.60        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 0.33/0.60        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_add_max_left
% 0.33/0.60  thf(fact_5111_nat__add__max__right,axiom,
% 0.33/0.60      ! [M: nat,N: nat,Q2: nat] :
% 0.33/0.60        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 0.33/0.60        = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_add_max_right
% 0.33/0.60  thf(fact_5112_nat__minus__add__max,axiom,
% 0.33/0.60      ! [N: nat,M: nat] :
% 0.33/0.60        ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 0.33/0.60        = ( ord_max_nat @ N @ M ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_minus_add_max
% 0.33/0.60  thf(fact_5113_max__Suc1,axiom,
% 0.33/0.60      ! [N: nat,M: nat] :
% 0.33/0.60        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 0.33/0.60        = ( case_nat_nat @ ( suc @ N )
% 0.33/0.60          @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ N @ M7 ) )
% 0.33/0.60          @ M ) ) ).
% 0.33/0.60  
% 0.33/0.60  % max_Suc1
% 0.33/0.60  thf(fact_5114_max__Suc2,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 0.33/0.60        = ( case_nat_nat @ ( suc @ N )
% 0.33/0.60          @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ M7 @ N ) )
% 0.33/0.60          @ M ) ) ).
% 0.33/0.60  
% 0.33/0.60  % max_Suc2
% 0.33/0.60  thf(fact_5115_set__encode__inf,axiom,
% 0.33/0.60      ! [A4: set_nat] :
% 0.33/0.60        ( ~ ( finite_finite_nat @ A4 )
% 0.33/0.60       => ( ( nat_set_encode @ A4 )
% 0.33/0.60          = zero_zero_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % set_encode_inf
% 0.33/0.60  thf(fact_5116_infinite__int__iff__unbounded__le,axiom,
% 0.33/0.60      ! [S3: set_int] :
% 0.33/0.60        ( ( ~ ( finite_finite_int @ S3 ) )
% 0.33/0.60        = ( ! [M2: int] :
% 0.33/0.60            ? [N3: int] :
% 0.33/0.60              ( ( ord_less_eq_int @ M2 @ ( abs_abs_int @ N3 ) )
% 0.33/0.60              & ( member_int @ N3 @ S3 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % infinite_int_iff_unbounded_le
% 0.33/0.60  thf(fact_5117_set__encode__insert,axiom,
% 0.33/0.60      ! [A4: set_nat,N: nat] :
% 0.33/0.60        ( ( finite_finite_nat @ A4 )
% 0.33/0.60       => ( ~ ( member_nat @ N @ A4 )
% 0.33/0.60         => ( ( nat_set_encode @ ( insert_nat @ N @ A4 ) )
% 0.33/0.60            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A4 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % set_encode_insert
% 0.33/0.60  thf(fact_5118_atMost__Suc,axiom,
% 0.33/0.60      ! [K: nat] :
% 0.33/0.60        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 0.33/0.60        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atMost_Suc
% 0.33/0.60  thf(fact_5119_atLeast0__atMost__Suc,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.33/0.60        = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeast0_atMost_Suc
% 0.33/0.60  thf(fact_5120_atLeast0__lessThan__Suc,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.33/0.60        = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeast0_lessThan_Suc
% 0.33/0.60  thf(fact_5121_Icc__eq__insert__lb__nat,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.60       => ( ( set_or1269000886237332187st_nat @ M @ N )
% 0.33/0.60          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Icc_eq_insert_lb_nat
% 0.33/0.60  thf(fact_5122_atLeastAtMostSuc__conv,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.33/0.60       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 0.33/0.60          = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastAtMostSuc_conv
% 0.33/0.60  thf(fact_5123_atLeastAtMost__insertL,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.60       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.33/0.60          = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastAtMost_insertL
% 0.33/0.60  thf(fact_5124_atMost__nat__numeral,axiom,
% 0.33/0.60      ! [K: num] :
% 0.33/0.60        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 0.33/0.60        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atMost_nat_numeral
% 0.33/0.60  thf(fact_5125_set__decode__plus__power__2,axiom,
% 0.33/0.60      ! [N: nat,Z2: nat] :
% 0.33/0.60        ( ~ ( member_nat @ N @ ( nat_set_decode @ Z2 ) )
% 0.33/0.60       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z2 ) )
% 0.33/0.60          = ( insert_nat @ N @ ( nat_set_decode @ Z2 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % set_decode_plus_power_2
% 0.33/0.60  thf(fact_5126_infinite__nat__iff__unbounded__le,axiom,
% 0.33/0.60      ! [S3: set_nat] :
% 0.33/0.60        ( ( ~ ( finite_finite_nat @ S3 ) )
% 0.33/0.60        = ( ! [M2: nat] :
% 0.33/0.60            ? [N3: nat] :
% 0.33/0.60              ( ( ord_less_eq_nat @ M2 @ N3 )
% 0.33/0.60              & ( member_nat @ N3 @ S3 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % infinite_nat_iff_unbounded_le
% 0.33/0.60  thf(fact_5127_integer__of__num_I3_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( code_integer_of_num @ ( bit1 @ N ) )
% 0.33/0.60        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_of_num(3)
% 0.33/0.60  thf(fact_5128_card__Collect__less__nat,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( finite_card_nat
% 0.33/0.60          @ ( collect_nat
% 0.33/0.60            @ ^ [I2: nat] : ( ord_less_nat @ I2 @ N ) ) )
% 0.33/0.60        = N ) ).
% 0.33/0.60  
% 0.33/0.60  % card_Collect_less_nat
% 0.33/0.60  thf(fact_5129_drop__bit__nonnegative__int__iff,axiom,
% 0.33/0.60      ! [N: nat,K: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 0.33/0.60        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.33/0.60  
% 0.33/0.60  % drop_bit_nonnegative_int_iff
% 0.33/0.60  thf(fact_5130_drop__bit__negative__int__iff,axiom,
% 0.33/0.60      ! [N: nat,K: int] :
% 0.33/0.60        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 0.33/0.60        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % drop_bit_negative_int_iff
% 0.33/0.60  thf(fact_5131_drop__bit__minus__one,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.33/0.60        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % drop_bit_minus_one
% 0.33/0.60  thf(fact_5132_card__atLeastLessThan,axiom,
% 0.33/0.60      ! [L: nat,U: nat] :
% 0.33/0.60        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.33/0.60        = ( minus_minus_nat @ U @ L ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_atLeastLessThan
% 0.33/0.60  thf(fact_5133_card__atMost,axiom,
% 0.33/0.60      ! [U: nat] :
% 0.33/0.60        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 0.33/0.60        = ( suc @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_atMost
% 0.33/0.60  thf(fact_5134_card__Collect__le__nat,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( finite_card_nat
% 0.33/0.60          @ ( collect_nat
% 0.33/0.60            @ ^ [I2: nat] : ( ord_less_eq_nat @ I2 @ N ) ) )
% 0.33/0.60        = ( suc @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_Collect_le_nat
% 0.33/0.60  thf(fact_5135_card__atLeastAtMost,axiom,
% 0.33/0.60      ! [L: nat,U: nat] :
% 0.33/0.60        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.33/0.60        = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_atLeastAtMost
% 0.33/0.60  thf(fact_5136_drop__bit__of__Suc__0,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.33/0.60        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % drop_bit_of_Suc_0
% 0.33/0.60  thf(fact_5137_card__atLeastLessThan__int,axiom,
% 0.33/0.60      ! [L: int,U: int] :
% 0.33/0.60        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.33/0.60        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_atLeastLessThan_int
% 0.33/0.60  thf(fact_5138_card__atLeastAtMost__int,axiom,
% 0.33/0.60      ! [L: int,U: int] :
% 0.33/0.60        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.33/0.60        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_atLeastAtMost_int
% 0.33/0.60  thf(fact_5139_drop__bit__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [Xa: nat,X2: int] :
% 0.33/0.60        ( ( bit_se3928097537394005634nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( code_integer_of_int @ ( bit_se8568078237143864401it_int @ Xa @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % drop_bit_integer.abs_eq
% 0.33/0.60  thf(fact_5140_integer__of__num__def,axiom,
% 0.33/0.60      code_integer_of_num = numera6620942414471956472nteger ).
% 0.33/0.60  
% 0.33/0.60  % integer_of_num_def
% 0.33/0.60  thf(fact_5141_card__less__Suc2,axiom,
% 0.33/0.60      ! [M3: set_nat,I: nat] :
% 0.33/0.60        ( ~ ( member_nat @ zero_zero_nat @ M3 )
% 0.33/0.60       => ( ( finite_card_nat
% 0.33/0.60            @ ( collect_nat
% 0.33/0.60              @ ^ [K2: nat] :
% 0.33/0.60                  ( ( member_nat @ ( suc @ K2 ) @ M3 )
% 0.33/0.60                  & ( ord_less_nat @ K2 @ I ) ) ) )
% 0.33/0.60          = ( finite_card_nat
% 0.33/0.60            @ ( collect_nat
% 0.33/0.60              @ ^ [K2: nat] :
% 0.33/0.60                  ( ( member_nat @ K2 @ M3 )
% 0.33/0.60                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_less_Suc2
% 0.33/0.60  thf(fact_5142_card__less__Suc,axiom,
% 0.33/0.60      ! [M3: set_nat,I: nat] :
% 0.33/0.60        ( ( member_nat @ zero_zero_nat @ M3 )
% 0.33/0.60       => ( ( suc
% 0.33/0.60            @ ( finite_card_nat
% 0.33/0.60              @ ( collect_nat
% 0.33/0.60                @ ^ [K2: nat] :
% 0.33/0.60                    ( ( member_nat @ ( suc @ K2 ) @ M3 )
% 0.33/0.60                    & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 0.33/0.60          = ( finite_card_nat
% 0.33/0.60            @ ( collect_nat
% 0.33/0.60              @ ^ [K2: nat] :
% 0.33/0.60                  ( ( member_nat @ K2 @ M3 )
% 0.33/0.60                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_less_Suc
% 0.33/0.60  thf(fact_5143_card__less,axiom,
% 0.33/0.60      ! [M3: set_nat,I: nat] :
% 0.33/0.60        ( ( member_nat @ zero_zero_nat @ M3 )
% 0.33/0.60       => ( ( finite_card_nat
% 0.33/0.60            @ ( collect_nat
% 0.33/0.60              @ ^ [K2: nat] :
% 0.33/0.60                  ( ( member_nat @ K2 @ M3 )
% 0.33/0.60                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 0.33/0.60         != zero_zero_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_less
% 0.33/0.60  thf(fact_5144_card__atLeastZeroLessThan__int,axiom,
% 0.33/0.60      ! [U: int] :
% 0.33/0.60        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 0.33/0.60        = ( nat2 @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_atLeastZeroLessThan_int
% 0.33/0.60  thf(fact_5145_subset__card__intvl__is__intvl,axiom,
% 0.33/0.60      ! [A4: set_nat,K: nat] :
% 0.33/0.60        ( ( ord_less_eq_set_nat @ A4 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) )
% 0.33/0.60       => ( A4
% 0.33/0.60          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % subset_card_intvl_is_intvl
% 0.33/0.60  thf(fact_5146_atLeastAtMostPlus1__int__conv,axiom,
% 0.33/0.60      ! [M: int,N: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.33/0.60       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.33/0.60          = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastAtMostPlus1_int_conv
% 0.33/0.60  thf(fact_5147_subset__eq__atLeast0__lessThan__card,axiom,
% 0.33/0.60      ! [N4: set_nat,N: nat] :
% 0.33/0.60        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.33/0.60       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % subset_eq_atLeast0_lessThan_card
% 0.33/0.60  thf(fact_5148_card__sum__le__nat__sum,axiom,
% 0.33/0.60      ! [S3: set_nat] :
% 0.33/0.60        ( ord_less_eq_nat
% 0.33/0.60        @ ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [X: nat] : X
% 0.33/0.60          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 0.33/0.60        @ ( groups3542108847815614940at_nat
% 0.33/0.60          @ ^ [X: nat] : X
% 0.33/0.60          @ S3 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_sum_le_nat_sum
% 0.33/0.60  thf(fact_5149_integer__of__num__triv_I1_J,axiom,
% 0.33/0.60      ( ( code_integer_of_num @ one )
% 0.33/0.60      = one_one_Code_integer ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_of_num_triv(1)
% 0.33/0.60  thf(fact_5150_integer__of__num_I2_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 0.33/0.60        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_of_num(2)
% 0.33/0.60  thf(fact_5151_integer__of__num__triv_I2_J,axiom,
% 0.33/0.60      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 0.33/0.60      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_of_num_triv(2)
% 0.33/0.60  thf(fact_5152_pred__def,axiom,
% 0.33/0.60      ( pred
% 0.33/0.60      = ( case_nat_nat @ zero_zero_nat
% 0.33/0.60        @ ^ [X24: nat] : X24 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % pred_def
% 0.33/0.60  thf(fact_5153_and__int_Osimps,axiom,
% 0.33/0.60      ( bit_se725231765392027082nd_int
% 0.33/0.60      = ( ^ [K2: int,L2: int] :
% 0.33/0.60            ( if_int
% 0.33/0.60            @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.60              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.60            @ ( uminus_uminus_int
% 0.33/0.60              @ ( zero_n2684676970156552555ol_int
% 0.33/0.60                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.33/0.60                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.33/0.60            @ ( plus_plus_int
% 0.33/0.60              @ ( zero_n2684676970156552555ol_int
% 0.33/0.60                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.33/0.60                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.33/0.60              @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_int.simps
% 0.33/0.60  thf(fact_5154_and__int_Oelims,axiom,
% 0.33/0.60      ! [X2: int,Xa: int,Y: int] :
% 0.33/0.60        ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa )
% 0.33/0.60          = Y )
% 0.33/0.60       => ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.60              & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.60           => ( Y
% 0.33/0.60              = ( uminus_uminus_int
% 0.33/0.60                @ ( zero_n2684676970156552555ol_int
% 0.33/0.60                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 0.33/0.60                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.33/0.60          & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.60                & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.60           => ( Y
% 0.33/0.60              = ( plus_plus_int
% 0.33/0.60                @ ( zero_n2684676970156552555ol_int
% 0.33/0.60                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 0.33/0.60                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.33/0.60                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_int.elims
% 0.33/0.60  thf(fact_5155_Suc__funpow,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( compow_nat_nat @ N @ suc )
% 0.33/0.60        = ( plus_plus_nat @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Suc_funpow
% 0.33/0.60  thf(fact_5156_atLeastLessThan__upto,axiom,
% 0.33/0.60      ( set_or4662586982721622107an_int
% 0.33/0.60      = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastLessThan_upto
% 0.33/0.60  thf(fact_5157_simp__from__to,axiom,
% 0.33/0.60      ( set_or1266510415728281911st_int
% 0.33/0.60      = ( ^ [I2: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I2 ) @ bot_bot_set_int @ ( insert_int @ I2 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % simp_from_to
% 0.33/0.60  thf(fact_5158_set__decode__zero,axiom,
% 0.33/0.60      ( ( nat_set_decode @ zero_zero_nat )
% 0.33/0.60      = bot_bot_set_nat ) ).
% 0.33/0.60  
% 0.33/0.60  % set_decode_zero
% 0.33/0.60  thf(fact_5159_set__encode__empty,axiom,
% 0.33/0.60      ( ( nat_set_encode @ bot_bot_set_nat )
% 0.33/0.60      = zero_zero_nat ) ).
% 0.33/0.60  
% 0.33/0.60  % set_encode_empty
% 0.33/0.60  thf(fact_5160_atLeastLessThan__singleton,axiom,
% 0.33/0.60      ! [M: nat] :
% 0.33/0.60        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 0.33/0.60        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastLessThan_singleton
% 0.33/0.60  thf(fact_5161_atMost__0,axiom,
% 0.33/0.60      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 0.33/0.60      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atMost_0
% 0.33/0.60  thf(fact_5162_bot__nat__def,axiom,
% 0.33/0.60      bot_bot_nat = zero_zero_nat ).
% 0.33/0.60  
% 0.33/0.60  % bot_nat_def
% 0.33/0.60  thf(fact_5163_atLeastLessThan0,axiom,
% 0.33/0.60      ! [M: nat] :
% 0.33/0.60        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 0.33/0.60        = bot_bot_set_nat ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastLessThan0
% 0.33/0.60  thf(fact_5164_atLeastLessThanSuc,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.60         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.33/0.60            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 0.33/0.60        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.33/0.60         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.33/0.60            = bot_bot_set_nat ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastLessThanSuc
% 0.33/0.60  thf(fact_5165_atLeast1__atMost__eq__remove0,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.60        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeast1_atMost_eq_remove0
% 0.33/0.60  thf(fact_5166_atLeastLessThan__nat__numeral,axiom,
% 0.33/0.60      ! [M: nat,K: num] :
% 0.33/0.60        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.33/0.60         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.33/0.60            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 0.33/0.60        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.33/0.60         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.33/0.60            = bot_bot_set_nat ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastLessThan_nat_numeral
% 0.33/0.60  thf(fact_5167_card__greaterThanLessThan__int,axiom,
% 0.33/0.60      ! [L: int,U: int] :
% 0.33/0.60        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.33/0.60        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_greaterThanLessThan_int
% 0.33/0.60  thf(fact_5168_finite__greaterThanLessThan__int,axiom,
% 0.33/0.60      ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_greaterThanLessThan_int
% 0.33/0.60  thf(fact_5169_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 0.33/0.60      ! [L: int,U: int] :
% 0.33/0.60        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.33/0.60        = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastPlusOneLessThan_greaterThanLessThan_int
% 0.33/0.60  thf(fact_5170_greaterThanLessThan__upto,axiom,
% 0.33/0.60      ( set_or5832277885323065728an_int
% 0.33/0.60      = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % greaterThanLessThan_upto
% 0.33/0.60  thf(fact_5171_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.33/0.60      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 0.33/0.60      @ ^ [X: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X )
% 0.33/0.60      @ ^ [X: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X ) ) ).
% 0.33/0.60  
% 0.33/0.60  % max_nat.semilattice_neutr_order_axioms
% 0.33/0.60  thf(fact_5172_finite__greaterThanLessThan,axiom,
% 0.33/0.60      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_greaterThanLessThan
% 0.33/0.60  thf(fact_5173_finite__greaterThanLessThan__integer,axiom,
% 0.33/0.60      ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_greaterThanLessThan_integer
% 0.33/0.60  thf(fact_5174_card__greaterThanLessThan,axiom,
% 0.33/0.60      ! [L: nat,U: nat] :
% 0.33/0.60        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 0.33/0.60        = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_greaterThanLessThan
% 0.33/0.60  thf(fact_5175_atLeastSucLessThan__greaterThanLessThan,axiom,
% 0.33/0.60      ! [L: nat,U: nat] :
% 0.33/0.60        ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 0.33/0.60        = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastSucLessThan_greaterThanLessThan
% 0.33/0.60  thf(fact_5176_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 0.33/0.60      ! [N: nat,J: nat,I: nat] :
% 0.33/0.60        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 0.33/0.60       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 0.33/0.60          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nth_sorted_list_of_set_greaterThanLessThan
% 0.33/0.60  thf(fact_5177_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 0.33/0.60      ! [L: code_integer,U: code_integer] :
% 0.33/0.60        ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 0.33/0.60        = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 0.33/0.60  thf(fact_5178_num__of__nat_Osimps_I2_J,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.60         => ( ( num_of_nat @ ( suc @ N ) )
% 0.33/0.60            = ( inc @ ( num_of_nat @ N ) ) ) )
% 0.33/0.60        & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.60         => ( ( num_of_nat @ ( suc @ N ) )
% 0.33/0.60            = one ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % num_of_nat.simps(2)
% 0.33/0.60  thf(fact_5179_num__of__nat__numeral__eq,axiom,
% 0.33/0.60      ! [Q2: num] :
% 0.33/0.60        ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 0.33/0.60        = Q2 ) ).
% 0.33/0.60  
% 0.33/0.60  % num_of_nat_numeral_eq
% 0.33/0.60  thf(fact_5180_pred__numeral__simps_I2_J,axiom,
% 0.33/0.60      ! [K: num] :
% 0.33/0.60        ( ( pred_numeral @ ( bit0 @ K ) )
% 0.33/0.60        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % pred_numeral_simps(2)
% 0.33/0.60  thf(fact_5181_inc__BitM__eq,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( inc @ ( bitM @ N ) )
% 0.33/0.60        = ( bit0 @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % inc_BitM_eq
% 0.33/0.60  thf(fact_5182_BitM__inc__eq,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( bitM @ ( inc @ N ) )
% 0.33/0.60        = ( bit1 @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % BitM_inc_eq
% 0.33/0.60  thf(fact_5183_num__of__nat_Osimps_I1_J,axiom,
% 0.33/0.60      ( ( num_of_nat @ zero_zero_nat )
% 0.33/0.60      = one ) ).
% 0.33/0.60  
% 0.33/0.60  % num_of_nat.simps(1)
% 0.33/0.60  thf(fact_5184_eval__nat__numeral_I2_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.33/0.60        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % eval_nat_numeral(2)
% 0.33/0.60  thf(fact_5185_BitM__plus__one,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 0.33/0.60        = ( bit0 @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % BitM_plus_one
% 0.33/0.60  thf(fact_5186_one__plus__BitM,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 0.33/0.60        = ( bit0 @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % one_plus_BitM
% 0.33/0.60  thf(fact_5187_numeral__num__of__nat,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.60       => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 0.33/0.60          = N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % numeral_num_of_nat
% 0.33/0.60  thf(fact_5188_num__of__nat__One,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 0.33/0.60       => ( ( num_of_nat @ N )
% 0.33/0.60          = one ) ) ).
% 0.33/0.60  
% 0.33/0.60  % num_of_nat_One
% 0.33/0.60  thf(fact_5189_sub__BitM__One__eq,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 0.33/0.60        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % sub_BitM_One_eq
% 0.33/0.60  thf(fact_5190_num__of__nat__double,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.60       => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 0.33/0.60          = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % num_of_nat_double
% 0.33/0.60  thf(fact_5191_num__of__nat__plus__distrib,axiom,
% 0.33/0.60      ! [M: nat,N: nat] :
% 0.33/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.33/0.60       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.60         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 0.33/0.60            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % num_of_nat_plus_distrib
% 0.33/0.60  thf(fact_5192_or__minus__numerals_I5_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.33/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_minus_numerals(5)
% 0.33/0.60  thf(fact_5193_or__minus__numerals_I1_J,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.33/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_minus_numerals(1)
% 0.33/0.60  thf(fact_5194_num__of__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [X2: int] :
% 0.33/0.60        ( ( code_num_of_integer @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( num_of_nat @ ( nat2 @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % num_of_integer.abs_eq
% 0.33/0.60  thf(fact_5195_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 0.33/0.60      ! [N: nat,J: nat,I: nat] :
% 0.33/0.60        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 0.33/0.60       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 0.33/0.60          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nth_sorted_list_of_set_greaterThanAtMost
% 0.33/0.60  thf(fact_5196_take__bit__numeral__minus__numeral__int,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.60        = ( case_option_int_num @ zero_zero_int
% 0.33/0.60          @ ^ [Q6: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q6 ) ) )
% 0.33/0.60          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_numeral_minus_numeral_int
% 0.33/0.60  thf(fact_5197_finite__greaterThanAtMost,axiom,
% 0.33/0.60      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_greaterThanAtMost
% 0.33/0.60  thf(fact_5198_card__greaterThanAtMost,axiom,
% 0.33/0.60      ! [L: nat,U: nat] :
% 0.33/0.60        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 0.33/0.60        = ( minus_minus_nat @ U @ L ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_greaterThanAtMost
% 0.33/0.60  thf(fact_5199_atLeastSucAtMost__greaterThanAtMost,axiom,
% 0.33/0.60      ! [L: nat,U: nat] :
% 0.33/0.60        ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 0.33/0.60        = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastSucAtMost_greaterThanAtMost
% 0.33/0.60  thf(fact_5200_sorted__list__of__set__greaterThanAtMost,axiom,
% 0.33/0.60      ! [I: nat,J: nat] :
% 0.33/0.60        ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 0.33/0.60       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 0.33/0.60          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % sorted_list_of_set_greaterThanAtMost
% 0.33/0.60  thf(fact_5201_and__minus__numerals_I7_J,axiom,
% 0.33/0.60      ! [N: num,M: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.33/0.60        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_minus_numerals(7)
% 0.33/0.60  thf(fact_5202_and__minus__numerals_I3_J,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.33/0.60        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_minus_numerals(3)
% 0.33/0.60  thf(fact_5203_and__minus__numerals_I8_J,axiom,
% 0.33/0.60      ! [N: num,M: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.33/0.60        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_minus_numerals(8)
% 0.33/0.60  thf(fact_5204_and__minus__numerals_I4_J,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.33/0.60        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_minus_numerals(4)
% 0.33/0.60  thf(fact_5205_finite__greaterThanAtMost__int,axiom,
% 0.33/0.60      ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_greaterThanAtMost_int
% 0.33/0.60  thf(fact_5206_finite__greaterThanAtMost__integer,axiom,
% 0.33/0.60      ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_greaterThanAtMost_integer
% 0.33/0.60  thf(fact_5207_card__greaterThanAtMost__int,axiom,
% 0.33/0.60      ! [L: int,U: int] :
% 0.33/0.60        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 0.33/0.60        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % card_greaterThanAtMost_int
% 0.33/0.60  thf(fact_5208_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 0.33/0.60      ! [L: int,U: int] :
% 0.33/0.60        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.33/0.60        = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastPlusOneAtMost_greaterThanAtMost_int
% 0.33/0.60  thf(fact_5209_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 0.33/0.60      ! [L: code_integer,U: code_integer] :
% 0.33/0.60        ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 0.33/0.60        = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 0.33/0.60  thf(fact_5210_greaterThanAtMost__upto,axiom,
% 0.33/0.60      ( set_or6656581121297822940st_int
% 0.33/0.60      = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % greaterThanAtMost_upto
% 0.33/0.60  thf(fact_5211_int__numeral__not__and__num,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.60        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_numeral_not_and_num
% 0.33/0.60  thf(fact_5212_int__numeral__and__not__num,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.60        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_numeral_and_not_num
% 0.33/0.60  thf(fact_5213_nat__of__integer__less__iff,axiom,
% 0.33/0.60      ! [X2: code_integer,Y: code_integer] :
% 0.33/0.60        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 0.33/0.60       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.33/0.60         => ( ( ord_less_nat @ ( code_nat_of_integer @ X2 ) @ ( code_nat_of_integer @ Y ) )
% 0.33/0.60            = ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_of_integer_less_iff
% 0.33/0.60  thf(fact_5214_nat__of__integer__of__nat,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( code_nat_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.33/0.60        = N ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_of_integer_of_nat
% 0.33/0.60  thf(fact_5215_of__nat__of__integer,axiom,
% 0.33/0.60      ! [K: code_integer] :
% 0.33/0.60        ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 0.33/0.60        = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 0.33/0.60  
% 0.33/0.60  % of_nat_of_integer
% 0.33/0.60  thf(fact_5216_nat__of__integer__non__positive,axiom,
% 0.33/0.60      ! [K: code_integer] :
% 0.33/0.60        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 0.33/0.60       => ( ( code_nat_of_integer @ K )
% 0.33/0.60          = zero_zero_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_of_integer_non_positive
% 0.33/0.60  thf(fact_5217_nat__of__integer_Oabs__eq,axiom,
% 0.33/0.60      ! [X2: int] :
% 0.33/0.60        ( ( code_nat_of_integer @ ( code_integer_of_int @ X2 ) )
% 0.33/0.60        = ( nat2 @ X2 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_of_integer.abs_eq
% 0.33/0.60  thf(fact_5218_upto__rec2,axiom,
% 0.33/0.60      ! [I: int,J: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ I @ J )
% 0.33/0.60       => ( ( upto @ I @ J )
% 0.33/0.60          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % upto_rec2
% 0.33/0.60  thf(fact_5219_upto__split2,axiom,
% 0.33/0.60      ! [I: int,J: int,K: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ I @ J )
% 0.33/0.60       => ( ( ord_less_eq_int @ J @ K )
% 0.33/0.60         => ( ( upto @ I @ K )
% 0.33/0.60            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % upto_split2
% 0.33/0.60  thf(fact_5220_upto__split1,axiom,
% 0.33/0.60      ! [I: int,J: int,K: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ I @ J )
% 0.33/0.60       => ( ( ord_less_eq_int @ J @ K )
% 0.33/0.60         => ( ( upto @ I @ K )
% 0.33/0.60            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % upto_split1
% 0.33/0.60  thf(fact_5221_upto__split3,axiom,
% 0.33/0.60      ! [I: int,J: int,K: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ I @ J )
% 0.33/0.60       => ( ( ord_less_eq_int @ J @ K )
% 0.33/0.60         => ( ( upto @ I @ K )
% 0.33/0.60            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % upto_split3
% 0.33/0.60  thf(fact_5222_Gcd__remove0__nat,axiom,
% 0.33/0.60      ! [M3: set_nat] :
% 0.33/0.60        ( ( finite_finite_nat @ M3 )
% 0.33/0.60       => ( ( gcd_Gcd_nat @ M3 )
% 0.33/0.60          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M3 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_remove0_nat
% 0.33/0.60  thf(fact_5223_Gcd__nat__eq__one,axiom,
% 0.33/0.60      ! [N4: set_nat] :
% 0.33/0.60        ( ( member_nat @ one_one_nat @ N4 )
% 0.33/0.60       => ( ( gcd_Gcd_nat @ N4 )
% 0.33/0.60          = one_one_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_nat_eq_one
% 0.33/0.60  thf(fact_5224_Gcd__dvd__nat,axiom,
% 0.33/0.60      ! [A: nat,A4: set_nat] :
% 0.33/0.60        ( ( member_nat @ A @ A4 )
% 0.33/0.60       => ( dvd_dvd_nat @ ( gcd_Gcd_nat @ A4 ) @ A ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_dvd_nat
% 0.33/0.60  thf(fact_5225_Gcd__greatest__nat,axiom,
% 0.33/0.60      ! [A4: set_nat,A: nat] :
% 0.33/0.60        ( ! [B3: nat] :
% 0.33/0.60            ( ( member_nat @ B3 @ A4 )
% 0.33/0.60           => ( dvd_dvd_nat @ A @ B3 ) )
% 0.33/0.60       => ( dvd_dvd_nat @ A @ ( gcd_Gcd_nat @ A4 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_greatest_nat
% 0.33/0.60  thf(fact_5226_abs__Gcd__eq,axiom,
% 0.33/0.60      ! [K5: set_int] :
% 0.33/0.60        ( ( abs_abs_int @ ( gcd_Gcd_int @ K5 ) )
% 0.33/0.60        = ( gcd_Gcd_int @ K5 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % abs_Gcd_eq
% 0.33/0.60  thf(fact_5227_finite__lessThan,axiom,
% 0.33/0.60      ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 0.33/0.60  
% 0.33/0.60  % finite_lessThan
% 0.33/0.60  thf(fact_5228_card__lessThan,axiom,
% 0.33/0.60      ! [U: nat] :
% 0.33/0.60        ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 0.33/0.60        = U ) ).
% 0.33/0.60  
% 0.33/0.60  % card_lessThan
% 0.33/0.60  thf(fact_5229_lessThan__0,axiom,
% 0.33/0.60      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 0.33/0.60      = bot_bot_set_nat ) ).
% 0.33/0.60  
% 0.33/0.60  % lessThan_0
% 0.33/0.60  thf(fact_5230_Gcd__dvd__int,axiom,
% 0.33/0.60      ! [A: int,A4: set_int] :
% 0.33/0.60        ( ( member_int @ A @ A4 )
% 0.33/0.60       => ( dvd_dvd_int @ ( gcd_Gcd_int @ A4 ) @ A ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_dvd_int
% 0.33/0.60  thf(fact_5231_Gcd__greatest__int,axiom,
% 0.33/0.60      ! [A4: set_int,A: int] :
% 0.33/0.60        ( ! [B3: int] :
% 0.33/0.60            ( ( member_int @ B3 @ A4 )
% 0.33/0.60           => ( dvd_dvd_int @ A @ B3 ) )
% 0.33/0.60       => ( dvd_dvd_int @ A @ ( gcd_Gcd_int @ A4 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_greatest_int
% 0.33/0.60  thf(fact_5232_lessThan__atLeast0,axiom,
% 0.33/0.60      ( set_ord_lessThan_nat
% 0.33/0.60      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % lessThan_atLeast0
% 0.33/0.60  thf(fact_5233_lessThan__Suc__atMost,axiom,
% 0.33/0.60      ! [K: nat] :
% 0.33/0.60        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.33/0.60        = ( set_ord_atMost_nat @ K ) ) ).
% 0.33/0.60  
% 0.33/0.60  % lessThan_Suc_atMost
% 0.33/0.60  thf(fact_5234_lessThan__empty__iff,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( ( set_ord_lessThan_nat @ N )
% 0.33/0.60          = bot_bot_set_nat )
% 0.33/0.60        = ( N = zero_zero_nat ) ) ).
% 0.33/0.60  
% 0.33/0.60  % lessThan_empty_iff
% 0.33/0.60  thf(fact_5235_lessThan__Suc,axiom,
% 0.33/0.60      ! [K: nat] :
% 0.33/0.60        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.33/0.60        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % lessThan_Suc
% 0.33/0.60  thf(fact_5236_Gcd__int__greater__eq__0,axiom,
% 0.33/0.60      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_int_greater_eq_0
% 0.33/0.60  thf(fact_5237_lessThan__nat__numeral,axiom,
% 0.33/0.60      ! [K: num] :
% 0.33/0.60        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 0.33/0.60        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % lessThan_nat_numeral
% 0.33/0.60  thf(fact_5238_atLeast1__lessThan__eq__remove0,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.33/0.60        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeast1_lessThan_eq_remove0
% 0.33/0.60  thf(fact_5239_image__atLeastZeroLessThan__integer,axiom,
% 0.33/0.60      ! [U: code_integer] :
% 0.33/0.60        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.33/0.60       => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 0.33/0.60          = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_atLeastZeroLessThan_integer
% 0.33/0.60  thf(fact_5240_take__bit__num__simps_I7_J,axiom,
% 0.33/0.60      ! [R: num,M: num] :
% 0.33/0.60        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 0.33/0.60        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_num_simps(7)
% 0.33/0.60  thf(fact_5241_take__bit__num__simps_I4_J,axiom,
% 0.33/0.60      ! [N: nat,M: num] :
% 0.33/0.60        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 0.33/0.60        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_num_simps(4)
% 0.33/0.60  thf(fact_5242_and__not__num_Osimps_I8_J,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.33/0.60        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.60          @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 0.33/0.60          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_not_num.simps(8)
% 0.33/0.60  thf(fact_5243_image__Suc__atLeastAtMost,axiom,
% 0.33/0.60      ! [I: nat,J: nat] :
% 0.33/0.60        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.33/0.60        = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_Suc_atLeastAtMost
% 0.33/0.60  thf(fact_5244_image__Suc__atLeastLessThan,axiom,
% 0.33/0.60      ! [I: nat,J: nat] :
% 0.33/0.60        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 0.33/0.60        = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_Suc_atLeastLessThan
% 0.33/0.60  thf(fact_5245_Gcd__abs__eq,axiom,
% 0.33/0.60      ! [K5: set_int] :
% 0.33/0.60        ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 0.33/0.60        = ( gcd_Gcd_int @ K5 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_abs_eq
% 0.33/0.60  thf(fact_5246_Gcd__int__eq,axiom,
% 0.33/0.60      ! [N4: set_nat] :
% 0.33/0.60        ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N4 ) )
% 0.33/0.60        = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N4 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_int_eq
% 0.33/0.60  thf(fact_5247_Gcd__nat__abs__eq,axiom,
% 0.33/0.60      ! [K5: set_int] :
% 0.33/0.60        ( ( gcd_Gcd_nat
% 0.33/0.60          @ ( image_int_nat
% 0.33/0.60            @ ^ [K2: int] : ( nat2 @ ( abs_abs_int @ K2 ) )
% 0.33/0.60            @ K5 ) )
% 0.33/0.60        = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_nat_abs_eq
% 0.33/0.60  thf(fact_5248_zero__notin__Suc__image,axiom,
% 0.33/0.60      ! [A4: set_nat] :
% 0.33/0.60        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % zero_notin_Suc_image
% 0.33/0.60  thf(fact_5249_image__int__atLeastAtMost,axiom,
% 0.33/0.60      ! [A: nat,B: nat] :
% 0.33/0.60        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.33/0.60        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_int_atLeastAtMost
% 0.33/0.60  thf(fact_5250_image__int__atLeastLessThan,axiom,
% 0.33/0.60      ! [A: nat,B: nat] :
% 0.33/0.60        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.33/0.60        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_int_atLeastLessThan
% 0.33/0.60  thf(fact_5251_image__Suc__atMost,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 0.33/0.60        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_Suc_atMost
% 0.33/0.60  thf(fact_5252_image__Suc__lessThan,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 0.33/0.60        = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_Suc_lessThan
% 0.33/0.60  thf(fact_5253_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.33/0.60        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeast0_atMost_Suc_eq_insert_0
% 0.33/0.60  thf(fact_5254_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.33/0.60        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atLeast0_lessThan_Suc_eq_insert_0
% 0.33/0.60  thf(fact_5255_atMost__Suc__eq__insert__0,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 0.33/0.60        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % atMost_Suc_eq_insert_0
% 0.33/0.60  thf(fact_5256_lessThan__Suc__eq__insert__0,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 0.33/0.60        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % lessThan_Suc_eq_insert_0
% 0.33/0.60  thf(fact_5257_image__add__int__atLeastLessThan,axiom,
% 0.33/0.60      ! [L: int,U: int] :
% 0.33/0.60        ( ( image_int_int
% 0.33/0.60          @ ^ [X: int] : ( plus_plus_int @ X @ L )
% 0.33/0.60          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 0.33/0.60        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_add_int_atLeastLessThan
% 0.33/0.60  thf(fact_5258_image__add__integer__atLeastLessThan,axiom,
% 0.33/0.60      ! [L: code_integer,U: code_integer] :
% 0.33/0.60        ( ( image_4470545334726330049nteger
% 0.33/0.60          @ ^ [X: code_integer] : ( plus_p5714425477246183910nteger @ X @ L )
% 0.33/0.60          @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 0.33/0.60        = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_add_integer_atLeastLessThan
% 0.33/0.60  thf(fact_5259_image__atLeastZeroLessThan__int,axiom,
% 0.33/0.60      ! [U: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.33/0.60       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 0.33/0.60          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_atLeastZeroLessThan_int
% 0.33/0.60  thf(fact_5260_image__minus__const__atLeastLessThan__nat,axiom,
% 0.33/0.60      ! [C: nat,Y: nat,X2: nat] :
% 0.33/0.60        ( ( ( ord_less_nat @ C @ Y )
% 0.33/0.60         => ( ( image_nat_nat
% 0.33/0.60              @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 0.33/0.60              @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 0.33/0.60            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 0.33/0.60        & ( ~ ( ord_less_nat @ C @ Y )
% 0.33/0.60         => ( ( ( ord_less_nat @ X2 @ Y )
% 0.33/0.60             => ( ( image_nat_nat
% 0.33/0.60                  @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 0.33/0.60                  @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 0.33/0.60                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.33/0.60            & ( ~ ( ord_less_nat @ X2 @ Y )
% 0.33/0.60             => ( ( image_nat_nat
% 0.33/0.60                  @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 0.33/0.60                  @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 0.33/0.60                = bot_bot_set_nat ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % image_minus_const_atLeastLessThan_nat
% 0.33/0.60  thf(fact_5261_take__bit__num__simps_I6_J,axiom,
% 0.33/0.60      ! [R: num,M: num] :
% 0.33/0.60        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 0.33/0.60        = ( case_o6005452278849405969um_num @ none_num
% 0.33/0.60          @ ^ [Q6: num] : ( some_num @ ( bit0 @ Q6 ) )
% 0.33/0.60          @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_num_simps(6)
% 0.33/0.60  thf(fact_5262_take__bit__num__simps_I1_J,axiom,
% 0.33/0.60      ! [M: num] :
% 0.33/0.60        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 0.33/0.60        = none_num ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_num_simps(1)
% 0.33/0.60  thf(fact_5263_take__bit__num__simps_I3_J,axiom,
% 0.33/0.60      ! [N: nat,M: num] :
% 0.33/0.60        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 0.33/0.60        = ( case_o6005452278849405969um_num @ none_num
% 0.33/0.60          @ ^ [Q6: num] : ( some_num @ ( bit0 @ Q6 ) )
% 0.33/0.60          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_num_simps(3)
% 0.33/0.60  thf(fact_5264_and__not__num__eq__None__iff,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( ( bit_and_not_num @ M @ N )
% 0.33/0.60          = none_num )
% 0.33/0.60        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.60          = zero_zero_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_not_num_eq_None_iff
% 0.33/0.60  thf(fact_5265_take__bit__num__def,axiom,
% 0.33/0.60      ( bit_take_bit_num
% 0.33/0.60      = ( ^ [N3: nat,M2: num] :
% 0.33/0.60            ( if_option_num
% 0.33/0.60            @ ( ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M2 ) )
% 0.33/0.60              = zero_zero_nat )
% 0.33/0.60            @ none_num
% 0.33/0.60            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M2 ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_num_def
% 0.33/0.60  thf(fact_5266_and__not__num_Oelims,axiom,
% 0.33/0.60      ! [X2: num,Xa: num,Y: option_num] :
% 0.33/0.60        ( ( ( bit_and_not_num @ X2 @ Xa )
% 0.33/0.60          = Y )
% 0.33/0.60       => ( ( ( X2 = one )
% 0.33/0.60           => ( ( Xa = one )
% 0.33/0.60             => ( Y != none_num ) ) )
% 0.33/0.60         => ( ( ( X2 = one )
% 0.33/0.60             => ( ? [N2: num] :
% 0.33/0.60                    ( Xa
% 0.33/0.60                    = ( bit0 @ N2 ) )
% 0.33/0.60               => ( Y
% 0.33/0.60                 != ( some_num @ one ) ) ) )
% 0.33/0.60           => ( ( ( X2 = one )
% 0.33/0.60               => ( ? [N2: num] :
% 0.33/0.60                      ( Xa
% 0.33/0.60                      = ( bit1 @ N2 ) )
% 0.33/0.60                 => ( Y != none_num ) ) )
% 0.33/0.60             => ( ! [M4: num] :
% 0.33/0.60                    ( ( X2
% 0.33/0.60                      = ( bit0 @ M4 ) )
% 0.33/0.60                   => ( ( Xa = one )
% 0.33/0.60                     => ( Y
% 0.33/0.60                       != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 0.33/0.60               => ( ! [M4: num] :
% 0.33/0.60                      ( ( X2
% 0.33/0.60                        = ( bit0 @ M4 ) )
% 0.33/0.60                     => ! [N2: num] :
% 0.33/0.60                          ( ( Xa
% 0.33/0.60                            = ( bit0 @ N2 ) )
% 0.33/0.60                         => ( Y
% 0.33/0.60                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 0.33/0.60                 => ( ! [M4: num] :
% 0.33/0.60                        ( ( X2
% 0.33/0.60                          = ( bit0 @ M4 ) )
% 0.33/0.60                       => ! [N2: num] :
% 0.33/0.60                            ( ( Xa
% 0.33/0.60                              = ( bit1 @ N2 ) )
% 0.33/0.60                           => ( Y
% 0.33/0.60                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 0.33/0.60                   => ( ! [M4: num] :
% 0.33/0.60                          ( ( X2
% 0.33/0.60                            = ( bit1 @ M4 ) )
% 0.33/0.60                         => ( ( Xa = one )
% 0.33/0.60                           => ( Y
% 0.33/0.60                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 0.33/0.60                     => ( ! [M4: num] :
% 0.33/0.60                            ( ( X2
% 0.33/0.60                              = ( bit1 @ M4 ) )
% 0.33/0.60                           => ! [N2: num] :
% 0.33/0.60                                ( ( Xa
% 0.33/0.60                                  = ( bit0 @ N2 ) )
% 0.33/0.60                               => ( Y
% 0.33/0.60                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.60                                    @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 0.33/0.60                                    @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 0.33/0.60                       => ~ ! [M4: num] :
% 0.33/0.60                              ( ( X2
% 0.33/0.60                                = ( bit1 @ M4 ) )
% 0.33/0.60                             => ! [N2: num] :
% 0.33/0.60                                  ( ( Xa
% 0.33/0.60                                    = ( bit1 @ N2 ) )
% 0.33/0.60                                 => ( Y
% 0.33/0.60                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_not_num.elims
% 0.33/0.60  thf(fact_5267_Gcd__int__def,axiom,
% 0.33/0.60      ( gcd_Gcd_int
% 0.33/0.60      = ( ^ [K6: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K6 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Gcd_int_def
% 0.33/0.60  thf(fact_5268_and__num_Oelims,axiom,
% 0.33/0.60      ! [X2: num,Xa: num,Y: option_num] :
% 0.33/0.60        ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa )
% 0.33/0.60          = Y )
% 0.33/0.60       => ( ( ( X2 = one )
% 0.33/0.60           => ( ( Xa = one )
% 0.33/0.60             => ( Y
% 0.33/0.60               != ( some_num @ one ) ) ) )
% 0.33/0.60         => ( ( ( X2 = one )
% 0.33/0.60             => ( ? [N2: num] :
% 0.33/0.60                    ( Xa
% 0.33/0.60                    = ( bit0 @ N2 ) )
% 0.33/0.60               => ( Y != none_num ) ) )
% 0.33/0.60           => ( ( ( X2 = one )
% 0.33/0.60               => ( ? [N2: num] :
% 0.33/0.60                      ( Xa
% 0.33/0.60                      = ( bit1 @ N2 ) )
% 0.33/0.60                 => ( Y
% 0.33/0.60                   != ( some_num @ one ) ) ) )
% 0.33/0.60             => ( ( ? [M4: num] :
% 0.33/0.60                      ( X2
% 0.33/0.60                      = ( bit0 @ M4 ) )
% 0.33/0.60                 => ( ( Xa = one )
% 0.33/0.60                   => ( Y != none_num ) ) )
% 0.33/0.60               => ( ! [M4: num] :
% 0.33/0.60                      ( ( X2
% 0.33/0.60                        = ( bit0 @ M4 ) )
% 0.33/0.60                     => ! [N2: num] :
% 0.33/0.60                          ( ( Xa
% 0.33/0.60                            = ( bit0 @ N2 ) )
% 0.33/0.60                         => ( Y
% 0.33/0.60                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 0.33/0.60                 => ( ! [M4: num] :
% 0.33/0.60                        ( ( X2
% 0.33/0.60                          = ( bit0 @ M4 ) )
% 0.33/0.60                       => ! [N2: num] :
% 0.33/0.60                            ( ( Xa
% 0.33/0.60                              = ( bit1 @ N2 ) )
% 0.33/0.60                           => ( Y
% 0.33/0.60                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 0.33/0.60                   => ( ( ? [M4: num] :
% 0.33/0.60                            ( X2
% 0.33/0.60                            = ( bit1 @ M4 ) )
% 0.33/0.60                       => ( ( Xa = one )
% 0.33/0.60                         => ( Y
% 0.33/0.60                           != ( some_num @ one ) ) ) )
% 0.33/0.60                     => ( ! [M4: num] :
% 0.33/0.60                            ( ( X2
% 0.33/0.60                              = ( bit1 @ M4 ) )
% 0.33/0.60                           => ! [N2: num] :
% 0.33/0.60                                ( ( Xa
% 0.33/0.60                                  = ( bit0 @ N2 ) )
% 0.33/0.60                               => ( Y
% 0.33/0.60                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 0.33/0.60                       => ~ ! [M4: num] :
% 0.33/0.60                              ( ( X2
% 0.33/0.60                                = ( bit1 @ M4 ) )
% 0.33/0.60                             => ! [N2: num] :
% 0.33/0.60                                  ( ( Xa
% 0.33/0.60                                    = ( bit1 @ N2 ) )
% 0.33/0.60                                 => ( Y
% 0.33/0.60                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.60                                      @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 0.33/0.60                                      @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_num.elims
% 0.33/0.60  thf(fact_5269_and__num_Osimps_I9_J,axiom,
% 0.33/0.60      ! [M: num,N: num] :
% 0.33/0.60        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.33/0.60        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.60          @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 0.33/0.60          @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_num.simps(9)
% 0.33/0.60  thf(fact_5270_Code__Numeral_Onegative__def,axiom,
% 0.33/0.60      ( code_negative
% 0.33/0.60      = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Code_Numeral.negative_def
% 0.33/0.60  thf(fact_5271_measure__function__int,axiom,
% 0.33/0.60      fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 0.33/0.60  
% 0.33/0.60  % measure_function_int
% 0.33/0.60  thf(fact_5272_nat__of__integer__code,axiom,
% 0.33/0.60      ( code_nat_of_integer
% 0.33/0.60      = ( ^ [K2: code_integer] :
% 0.33/0.60            ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.33/0.60            @ ( produc1555791787009142072er_nat
% 0.33/0.60              @ ^ [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 ) )
% 0.33/0.60              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_of_integer_code
% 0.33/0.60  thf(fact_5273_num__of__integer__code,axiom,
% 0.33/0.60      ( code_num_of_integer
% 0.33/0.60      = ( ^ [K2: code_integer] :
% 0.33/0.60            ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 0.33/0.60            @ ( produc7336495610019696514er_num
% 0.33/0.60              @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 0.33/0.60              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % num_of_integer_code
% 0.33/0.60  thf(fact_5274_int__of__integer__code,axiom,
% 0.33/0.60      ( code_int_of_integer
% 0.33/0.60      = ( ^ [K2: code_integer] :
% 0.33/0.60            ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 0.33/0.60            @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.33/0.60              @ ( produc1553301316500091796er_int
% 0.33/0.60                @ ^ [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 ) )
% 0.33/0.60                @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_code
% 0.33/0.60  thf(fact_5275_int__of__integer__inverse,axiom,
% 0.33/0.60      ! [X2: code_integer] :
% 0.33/0.60        ( ( code_integer_of_int @ ( code_int_of_integer @ X2 ) )
% 0.33/0.60        = X2 ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_inverse
% 0.33/0.60  thf(fact_5276_int__of__integer__integer__of__int,axiom,
% 0.33/0.60      ! [K: int] :
% 0.33/0.60        ( ( code_int_of_integer @ ( code_integer_of_int @ K ) )
% 0.33/0.60        = K ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_integer_of_int
% 0.33/0.60  thf(fact_5277_integer__of__int__int__of__integer,axiom,
% 0.33/0.60      ! [K: code_integer] :
% 0.33/0.60        ( ( code_integer_of_int @ ( code_int_of_integer @ K ) )
% 0.33/0.60        = K ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_of_int_int_of_integer
% 0.33/0.60  thf(fact_5278_int__of__integer__sub,axiom,
% 0.33/0.60      ! [K: num,L: num] :
% 0.33/0.60        ( ( code_int_of_integer @ ( neg_nu5755505904847501662nteger @ K @ L ) )
% 0.33/0.60        = ( neg_numeral_sub_int @ K @ L ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_sub
% 0.33/0.60  thf(fact_5279_of__int__integer__of,axiom,
% 0.33/0.60      ! [K: code_integer] :
% 0.33/0.60        ( ( ring_18347121197199848620nteger @ ( code_int_of_integer @ K ) )
% 0.33/0.60        = K ) ).
% 0.33/0.60  
% 0.33/0.60  % of_int_integer_of
% 0.33/0.60  thf(fact_5280_int__of__integer__of__int,axiom,
% 0.33/0.60      ! [K: int] :
% 0.33/0.60        ( ( code_int_of_integer @ ( ring_18347121197199848620nteger @ K ) )
% 0.33/0.60        = K ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_of_int
% 0.33/0.60  thf(fact_5281_zero__integer_Orep__eq,axiom,
% 0.33/0.60      ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 0.33/0.60      = zero_zero_int ) ).
% 0.33/0.60  
% 0.33/0.60  % zero_integer.rep_eq
% 0.33/0.60  thf(fact_5282_int__of__integer__numeral,axiom,
% 0.33/0.60      ! [K: num] :
% 0.33/0.60        ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.33/0.60        = ( numeral_numeral_int @ K ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_numeral
% 0.33/0.60  thf(fact_5283_plus__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( plus_plus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % plus_integer.rep_eq
% 0.33/0.60  thf(fact_5284_one__integer_Orep__eq,axiom,
% 0.33/0.60      ( ( code_int_of_integer @ one_one_Code_integer )
% 0.33/0.60      = one_one_int ) ).
% 0.33/0.60  
% 0.33/0.60  % one_integer.rep_eq
% 0.33/0.60  thf(fact_5285_uminus__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X2 ) )
% 0.33/0.60        = ( uminus_uminus_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % uminus_integer.rep_eq
% 0.33/0.60  thf(fact_5286_times__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( times_times_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % times_integer.rep_eq
% 0.33/0.60  thf(fact_5287_minus__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( minus_minus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % minus_integer.rep_eq
% 0.33/0.60  thf(fact_5288_abs__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( abs_abs_Code_integer @ X2 ) )
% 0.33/0.60        = ( abs_abs_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % abs_integer.rep_eq
% 0.33/0.60  thf(fact_5289_divide__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( divide_divide_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divide_integer.rep_eq
% 0.33/0.60  thf(fact_5290_modulo__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( modulo_modulo_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % modulo_integer.rep_eq
% 0.33/0.60  thf(fact_5291_int__of__integer__of__nat,axiom,
% 0.33/0.60      ! [N: nat] :
% 0.33/0.60        ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.33/0.60        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_of_nat
% 0.33/0.60  thf(fact_5292_sgn__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( sgn_sgn_Code_integer @ X2 ) )
% 0.33/0.60        = ( sgn_sgn_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % sgn_integer.rep_eq
% 0.33/0.60  thf(fact_5293_int__of__integer__max,axiom,
% 0.33/0.60      ! [K: code_integer,L: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( ord_max_Code_integer @ K @ L ) )
% 0.33/0.60        = ( ord_max_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_max
% 0.33/0.60  thf(fact_5294_integer__eq__iff,axiom,
% 0.33/0.60      ( ( ^ [Y3: code_integer,Z: code_integer] : ( Y3 = Z ) )
% 0.33/0.60      = ( ^ [K2: code_integer,L2: code_integer] :
% 0.33/0.60            ( ( code_int_of_integer @ K2 )
% 0.33/0.60            = ( code_int_of_integer @ L2 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_eq_iff
% 0.33/0.60  thf(fact_5295_integer__eqI,axiom,
% 0.33/0.60      ! [K: code_integer,L: code_integer] :
% 0.33/0.60        ( ( ( code_int_of_integer @ K )
% 0.33/0.60          = ( code_int_of_integer @ L ) )
% 0.33/0.60       => ( K = L ) ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_eqI
% 0.33/0.60  thf(fact_5296_int__of__integer__inject,axiom,
% 0.33/0.60      ! [X2: code_integer,Y: code_integer] :
% 0.33/0.60        ( ( ( code_int_of_integer @ X2 )
% 0.33/0.60          = ( code_int_of_integer @ Y ) )
% 0.33/0.60        = ( X2 = Y ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_inject
% 0.33/0.60  thf(fact_5297_less__integer_Orep__eq,axiom,
% 0.33/0.60      ( ord_le6747313008572928689nteger
% 0.33/0.60      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % less_integer.rep_eq
% 0.33/0.60  thf(fact_5298_integer__less__iff,axiom,
% 0.33/0.60      ( ord_le6747313008572928689nteger
% 0.33/0.60      = ( ^ [K2: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_less_iff
% 0.33/0.60  thf(fact_5299_int__of__integer__less__iff,axiom,
% 0.33/0.60      ! [X2: code_integer,Y: code_integer] :
% 0.33/0.60        ( ( ord_less_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Y ) )
% 0.33/0.60        = ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_of_integer_less_iff
% 0.33/0.60  thf(fact_5300_less__eq__integer_Orep__eq,axiom,
% 0.33/0.60      ( ord_le3102999989581377725nteger
% 0.33/0.60      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % less_eq_integer.rep_eq
% 0.33/0.60  thf(fact_5301_integer__less__eq__iff,axiom,
% 0.33/0.60      ( ord_le3102999989581377725nteger
% 0.33/0.60      = ( ^ [K2: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % integer_less_eq_iff
% 0.33/0.60  thf(fact_5302_nat__of__integer_Orep__eq,axiom,
% 0.33/0.60      ( code_nat_of_integer
% 0.33/0.60      = ( ^ [X: code_integer] : ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % nat_of_integer.rep_eq
% 0.33/0.60  thf(fact_5303_take__bit__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: nat,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se1745604003318907178nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( bit_se2923211474154528505it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_integer.rep_eq
% 0.33/0.60  thf(fact_5304_not__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_ri7632146776885996613nteger @ X2 ) )
% 0.33/0.60        = ( bit_ri7919022796975470100ot_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % not_integer.rep_eq
% 0.33/0.60  thf(fact_5305_and__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se3949692690581998587nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( bit_se725231765392027082nd_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % and_integer.rep_eq
% 0.33/0.60  thf(fact_5306_or__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se1080825931792720795nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( bit_se1409905431419307370or_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % or_integer.rep_eq
% 0.33/0.60  thf(fact_5307_bit__integer_Orep__eq,axiom,
% 0.33/0.60      ( bit_se9216721137139052372nteger
% 0.33/0.60      = ( ^ [X: code_integer] : ( bit_se1146084159140164899it_int @ ( code_int_of_integer @ X ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % bit_integer.rep_eq
% 0.33/0.60  thf(fact_5308_xor__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: code_integer,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se3222712562003087583nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( bit_se6526347334894502574or_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % xor_integer.rep_eq
% 0.33/0.60  thf(fact_5309_push__bit__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: nat,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se7788150548672797655nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( bit_se545348938243370406it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % push_bit_integer.rep_eq
% 0.33/0.60  thf(fact_5310_drop__bit__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: nat,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se3928097537394005634nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( bit_se8568078237143864401it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % drop_bit_integer.rep_eq
% 0.33/0.60  thf(fact_5311_mask__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: nat] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se2119862282449309892nteger @ X2 ) )
% 0.33/0.60        = ( bit_se2000444600071755411sk_int @ X2 ) ) ).
% 0.33/0.60  
% 0.33/0.60  % mask_integer.rep_eq
% 0.33/0.60  thf(fact_5312_unset__bit__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: nat,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se8260200283734997820nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( bit_se4203085406695923979it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % unset_bit_integer.rep_eq
% 0.33/0.60  thf(fact_5313_set__bit__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: nat,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se2793503036327961859nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( bit_se7879613467334960850it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % set_bit_integer.rep_eq
% 0.33/0.60  thf(fact_5314_flip__bit__integer_Orep__eq,axiom,
% 0.33/0.60      ! [X2: nat,Xa: code_integer] :
% 0.33/0.60        ( ( code_int_of_integer @ ( bit_se1345352211410354436nteger @ X2 @ Xa ) )
% 0.33/0.60        = ( bit_se2159334234014336723it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % flip_bit_integer.rep_eq
% 0.33/0.60  thf(fact_5315_num__of__integer_Orep__eq,axiom,
% 0.33/0.60      ( code_num_of_integer
% 0.33/0.60      = ( ^ [X: code_integer] : ( num_of_nat @ ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % num_of_integer.rep_eq
% 0.33/0.60  thf(fact_5316_int__ge__less__than__def,axiom,
% 0.33/0.60      ( int_ge_less_than
% 0.33/0.60      = ( ^ [D4: int] :
% 0.33/0.60            ( collec213857154873943460nt_int
% 0.33/0.60            @ ( produc4947309494688390418_int_o
% 0.33/0.60              @ ^ [Z7: int,Z3: int] :
% 0.33/0.60                  ( ( ord_less_eq_int @ D4 @ Z7 )
% 0.33/0.60                  & ( ord_less_int @ Z7 @ Z3 ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_ge_less_than_def
% 0.33/0.60  thf(fact_5317_int__ge__less__than2__def,axiom,
% 0.33/0.60      ( int_ge_less_than2
% 0.33/0.60      = ( ^ [D4: int] :
% 0.33/0.60            ( collec213857154873943460nt_int
% 0.33/0.60            @ ( produc4947309494688390418_int_o
% 0.33/0.60              @ ^ [Z7: int,Z3: int] :
% 0.33/0.60                  ( ( ord_less_eq_int @ D4 @ Z3 )
% 0.33/0.60                  & ( ord_less_int @ Z7 @ Z3 ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % int_ge_less_than2_def
% 0.33/0.60  thf(fact_5318_Divides_Oadjust__div__def,axiom,
% 0.33/0.60      ( adjust_div
% 0.33/0.60      = ( produc8211389475949308722nt_int
% 0.33/0.60        @ ^ [Q6: int,R2: int] : ( plus_plus_int @ Q6 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Divides.adjust_div_def
% 0.33/0.60  thf(fact_5319_divmod__step__integer__def,axiom,
% 0.33/0.60      ( unique4921790084139445826nteger
% 0.33/0.60      = ( ^ [L2: num] :
% 0.33/0.60            ( produc6916734918728496179nteger
% 0.33/0.60            @ ^ [Q6: code_integer,R2: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ R2 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divmod_step_integer_def
% 0.33/0.60  thf(fact_5320_divmod__integer__def,axiom,
% 0.33/0.60      ( code_divmod_integer
% 0.33/0.60      = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K2 @ L2 ) @ ( modulo364778990260209775nteger @ K2 @ L2 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divmod_integer_def
% 0.33/0.60  thf(fact_5321_Divides_Oadjust__div__eq,axiom,
% 0.33/0.60      ! [Q2: int,R: int] :
% 0.33/0.60        ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.33/0.60        = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % Divides.adjust_div_eq
% 0.33/0.60  thf(fact_5322_divmod__step__nat__def,axiom,
% 0.33/0.60      ( unique5026877609467782581ep_nat
% 0.33/0.60      = ( ^ [L2: num] :
% 0.33/0.60            ( produc2626176000494625587at_nat
% 0.33/0.60            @ ^ [Q6: nat,R2: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ R2 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divmod_step_nat_def
% 0.33/0.60  thf(fact_5323_divmod__step__int__def,axiom,
% 0.33/0.60      ( unique5024387138958732305ep_int
% 0.33/0.60      = ( ^ [L2: num] :
% 0.33/0.60            ( produc4245557441103728435nt_int
% 0.33/0.60            @ ^ [Q6: int,R2: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ R2 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divmod_step_int_def
% 0.33/0.60  thf(fact_5324_take__bit__num__code,axiom,
% 0.33/0.60      ( bit_take_bit_num
% 0.33/0.60      = ( ^ [N3: nat,M2: num] :
% 0.33/0.60            ( produc478579273971653890on_num
% 0.33/0.60            @ ^ [A2: nat,X: num] :
% 0.33/0.60                ( case_nat_option_num @ none_num
% 0.33/0.60                @ ^ [O: nat] :
% 0.33/0.60                    ( case_num_option_num @ ( some_num @ one )
% 0.33/0.60                    @ ^ [P6: num] :
% 0.33/0.60                        ( case_o6005452278849405969um_num @ none_num
% 0.33/0.60                        @ ^ [Q6: num] : ( some_num @ ( bit0 @ Q6 ) )
% 0.33/0.60                        @ ( bit_take_bit_num @ O @ P6 ) )
% 0.33/0.60                    @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 0.33/0.60                    @ X )
% 0.33/0.60                @ A2 )
% 0.33/0.60            @ ( product_Pair_nat_num @ N3 @ M2 ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % take_bit_num_code
% 0.33/0.60  thf(fact_5325_minus__one__div__numeral,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.60        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % minus_one_div_numeral
% 0.33/0.60  thf(fact_5326_one__div__minus__numeral,axiom,
% 0.33/0.60      ! [N: num] :
% 0.33/0.60        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.60        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % one_div_minus_numeral
% 0.33/0.60  thf(fact_5327_divmod__BitM__2__eq,axiom,
% 0.33/0.60      ! [M: num] :
% 0.33/0.60        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 0.33/0.60        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divmod_BitM_2_eq
% 0.33/0.60  thf(fact_5328_divmod__integer_H__def,axiom,
% 0.33/0.60      ( unique3479559517661332726nteger
% 0.33/0.60      = ( ^ [M2: num,N3: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N3 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N3 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divmod_integer'_def
% 0.33/0.60  thf(fact_5329_divmod__nat__if,axiom,
% 0.33/0.60      ( divmod_nat
% 0.33/0.60      = ( ^ [M2: nat,N3: nat] :
% 0.33/0.60            ( if_Pro6206227464963214023at_nat
% 0.33/0.60            @ ( ( N3 = zero_zero_nat )
% 0.33/0.60              | ( ord_less_nat @ M2 @ N3 ) )
% 0.33/0.60            @ ( product_Pair_nat_nat @ zero_zero_nat @ M2 )
% 0.33/0.60            @ ( produc2626176000494625587at_nat
% 0.33/0.60              @ ^ [Q6: nat] : ( product_Pair_nat_nat @ ( suc @ Q6 ) )
% 0.33/0.60              @ ( divmod_nat @ ( minus_minus_nat @ M2 @ N3 ) @ N3 ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % divmod_nat_if
% 0.33/0.60  thf(fact_5330_neg__eucl__rel__int__mult__2,axiom,
% 0.33/0.60      ! [B: int,A: int,Q2: int,R: int] :
% 0.33/0.60        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.33/0.60       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.33/0.60         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % neg_eucl_rel_int_mult_2
% 0.33/0.60  thf(fact_5331_eucl__rel__int__by0,axiom,
% 0.33/0.60      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 0.33/0.60  
% 0.33/0.60  % eucl_rel_int_by0
% 0.33/0.60  thf(fact_5332_eucl__rel__int__dividesI,axiom,
% 0.33/0.60      ! [L: int,K: int,Q2: int] :
% 0.33/0.60        ( ( L != zero_zero_int )
% 0.33/0.60       => ( ( K
% 0.33/0.60            = ( times_times_int @ Q2 @ L ) )
% 0.33/0.60         => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % eucl_rel_int_dividesI
% 0.33/0.60  thf(fact_5333_zminus1__lemma,axiom,
% 0.33/0.60      ! [A: int,B: int,Q2: int,R: int] :
% 0.33/0.60        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.33/0.60       => ( ( B != zero_zero_int )
% 0.33/0.60         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % zminus1_lemma
% 0.33/0.60  thf(fact_5334_eucl__rel__int__iff,axiom,
% 0.33/0.60      ! [K: int,L: int,Q2: int,R: int] :
% 0.33/0.60        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.33/0.60        = ( ( K
% 0.33/0.60            = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R ) )
% 0.33/0.60          & ( ( ord_less_int @ zero_zero_int @ L )
% 0.33/0.60           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.33/0.60              & ( ord_less_int @ R @ L ) ) )
% 0.33/0.60          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 0.33/0.60           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 0.33/0.60               => ( ( ord_less_int @ L @ R )
% 0.33/0.60                  & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 0.33/0.60              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 0.33/0.60               => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % eucl_rel_int_iff
% 0.33/0.60  thf(fact_5335_eucl__rel__int__remainderI,axiom,
% 0.33/0.60      ! [R: int,L: int,K: int,Q2: int] :
% 0.33/0.60        ( ( ( sgn_sgn_int @ R )
% 0.33/0.60          = ( sgn_sgn_int @ L ) )
% 0.33/0.60       => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L ) )
% 0.33/0.60         => ( ( K
% 0.33/0.60              = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R ) )
% 0.33/0.60           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % eucl_rel_int_remainderI
% 0.33/0.60  thf(fact_5336_eucl__rel__int_Osimps,axiom,
% 0.33/0.60      ( eucl_rel_int
% 0.33/0.60      = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 0.33/0.60            ( ? [K2: int] :
% 0.33/0.60                ( ( A1 = K2 )
% 0.33/0.60                & ( A22 = zero_zero_int )
% 0.33/0.60                & ( A32
% 0.33/0.60                  = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 0.33/0.60            | ? [L2: int,K2: int,Q6: int] :
% 0.33/0.60                ( ( A1 = K2 )
% 0.33/0.60                & ( A22 = L2 )
% 0.33/0.60                & ( A32
% 0.33/0.60                  = ( product_Pair_int_int @ Q6 @ zero_zero_int ) )
% 0.33/0.60                & ( L2 != zero_zero_int )
% 0.33/0.60                & ( K2
% 0.33/0.60                  = ( times_times_int @ Q6 @ L2 ) ) )
% 0.33/0.60            | ? [R2: int,L2: int,K2: int,Q6: int] :
% 0.33/0.60                ( ( A1 = K2 )
% 0.33/0.60                & ( A22 = L2 )
% 0.33/0.60                & ( A32
% 0.33/0.60                  = ( product_Pair_int_int @ Q6 @ R2 ) )
% 0.33/0.60                & ( ( sgn_sgn_int @ R2 )
% 0.33/0.60                  = ( sgn_sgn_int @ L2 ) )
% 0.33/0.60                & ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L2 ) )
% 0.33/0.60                & ( K2
% 0.33/0.60                  = ( plus_plus_int @ ( times_times_int @ Q6 @ L2 ) @ R2 ) ) ) ) ) ) ).
% 0.33/0.60  
% 0.33/0.60  % eucl_rel_int.simps
% 0.33/0.60  thf(fact_5337_eucl__rel__int_Ocases,axiom,
% 0.33/0.60      ! [A12: int,A23: int,A33: product_prod_int_int] :
% 0.33/0.60        ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 0.33/0.60       => ( ( ( A23 = zero_zero_int )
% 0.33/0.60           => ( A33
% 0.33/0.60             != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 0.33/0.60         => ( ! [Q4: int] :
% 0.33/0.60                ( ( A33
% 0.33/0.60                  = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 0.33/0.60               => ( ( A23 != zero_zero_int )
% 0.33/0.60                 => ( A12
% 0.33/0.60                   != ( times_times_int @ Q4 @ A23 ) ) ) )
% 0.33/0.61           => ~ ! [R5: int,Q4: int] :
% 0.33/0.61                  ( ( A33
% 0.33/0.61                    = ( product_Pair_int_int @ Q4 @ R5 ) )
% 0.33/0.61                 => ( ( ( sgn_sgn_int @ R5 )
% 0.33/0.61                      = ( sgn_sgn_int @ A23 ) )
% 0.33/0.61                   => ( ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ A23 ) )
% 0.33/0.61                     => ( A12
% 0.33/0.61                       != ( plus_plus_int @ ( times_times_int @ Q4 @ A23 ) @ R5 ) ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % eucl_rel_int.cases
% 0.33/0.61  thf(fact_5338_pos__eucl__rel__int__mult__2,axiom,
% 0.33/0.61      ! [B: int,A: int,Q2: int,R: int] :
% 0.33/0.61        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.33/0.61         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % pos_eucl_rel_int_mult_2
% 0.33/0.61  thf(fact_5339_and__int_Opsimps,axiom,
% 0.33/0.61      ! [K: int,L: int] :
% 0.33/0.61        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 0.33/0.61       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.33/0.61              = ( uminus_uminus_int
% 0.33/0.61                @ ( zero_n2684676970156552555ol_int
% 0.33/0.61                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.33/0.61                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 0.33/0.61          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.33/0.61              = ( plus_plus_int
% 0.33/0.61                @ ( zero_n2684676970156552555ol_int
% 0.33/0.61                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.33/0.61                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.33/0.61                @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % and_int.psimps
% 0.33/0.61  thf(fact_5340_and__int_Opelims,axiom,
% 0.33/0.61      ! [X2: int,Xa: int,Y: int] :
% 0.33/0.61        ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa ) )
% 0.33/0.61         => ~ ( ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61                    & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61                 => ( Y
% 0.33/0.61                    = ( uminus_uminus_int
% 0.33/0.61                      @ ( zero_n2684676970156552555ol_int
% 0.33/0.61                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 0.33/0.61                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.33/0.61                & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61                      & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61                 => ( Y
% 0.33/0.61                    = ( plus_plus_int
% 0.33/0.61                      @ ( zero_n2684676970156552555ol_int
% 0.33/0.61                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 0.33/0.61                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.33/0.61                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.33/0.61             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % and_int.pelims
% 0.33/0.61  thf(fact_5341_and__int_Opinduct,axiom,
% 0.33/0.61      ! [A0: int,A12: int,P: int > int > $o] :
% 0.33/0.61        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 0.33/0.61       => ( ! [K3: int,L3: int] :
% 0.33/0.61              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L3 ) )
% 0.33/0.61             => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.33/0.61                      & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.33/0.61                 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.33/0.61               => ( P @ K3 @ L3 ) ) )
% 0.33/0.61         => ( P @ A0 @ A12 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % and_int.pinduct
% 0.33/0.61  thf(fact_5342_upto_Opelims,axiom,
% 0.33/0.61      ! [X2: int,Xa: int,Y: list_int] :
% 0.33/0.61        ( ( ( upto @ X2 @ Xa )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa ) )
% 0.33/0.61         => ~ ( ( ( ( ord_less_eq_int @ X2 @ Xa )
% 0.33/0.61                 => ( Y
% 0.33/0.61                    = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa ) ) ) )
% 0.33/0.61                & ( ~ ( ord_less_eq_int @ X2 @ Xa )
% 0.33/0.61                 => ( Y = nil_int ) ) )
% 0.33/0.61             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upto.pelims
% 0.33/0.61  thf(fact_5343_upto_Opsimps,axiom,
% 0.33/0.61      ! [I: int,J: int] :
% 0.33/0.61        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 0.33/0.61       => ( ( ( ord_less_eq_int @ I @ J )
% 0.33/0.61           => ( ( upto @ I @ J )
% 0.33/0.61              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 0.33/0.61          & ( ~ ( ord_less_eq_int @ I @ J )
% 0.33/0.61           => ( ( upto @ I @ J )
% 0.33/0.61              = nil_int ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upto.psimps
% 0.33/0.61  thf(fact_5344_upto_Opinduct,axiom,
% 0.33/0.61      ! [A0: int,A12: int,P: int > int > $o] :
% 0.33/0.61        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 0.33/0.61       => ( ! [I3: int,J2: int] :
% 0.33/0.61              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 0.33/0.61             => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 0.33/0.61                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 0.33/0.61               => ( P @ I3 @ J2 ) ) )
% 0.33/0.61         => ( P @ A0 @ A12 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upto.pinduct
% 0.33/0.61  thf(fact_5345_divmod__integer__eq__cases,axiom,
% 0.33/0.61      ( code_divmod_integer
% 0.33/0.61      = ( ^ [K2: code_integer,L2: code_integer] :
% 0.33/0.61            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.33/0.61            @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 0.33/0.61              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 0.33/0.61                @ ( if_Pro6119634080678213985nteger
% 0.33/0.61                  @ ( ( sgn_sgn_Code_integer @ K2 )
% 0.33/0.61                    = ( sgn_sgn_Code_integer @ L2 ) )
% 0.33/0.61                  @ ( code_divmod_abs @ K2 @ L2 )
% 0.33/0.61                  @ ( produc6916734918728496179nteger
% 0.33/0.61                    @ ^ [R2: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R2 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S4 ) ) )
% 0.33/0.61                    @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % divmod_integer_eq_cases
% 0.33/0.61  thf(fact_5346_divmod__abs__code_I6_J,axiom,
% 0.33/0.61      ! [J: code_integer] :
% 0.33/0.61        ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 0.33/0.61        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 0.33/0.61  
% 0.33/0.61  % divmod_abs_code(6)
% 0.33/0.61  thf(fact_5347_divmod__abs__code_I5_J,axiom,
% 0.33/0.61      ! [J: code_integer] :
% 0.33/0.61        ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 0.33/0.61        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % divmod_abs_code(5)
% 0.33/0.61  thf(fact_5348_divmod__integer__code,axiom,
% 0.33/0.61      ( code_divmod_integer
% 0.33/0.61      = ( ^ [K2: code_integer,L2: code_integer] :
% 0.33/0.61            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.33/0.61            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 0.33/0.61              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L2 )
% 0.33/0.61                @ ( produc6916734918728496179nteger
% 0.33/0.61                  @ ^ [R2: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R2 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S4 ) ) )
% 0.33/0.61                  @ ( code_divmod_abs @ K2 @ L2 ) ) )
% 0.33/0.61              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 0.33/0.61                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.33/0.61                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L2 )
% 0.33/0.61                    @ ( produc6916734918728496179nteger
% 0.33/0.61                      @ ^ [R2: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R2 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S4 ) ) )
% 0.33/0.61                      @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % divmod_integer_code
% 0.33/0.61  thf(fact_5349_divmod__abs__def,axiom,
% 0.33/0.61      ( code_divmod_abs
% 0.33/0.61      = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % divmod_abs_def
% 0.33/0.61  thf(fact_5350_bit__cut__integer__code,axiom,
% 0.33/0.61      ( code_bit_cut_integer
% 0.33/0.61      = ( ^ [K2: code_integer] :
% 0.33/0.61            ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.33/0.61            @ ( produc9125791028180074456eger_o
% 0.33/0.61              @ ^ [R2: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R2 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R2 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 0.33/0.61              @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bit_cut_integer_code
% 0.33/0.61  thf(fact_5351_normalize__negative,axiom,
% 0.33/0.61      ! [Q2: int,P3: int] :
% 0.33/0.61        ( ( ord_less_int @ Q2 @ zero_zero_int )
% 0.33/0.61       => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q2 ) )
% 0.33/0.61          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P3 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % normalize_negative
% 0.33/0.61  thf(fact_5352_bit__cut__integer__def,axiom,
% 0.33/0.61      ( code_bit_cut_integer
% 0.33/0.61      = ( ^ [K2: code_integer] :
% 0.33/0.61            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.33/0.61            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bit_cut_integer_def
% 0.33/0.61  thf(fact_5353_normalize__denom__zero,axiom,
% 0.33/0.61      ! [P3: int] :
% 0.33/0.61        ( ( normalize @ ( product_Pair_int_int @ P3 @ zero_zero_int ) )
% 0.33/0.61        = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % normalize_denom_zero
% 0.33/0.61  thf(fact_5354_normalize__denom__pos,axiom,
% 0.33/0.61      ! [R: product_prod_int_int,P3: int,Q2: int] :
% 0.33/0.61        ( ( ( normalize @ R )
% 0.33/0.61          = ( product_Pair_int_int @ P3 @ Q2 ) )
% 0.33/0.61       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % normalize_denom_pos
% 0.33/0.61  thf(fact_5355_normalize__crossproduct,axiom,
% 0.33/0.61      ! [Q2: int,S: int,P3: int,R: int] :
% 0.33/0.61        ( ( Q2 != zero_zero_int )
% 0.33/0.61       => ( ( S != zero_zero_int )
% 0.33/0.61         => ( ( ( normalize @ ( product_Pair_int_int @ P3 @ Q2 ) )
% 0.33/0.61              = ( normalize @ ( product_Pair_int_int @ R @ S ) ) )
% 0.33/0.61           => ( ( times_times_int @ P3 @ S )
% 0.33/0.61              = ( times_times_int @ R @ Q2 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % normalize_crossproduct
% 0.33/0.61  thf(fact_5356_prod__decode__aux_Oelims,axiom,
% 0.33/0.61      ! [X2: nat,Xa: nat,Y: product_prod_nat_nat] :
% 0.33/0.61        ( ( ( nat_prod_decode_aux @ X2 @ Xa )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( ( ord_less_eq_nat @ Xa @ X2 )
% 0.33/0.61           => ( Y
% 0.33/0.61              = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X2 @ Xa ) ) ) )
% 0.33/0.61          & ( ~ ( ord_less_eq_nat @ Xa @ X2 )
% 0.33/0.61           => ( Y
% 0.33/0.61              = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa @ ( suc @ X2 ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % prod_decode_aux.elims
% 0.33/0.61  thf(fact_5357_prod__decode__aux_Osimps,axiom,
% 0.33/0.61      ( nat_prod_decode_aux
% 0.33/0.61      = ( ^ [K2: nat,M2: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M2 @ K2 ) @ ( product_Pair_nat_nat @ M2 @ ( minus_minus_nat @ K2 @ M2 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M2 @ ( suc @ K2 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % prod_decode_aux.simps
% 0.33/0.61  thf(fact_5358_bezw__0,axiom,
% 0.33/0.61      ! [X2: nat] :
% 0.33/0.61        ( ( bezw @ X2 @ zero_zero_nat )
% 0.33/0.61        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bezw_0
% 0.33/0.61  thf(fact_5359_times__int_Oabs__eq,axiom,
% 0.33/0.61      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.33/0.61        ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 0.33/0.61        = ( abs_Integ
% 0.33/0.61          @ ( produc27273713700761075at_nat
% 0.33/0.61            @ ^ [X: nat,Y4: nat] :
% 0.33/0.61                ( produc2626176000494625587at_nat
% 0.33/0.61                @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) )
% 0.33/0.61            @ Xa
% 0.33/0.61            @ X2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % times_int.abs_eq
% 0.33/0.61  thf(fact_5360_int_Oabs__induct,axiom,
% 0.33/0.61      ! [P: int > $o,X2: int] :
% 0.33/0.61        ( ! [Y2: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y2 ) )
% 0.33/0.61       => ( P @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % int.abs_induct
% 0.33/0.61  thf(fact_5361_eq__Abs__Integ,axiom,
% 0.33/0.61      ! [Z2: int] :
% 0.33/0.61        ~ ! [X3: nat,Y2: nat] :
% 0.33/0.61            ( Z2
% 0.33/0.61           != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % eq_Abs_Integ
% 0.33/0.61  thf(fact_5362_nat_Oabs__eq,axiom,
% 0.33/0.61      ! [X2: product_prod_nat_nat] :
% 0.33/0.61        ( ( nat2 @ ( abs_Integ @ X2 ) )
% 0.33/0.61        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % nat.abs_eq
% 0.33/0.61  thf(fact_5363_zero__int__def,axiom,
% 0.33/0.61      ( zero_zero_int
% 0.33/0.61      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % zero_int_def
% 0.33/0.61  thf(fact_5364_int__def,axiom,
% 0.33/0.61      ( semiri1314217659103216013at_int
% 0.33/0.61      = ( ^ [N3: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N3 @ zero_zero_nat ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % int_def
% 0.33/0.61  thf(fact_5365_uminus__int_Oabs__eq,axiom,
% 0.33/0.61      ! [X2: product_prod_nat_nat] :
% 0.33/0.61        ( ( uminus_uminus_int @ ( abs_Integ @ X2 ) )
% 0.33/0.61        = ( abs_Integ
% 0.33/0.61          @ ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X )
% 0.33/0.61            @ X2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % uminus_int.abs_eq
% 0.33/0.61  thf(fact_5366_one__int__def,axiom,
% 0.33/0.61      ( one_one_int
% 0.33/0.61      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % one_int_def
% 0.33/0.61  thf(fact_5367_less__int_Oabs__eq,axiom,
% 0.33/0.61      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.33/0.61        ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 0.33/0.61        = ( produc8739625826339149834_nat_o
% 0.33/0.61          @ ^ [X: nat,Y4: nat] :
% 0.33/0.61              ( produc6081775807080527818_nat_o
% 0.33/0.61              @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) )
% 0.33/0.61          @ Xa
% 0.33/0.61          @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_int.abs_eq
% 0.33/0.61  thf(fact_5368_less__eq__int_Oabs__eq,axiom,
% 0.33/0.61      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.33/0.61        ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 0.33/0.61        = ( produc8739625826339149834_nat_o
% 0.33/0.61          @ ^ [X: nat,Y4: nat] :
% 0.33/0.61              ( produc6081775807080527818_nat_o
% 0.33/0.61              @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) )
% 0.33/0.61          @ Xa
% 0.33/0.61          @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_eq_int.abs_eq
% 0.33/0.61  thf(fact_5369_plus__int_Oabs__eq,axiom,
% 0.33/0.61      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.33/0.61        ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 0.33/0.61        = ( abs_Integ
% 0.33/0.61          @ ( produc27273713700761075at_nat
% 0.33/0.61            @ ^ [X: nat,Y4: nat] :
% 0.33/0.61                ( produc2626176000494625587at_nat
% 0.33/0.61                @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) )
% 0.33/0.61            @ Xa
% 0.33/0.61            @ X2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_int.abs_eq
% 0.33/0.61  thf(fact_5370_minus__int_Oabs__eq,axiom,
% 0.33/0.61      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 0.33/0.61        ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 0.33/0.61        = ( abs_Integ
% 0.33/0.61          @ ( produc27273713700761075at_nat
% 0.33/0.61            @ ^ [X: nat,Y4: nat] :
% 0.33/0.61                ( produc2626176000494625587at_nat
% 0.33/0.61                @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) )
% 0.33/0.61            @ Xa
% 0.33/0.61            @ X2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % minus_int.abs_eq
% 0.33/0.61  thf(fact_5371_rat__minus__code,axiom,
% 0.33/0.61      ! [P3: rat,Q2: rat] :
% 0.33/0.61        ( ( quotient_of @ ( minus_minus_rat @ P3 @ Q2 ) )
% 0.33/0.61        = ( produc4245557441103728435nt_int
% 0.33/0.61          @ ^ [A2: int,C4: int] :
% 0.33/0.61              ( produc4245557441103728435nt_int
% 0.33/0.61              @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ B2 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 0.33/0.61              @ ( quotient_of @ Q2 ) )
% 0.33/0.61          @ ( quotient_of @ P3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_minus_code
% 0.33/0.61  thf(fact_5372_rat__plus__code,axiom,
% 0.33/0.61      ! [P3: rat,Q2: rat] :
% 0.33/0.61        ( ( quotient_of @ ( plus_plus_rat @ P3 @ Q2 ) )
% 0.33/0.61        = ( produc4245557441103728435nt_int
% 0.33/0.61          @ ^ [A2: int,C4: int] :
% 0.33/0.61              ( produc4245557441103728435nt_int
% 0.33/0.61              @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ B2 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 0.33/0.61              @ ( quotient_of @ Q2 ) )
% 0.33/0.61          @ ( quotient_of @ P3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_plus_code
% 0.33/0.61  thf(fact_5373_sort__upto,axiom,
% 0.33/0.61      ! [I: int,J: int] :
% 0.33/0.61        ( ( linord1735203802627413978nt_int
% 0.33/0.61          @ ^ [X: int] : X
% 0.33/0.61          @ ( upto @ I @ J ) )
% 0.33/0.61        = ( upto @ I @ J ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sort_upto
% 0.33/0.61  thf(fact_5374_rat__one__code,axiom,
% 0.33/0.61      ( ( quotient_of @ one_one_rat )
% 0.33/0.61      = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_one_code
% 0.33/0.61  thf(fact_5375_rat__zero__code,axiom,
% 0.33/0.61      ( ( quotient_of @ zero_zero_rat )
% 0.33/0.61      = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_zero_code
% 0.33/0.61  thf(fact_5376_quotient__of__number_I3_J,axiom,
% 0.33/0.61      ! [K: num] :
% 0.33/0.61        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 0.33/0.61        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % quotient_of_number(3)
% 0.33/0.61  thf(fact_5377_quotient__of__number_I4_J,axiom,
% 0.33/0.61      ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.33/0.61      = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % quotient_of_number(4)
% 0.33/0.61  thf(fact_5378_quotient__of__number_I5_J,axiom,
% 0.33/0.61      ! [K: num] :
% 0.33/0.61        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.33/0.61        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % quotient_of_number(5)
% 0.33/0.61  thf(fact_5379_diff__rat__def,axiom,
% 0.33/0.61      ( minus_minus_rat
% 0.33/0.61      = ( ^ [Q6: rat,R2: rat] : ( plus_plus_rat @ Q6 @ ( uminus_uminus_rat @ R2 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % diff_rat_def
% 0.33/0.61  thf(fact_5380_quotient__of__denom__pos,axiom,
% 0.33/0.61      ! [R: rat,P3: int,Q2: int] :
% 0.33/0.61        ( ( ( quotient_of @ R )
% 0.33/0.61          = ( product_Pair_int_int @ P3 @ Q2 ) )
% 0.33/0.61       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % quotient_of_denom_pos
% 0.33/0.61  thf(fact_5381_rat__floor__code,axiom,
% 0.33/0.61      ( archim3151403230148437115or_rat
% 0.33/0.61      = ( ^ [P6: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P6 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_floor_code
% 0.33/0.61  thf(fact_5382_rat__uminus__code,axiom,
% 0.33/0.61      ! [P3: rat] :
% 0.33/0.61        ( ( quotient_of @ ( uminus_uminus_rat @ P3 ) )
% 0.33/0.61        = ( produc4245557441103728435nt_int
% 0.33/0.61          @ ^ [A2: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A2 ) )
% 0.33/0.61          @ ( quotient_of @ P3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_uminus_code
% 0.33/0.61  thf(fact_5383_rat__abs__code,axiom,
% 0.33/0.61      ! [P3: rat] :
% 0.33/0.61        ( ( quotient_of @ ( abs_abs_rat @ P3 ) )
% 0.33/0.61        = ( produc4245557441103728435nt_int
% 0.33/0.61          @ ^ [A2: int] : ( product_Pair_int_int @ ( abs_abs_int @ A2 ) )
% 0.33/0.61          @ ( quotient_of @ P3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_abs_code
% 0.33/0.61  thf(fact_5384_rat__less__eq__code,axiom,
% 0.33/0.61      ( ord_less_eq_rat
% 0.33/0.61      = ( ^ [P6: rat,Q6: rat] :
% 0.33/0.61            ( produc4947309494688390418_int_o
% 0.33/0.61            @ ^ [A2: int,C4: int] :
% 0.33/0.61                ( produc4947309494688390418_int_o
% 0.33/0.61                @ ^ [B2: int,D4: int] : ( ord_less_eq_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ C4 @ B2 ) )
% 0.33/0.61                @ ( quotient_of @ Q6 ) )
% 0.33/0.61            @ ( quotient_of @ P6 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_less_eq_code
% 0.33/0.61  thf(fact_5385_rat__less__code,axiom,
% 0.33/0.61      ( ord_less_rat
% 0.33/0.61      = ( ^ [P6: rat,Q6: rat] :
% 0.33/0.61            ( produc4947309494688390418_int_o
% 0.33/0.61            @ ^ [A2: int,C4: int] :
% 0.33/0.61                ( produc4947309494688390418_int_o
% 0.33/0.61                @ ^ [B2: int,D4: int] : ( ord_less_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ C4 @ B2 ) )
% 0.33/0.61                @ ( quotient_of @ Q6 ) )
% 0.33/0.61            @ ( quotient_of @ P6 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_less_code
% 0.33/0.61  thf(fact_5386_rat__divide__code,axiom,
% 0.33/0.61      ! [P3: rat,Q2: rat] :
% 0.33/0.61        ( ( quotient_of @ ( divide_divide_rat @ P3 @ Q2 ) )
% 0.33/0.61        = ( produc4245557441103728435nt_int
% 0.33/0.61          @ ^ [A2: int,C4: int] :
% 0.33/0.61              ( produc4245557441103728435nt_int
% 0.33/0.61              @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ C4 @ B2 ) ) )
% 0.33/0.61              @ ( quotient_of @ Q2 ) )
% 0.33/0.61          @ ( quotient_of @ P3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_divide_code
% 0.33/0.61  thf(fact_5387_rat__times__code,axiom,
% 0.33/0.61      ! [P3: rat,Q2: rat] :
% 0.33/0.61        ( ( quotient_of @ ( times_times_rat @ P3 @ Q2 ) )
% 0.33/0.61        = ( produc4245557441103728435nt_int
% 0.33/0.61          @ ^ [A2: int,C4: int] :
% 0.33/0.61              ( produc4245557441103728435nt_int
% 0.33/0.61              @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ C4 @ D4 ) ) )
% 0.33/0.61              @ ( quotient_of @ Q2 ) )
% 0.33/0.61          @ ( quotient_of @ P3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_times_code
% 0.33/0.61  thf(fact_5388_quotient__of__int,axiom,
% 0.33/0.61      ! [A: int] :
% 0.33/0.61        ( ( quotient_of @ ( of_int @ A ) )
% 0.33/0.61        = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % quotient_of_int
% 0.33/0.61  thf(fact_5389_rat__inverse__code,axiom,
% 0.33/0.61      ! [P3: rat] :
% 0.33/0.61        ( ( quotient_of @ ( inverse_inverse_rat @ P3 ) )
% 0.33/0.61        = ( produc4245557441103728435nt_int
% 0.33/0.61          @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A2 ) @ B2 ) @ ( abs_abs_int @ A2 ) ) )
% 0.33/0.61          @ ( quotient_of @ P3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_inverse_code
% 0.33/0.61  thf(fact_5390_sgn__rat__def,axiom,
% 0.33/0.61      ( sgn_sgn_rat
% 0.33/0.61      = ( ^ [A2: rat] : ( if_rat @ ( A2 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A2 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sgn_rat_def
% 0.33/0.61  thf(fact_5391_Frct__code__post_I5_J,axiom,
% 0.33/0.61      ! [K: num] :
% 0.33/0.61        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 0.33/0.61        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Frct_code_post(5)
% 0.33/0.61  thf(fact_5392_pow_Osimps_I1_J,axiom,
% 0.33/0.61      ! [X2: num] :
% 0.33/0.61        ( ( pow @ X2 @ one )
% 0.33/0.61        = X2 ) ).
% 0.33/0.61  
% 0.33/0.61  % pow.simps(1)
% 0.33/0.61  thf(fact_5393_Frct__code__post_I1_J,axiom,
% 0.33/0.61      ! [A: int] :
% 0.33/0.61        ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 0.33/0.61        = zero_zero_rat ) ).
% 0.33/0.61  
% 0.33/0.61  % Frct_code_post(1)
% 0.33/0.61  thf(fact_5394_Frct__code__post_I2_J,axiom,
% 0.33/0.61      ! [A: int] :
% 0.33/0.61        ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 0.33/0.61        = zero_zero_rat ) ).
% 0.33/0.61  
% 0.33/0.61  % Frct_code_post(2)
% 0.33/0.61  thf(fact_5395_Frct__code__post_I3_J,axiom,
% 0.33/0.61      ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 0.33/0.61      = one_one_rat ) ).
% 0.33/0.61  
% 0.33/0.61  % Frct_code_post(3)
% 0.33/0.61  thf(fact_5396_Frct__code__post_I4_J,axiom,
% 0.33/0.61      ! [K: num] :
% 0.33/0.61        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 0.33/0.61        = ( numeral_numeral_rat @ K ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Frct_code_post(4)
% 0.33/0.61  thf(fact_5397_less__eq__int_Orep__eq,axiom,
% 0.33/0.61      ( ord_less_eq_int
% 0.33/0.61      = ( ^ [X: int,Xa4: int] :
% 0.33/0.61            ( produc8739625826339149834_nat_o
% 0.33/0.61            @ ^ [Y4: nat,Z3: nat] :
% 0.33/0.61                ( produc6081775807080527818_nat_o
% 0.33/0.61                @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y4 @ V3 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 0.33/0.61            @ ( rep_Integ @ X )
% 0.33/0.61            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_eq_int.rep_eq
% 0.33/0.61  thf(fact_5398_nat_Orep__eq,axiom,
% 0.33/0.61      ( nat2
% 0.33/0.61      = ( ^ [X: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % nat.rep_eq
% 0.33/0.61  thf(fact_5399_less__int_Orep__eq,axiom,
% 0.33/0.61      ( ord_less_int
% 0.33/0.61      = ( ^ [X: int,Xa4: int] :
% 0.33/0.61            ( produc8739625826339149834_nat_o
% 0.33/0.61            @ ^ [Y4: nat,Z3: nat] :
% 0.33/0.61                ( produc6081775807080527818_nat_o
% 0.33/0.61                @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y4 @ V3 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 0.33/0.61            @ ( rep_Integ @ X )
% 0.33/0.61            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_int.rep_eq
% 0.33/0.61  thf(fact_5400_sort__upt,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( linord738340561235409698at_nat
% 0.33/0.61          @ ^ [X: nat] : X
% 0.33/0.61          @ ( upt @ M @ N ) )
% 0.33/0.61        = ( upt @ M @ N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sort_upt
% 0.33/0.61  thf(fact_5401_upt__0__eq__Nil__conv,axiom,
% 0.33/0.61      ! [J: nat] :
% 0.33/0.61        ( ( ( upt @ zero_zero_nat @ J )
% 0.33/0.61          = nil_nat )
% 0.33/0.61        = ( J = zero_zero_nat ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_0_eq_Nil_conv
% 0.33/0.61  thf(fact_5402_upt__merge,axiom,
% 0.33/0.61      ! [I: nat,J: nat,K: nat] :
% 0.33/0.61        ( ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.61          & ( ord_less_eq_nat @ J @ K ) )
% 0.33/0.61       => ( ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ K ) )
% 0.33/0.61          = ( upt @ I @ K ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_merge
% 0.33/0.61  thf(fact_5403_upt__conv__Nil,axiom,
% 0.33/0.61      ! [J: nat,I: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ J @ I )
% 0.33/0.61       => ( ( upt @ I @ J )
% 0.33/0.61          = nil_nat ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_conv_Nil
% 0.33/0.61  thf(fact_5404_drop__upt,axiom,
% 0.33/0.61      ! [M: nat,I: nat,J: nat] :
% 0.33/0.61        ( ( drop_nat @ M @ ( upt @ I @ J ) )
% 0.33/0.61        = ( upt @ ( plus_plus_nat @ I @ M ) @ J ) ) ).
% 0.33/0.61  
% 0.33/0.61  % drop_upt
% 0.33/0.61  thf(fact_5405_upt__eq__Nil__conv,axiom,
% 0.33/0.61      ! [I: nat,J: nat] :
% 0.33/0.61        ( ( ( upt @ I @ J )
% 0.33/0.61          = nil_nat )
% 0.33/0.61        = ( ( J = zero_zero_nat )
% 0.33/0.61          | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_eq_Nil_conv
% 0.33/0.61  thf(fact_5406_take__upt,axiom,
% 0.33/0.61      ! [I: nat,M: nat,N: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 0.33/0.61       => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 0.33/0.61          = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % take_upt
% 0.33/0.61  thf(fact_5407_length__upt,axiom,
% 0.33/0.61      ! [I: nat,J: nat] :
% 0.33/0.61        ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 0.33/0.61        = ( minus_minus_nat @ J @ I ) ) ).
% 0.33/0.61  
% 0.33/0.61  % length_upt
% 0.33/0.61  thf(fact_5408_last__upt,axiom,
% 0.33/0.61      ! [I: nat,J: nat] :
% 0.33/0.61        ( ( ord_less_nat @ I @ J )
% 0.33/0.61       => ( ( last_nat @ ( upt @ I @ J ) )
% 0.33/0.61          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % last_upt
% 0.33/0.61  thf(fact_5409_nth__upt,axiom,
% 0.33/0.61      ! [I: nat,K: nat,J: nat] :
% 0.33/0.61        ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 0.33/0.61       => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 0.33/0.61          = ( plus_plus_nat @ I @ K ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % nth_upt
% 0.33/0.61  thf(fact_5410_map__add__upt_H,axiom,
% 0.33/0.61      ! [Ofs: nat,A: nat,B: nat] :
% 0.33/0.61        ( ( map_nat_nat
% 0.33/0.61          @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ Ofs )
% 0.33/0.61          @ ( upt @ A @ B ) )
% 0.33/0.61        = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % map_add_upt'
% 0.33/0.61  thf(fact_5411_upt__eq__append__conv,axiom,
% 0.33/0.61      ! [I: nat,J: nat,Xs: list_nat,Ys: list_nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.61       => ( ( ( upt @ I @ J )
% 0.33/0.61            = ( append_nat @ Xs @ Ys ) )
% 0.33/0.61          = ( ? [K2: nat] :
% 0.33/0.61                ( ( ord_less_eq_nat @ I @ K2 )
% 0.33/0.61                & ( ord_less_eq_nat @ K2 @ J )
% 0.33/0.61                & ( ( upt @ I @ K2 )
% 0.33/0.61                  = Xs )
% 0.33/0.61                & ( ( upt @ K2 @ J )
% 0.33/0.61                  = Ys ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_eq_append_conv
% 0.33/0.61  thf(fact_5412_upt__0,axiom,
% 0.33/0.61      ! [I: nat] :
% 0.33/0.61        ( ( upt @ I @ zero_zero_nat )
% 0.33/0.61        = nil_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_0
% 0.33/0.61  thf(fact_5413_upt__append,axiom,
% 0.33/0.61      ! [I: nat,J: nat] :
% 0.33/0.61        ( ( ord_less_nat @ I @ J )
% 0.33/0.61       => ( ( append_nat @ ( upt @ zero_zero_nat @ I ) @ ( upt @ I @ J ) )
% 0.33/0.61          = ( upt @ zero_zero_nat @ J ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_append
% 0.33/0.61  thf(fact_5414_upt__add__eq__append,axiom,
% 0.33/0.61      ! [I: nat,J: nat,K: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.61       => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 0.33/0.61          = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_add_eq_append
% 0.33/0.61  thf(fact_5415_butlast__upt,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( butlast_nat @ ( upt @ M @ N ) )
% 0.33/0.61        = ( upt @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % butlast_upt
% 0.33/0.61  thf(fact_5416_atLeast__upt,axiom,
% 0.33/0.61      ( set_ord_lessThan_nat
% 0.33/0.61      = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % atLeast_upt
% 0.33/0.61  thf(fact_5417_map__add__upt,axiom,
% 0.33/0.61      ! [N: nat,M: nat] :
% 0.33/0.61        ( ( map_nat_nat
% 0.33/0.61          @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ N )
% 0.33/0.61          @ ( upt @ zero_zero_nat @ M ) )
% 0.33/0.61        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % map_add_upt
% 0.33/0.61  thf(fact_5418_sorted__upt,axiom,
% 0.33/0.61      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sorted_upt
% 0.33/0.61  thf(fact_5419_atMost__upto,axiom,
% 0.33/0.61      ( set_ord_atMost_nat
% 0.33/0.61      = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N3 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % atMost_upto
% 0.33/0.61  thf(fact_5420_upt__Suc__append,axiom,
% 0.33/0.61      ! [I: nat,J: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.61       => ( ( upt @ I @ ( suc @ J ) )
% 0.33/0.61          = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_Suc_append
% 0.33/0.61  thf(fact_5421_upt__Suc,axiom,
% 0.33/0.61      ! [I: nat,J: nat] :
% 0.33/0.61        ( ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.61         => ( ( upt @ I @ ( suc @ J ) )
% 0.33/0.61            = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 0.33/0.61        & ( ~ ( ord_less_eq_nat @ I @ J )
% 0.33/0.61         => ( ( upt @ I @ ( suc @ J ) )
% 0.33/0.61            = nil_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_Suc
% 0.33/0.61  thf(fact_5422_upt__filter__extend,axiom,
% 0.33/0.61      ! [U: nat,U3: nat,P: nat > $o] :
% 0.33/0.61        ( ( ord_less_eq_nat @ U @ U3 )
% 0.33/0.61       => ( ! [I3: nat] :
% 0.33/0.61              ( ( ( ord_less_eq_nat @ U @ I3 )
% 0.33/0.61                & ( ord_less_nat @ I3 @ U3 ) )
% 0.33/0.61             => ~ ( P @ I3 ) )
% 0.33/0.61         => ( ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U ) )
% 0.33/0.61            = ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U3 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_filter_extend
% 0.33/0.61  thf(fact_5423_map__decr__upt,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( map_nat_nat
% 0.33/0.61          @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 0.33/0.61          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.33/0.61        = ( upt @ M @ N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % map_decr_upt
% 0.33/0.61  thf(fact_5424_upt__eq__lel__conv,axiom,
% 0.33/0.61      ! [L: nat,H: nat,Is1: list_nat,I: nat,Is2: list_nat] :
% 0.33/0.61        ( ( ( upt @ L @ H )
% 0.33/0.61          = ( append_nat @ Is1 @ ( cons_nat @ I @ Is2 ) ) )
% 0.33/0.61        = ( ( Is1
% 0.33/0.61            = ( upt @ L @ I ) )
% 0.33/0.61          & ( Is2
% 0.33/0.61            = ( upt @ ( suc @ I ) @ H ) )
% 0.33/0.61          & ( ord_less_eq_nat @ L @ I )
% 0.33/0.61          & ( ord_less_nat @ I @ H ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_eq_lel_conv
% 0.33/0.61  thf(fact_5425_upt__eq__Cons__conv,axiom,
% 0.33/0.61      ! [I: nat,J: nat,X2: nat,Xs: list_nat] :
% 0.33/0.61        ( ( ( upt @ I @ J )
% 0.33/0.61          = ( cons_nat @ X2 @ Xs ) )
% 0.33/0.61        = ( ( ord_less_nat @ I @ J )
% 0.33/0.61          & ( I = X2 )
% 0.33/0.61          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 0.33/0.61            = Xs ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % upt_eq_Cons_conv
% 0.33/0.61  thf(fact_5426_sum__list__upt,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.61       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 0.33/0.61          = ( groups3542108847815614940at_nat
% 0.33/0.61            @ ^ [X: nat] : X
% 0.33/0.61            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sum_list_upt
% 0.33/0.61  thf(fact_5427_card__length__sum__list__rec,axiom,
% 0.33/0.61      ! [M: nat,N4: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.33/0.61       => ( ( finite_card_list_nat
% 0.33/0.61            @ ( collect_list_nat
% 0.33/0.61              @ ^ [L2: list_nat] :
% 0.33/0.61                  ( ( ( size_size_list_nat @ L2 )
% 0.33/0.61                    = M )
% 0.33/0.61                  & ( ( groups4561878855575611511st_nat @ L2 )
% 0.33/0.61                    = N4 ) ) ) )
% 0.33/0.61          = ( plus_plus_nat
% 0.33/0.61            @ ( finite_card_list_nat
% 0.33/0.61              @ ( collect_list_nat
% 0.33/0.61                @ ^ [L2: list_nat] :
% 0.33/0.61                    ( ( ( size_size_list_nat @ L2 )
% 0.33/0.61                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 0.33/0.61                    & ( ( groups4561878855575611511st_nat @ L2 )
% 0.33/0.61                      = N4 ) ) ) )
% 0.33/0.61            @ ( finite_card_list_nat
% 0.33/0.61              @ ( collect_list_nat
% 0.33/0.61                @ ^ [L2: list_nat] :
% 0.33/0.61                    ( ( ( size_size_list_nat @ L2 )
% 0.33/0.61                      = M )
% 0.33/0.61                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 0.33/0.61                      = N4 ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % card_length_sum_list_rec
% 0.33/0.61  thf(fact_5428_card__length__sum__list,axiom,
% 0.33/0.61      ! [M: nat,N4: nat] :
% 0.33/0.61        ( ( finite_card_list_nat
% 0.33/0.61          @ ( collect_list_nat
% 0.33/0.61            @ ^ [L2: list_nat] :
% 0.33/0.61                ( ( ( size_size_list_nat @ L2 )
% 0.33/0.61                  = M )
% 0.33/0.61                & ( ( groups4561878855575611511st_nat @ L2 )
% 0.33/0.61                  = N4 ) ) ) )
% 0.33/0.61        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % card_length_sum_list
% 0.33/0.61  thf(fact_5429_floor__rat__def,axiom,
% 0.33/0.61      ( archim3151403230148437115or_rat
% 0.33/0.61      = ( ^ [X: rat] :
% 0.33/0.61            ( the_int
% 0.33/0.61            @ ^ [Z3: int] :
% 0.33/0.61                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 0.33/0.61                & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % floor_rat_def
% 0.33/0.61  thf(fact_5430_uminus__int__def,axiom,
% 0.33/0.61      ( uminus_uminus_int
% 0.33/0.61      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 0.33/0.61        @ ( produc2626176000494625587at_nat
% 0.33/0.61          @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % uminus_int_def
% 0.33/0.61  thf(fact_5431_times__int__def,axiom,
% 0.33/0.61      ( times_times_int
% 0.33/0.61      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.33/0.61        @ ( produc27273713700761075at_nat
% 0.33/0.61          @ ^ [X: nat,Y4: nat] :
% 0.33/0.61              ( produc2626176000494625587at_nat
% 0.33/0.61              @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % times_int_def
% 0.33/0.61  thf(fact_5432_minus__int__def,axiom,
% 0.33/0.61      ( minus_minus_int
% 0.33/0.61      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.33/0.61        @ ( produc27273713700761075at_nat
% 0.33/0.61          @ ^ [X: nat,Y4: nat] :
% 0.33/0.61              ( produc2626176000494625587at_nat
% 0.33/0.61              @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % minus_int_def
% 0.33/0.61  thf(fact_5433_plus__int__def,axiom,
% 0.33/0.61      ( plus_plus_int
% 0.33/0.61      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.33/0.61        @ ( produc27273713700761075at_nat
% 0.33/0.61          @ ^ [X: nat,Y4: nat] :
% 0.33/0.61              ( produc2626176000494625587at_nat
% 0.33/0.61              @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_int_def
% 0.33/0.61  thf(fact_5434_prod__encode__def,axiom,
% 0.33/0.61      ( nat_prod_encode
% 0.33/0.61      = ( produc6842872674320459806at_nat
% 0.33/0.61        @ ^ [M2: nat,N3: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M2 @ N3 ) ) @ M2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % prod_encode_def
% 0.33/0.61  thf(fact_5435_le__prod__encode__1,axiom,
% 0.33/0.61      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % le_prod_encode_1
% 0.33/0.61  thf(fact_5436_le__prod__encode__2,axiom,
% 0.33/0.61      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % le_prod_encode_2
% 0.33/0.61  thf(fact_5437_prod__encode__prod__decode__aux,axiom,
% 0.33/0.61      ! [K: nat,M: nat] :
% 0.33/0.61        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 0.33/0.61        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 0.33/0.61  
% 0.33/0.61  % prod_encode_prod_decode_aux
% 0.33/0.61  thf(fact_5438_list__encode_Oelims,axiom,
% 0.33/0.61      ! [X2: list_nat,Y: nat] :
% 0.33/0.61        ( ( ( nat_list_encode @ X2 )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( ( X2 = nil_nat )
% 0.33/0.61           => ( Y != zero_zero_nat ) )
% 0.33/0.61         => ~ ! [X3: nat,Xs2: list_nat] :
% 0.33/0.61                ( ( X2
% 0.33/0.61                  = ( cons_nat @ X3 @ Xs2 ) )
% 0.33/0.61               => ( Y
% 0.33/0.61                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % list_encode.elims
% 0.33/0.61  thf(fact_5439_list__encode_Opelims,axiom,
% 0.33/0.61      ! [X2: list_nat,Y: nat] :
% 0.33/0.61        ( ( ( nat_list_encode @ X2 )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( accp_list_nat @ nat_list_encode_rel @ X2 )
% 0.33/0.61         => ( ( ( X2 = nil_nat )
% 0.33/0.61             => ( ( Y = zero_zero_nat )
% 0.33/0.61               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 0.33/0.61           => ~ ! [X3: nat,Xs2: list_nat] :
% 0.33/0.61                  ( ( X2
% 0.33/0.61                    = ( cons_nat @ X3 @ Xs2 ) )
% 0.33/0.61                 => ( ( Y
% 0.33/0.61                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 0.33/0.61                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs2 ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % list_encode.pelims
% 0.33/0.61  thf(fact_5440_list__encode_Osimps_I1_J,axiom,
% 0.33/0.61      ( ( nat_list_encode @ nil_nat )
% 0.33/0.61      = zero_zero_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % list_encode.simps(1)
% 0.33/0.61  thf(fact_5441_rat__floor__lemma,axiom,
% 0.33/0.61      ! [A: int,B: int] :
% 0.33/0.61        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 0.33/0.61        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_floor_lemma
% 0.33/0.61  thf(fact_5442_less__rat,axiom,
% 0.33/0.61      ! [B: int,D: int,A: int,C: int] :
% 0.33/0.61        ( ( B != zero_zero_int )
% 0.33/0.61       => ( ( D != zero_zero_int )
% 0.33/0.61         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.33/0.61            = ( 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 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_rat
% 0.33/0.61  thf(fact_5443_le__rat,axiom,
% 0.33/0.61      ! [B: int,D: int,A: int,C: int] :
% 0.33/0.61        ( ( B != zero_zero_int )
% 0.33/0.61       => ( ( D != zero_zero_int )
% 0.33/0.61         => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.33/0.61            = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % le_rat
% 0.33/0.61  thf(fact_5444_add__rat,axiom,
% 0.33/0.61      ! [B: int,D: int,A: int,C: int] :
% 0.33/0.61        ( ( B != zero_zero_int )
% 0.33/0.61       => ( ( D != zero_zero_int )
% 0.33/0.61         => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.33/0.61            = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % add_rat
% 0.33/0.61  thf(fact_5445_diff__rat,axiom,
% 0.33/0.61      ! [B: int,D: int,A: int,C: int] :
% 0.33/0.61        ( ( B != zero_zero_int )
% 0.33/0.61       => ( ( D != zero_zero_int )
% 0.33/0.61         => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.33/0.61            = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % diff_rat
% 0.33/0.61  thf(fact_5446_eq__rat_I3_J,axiom,
% 0.33/0.61      ! [A: int,C: int] :
% 0.33/0.61        ( ( fract @ zero_zero_int @ A )
% 0.33/0.61        = ( fract @ zero_zero_int @ C ) ) ).
% 0.33/0.61  
% 0.33/0.61  % eq_rat(3)
% 0.33/0.61  thf(fact_5447_Rat__induct__pos,axiom,
% 0.33/0.61      ! [P: rat > $o,Q2: rat] :
% 0.33/0.61        ( ! [A3: int,B3: int] :
% 0.33/0.61            ( ( ord_less_int @ zero_zero_int @ B3 )
% 0.33/0.61           => ( P @ ( fract @ A3 @ B3 ) ) )
% 0.33/0.61       => ( P @ Q2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Rat_induct_pos
% 0.33/0.61  thf(fact_5448_eq__rat_I2_J,axiom,
% 0.33/0.61      ! [A: int] :
% 0.33/0.61        ( ( fract @ A @ zero_zero_int )
% 0.33/0.61        = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % eq_rat(2)
% 0.33/0.61  thf(fact_5449_mult__rat__cancel,axiom,
% 0.33/0.61      ! [C: int,A: int,B: int] :
% 0.33/0.61        ( ( C != zero_zero_int )
% 0.33/0.61       => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.33/0.61          = ( fract @ A @ B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % mult_rat_cancel
% 0.33/0.61  thf(fact_5450_eq__rat_I1_J,axiom,
% 0.33/0.61      ! [B: int,D: int,A: int,C: int] :
% 0.33/0.61        ( ( B != zero_zero_int )
% 0.33/0.61       => ( ( D != zero_zero_int )
% 0.33/0.61         => ( ( ( fract @ A @ B )
% 0.33/0.61              = ( fract @ C @ D ) )
% 0.33/0.61            = ( ( times_times_int @ A @ D )
% 0.33/0.61              = ( times_times_int @ C @ B ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % eq_rat(1)
% 0.33/0.61  thf(fact_5451_Fract__of__nat__eq,axiom,
% 0.33/0.61      ! [K: nat] :
% 0.33/0.61        ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 0.33/0.61        = ( semiri681578069525770553at_rat @ K ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract_of_nat_eq
% 0.33/0.61  thf(fact_5452_rat__number__collapse_I1_J,axiom,
% 0.33/0.61      ! [K: int] :
% 0.33/0.61        ( ( fract @ zero_zero_int @ K )
% 0.33/0.61        = zero_zero_rat ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_number_collapse(1)
% 0.33/0.61  thf(fact_5453_rat__number__collapse_I6_J,axiom,
% 0.33/0.61      ! [K: int] :
% 0.33/0.61        ( ( fract @ K @ zero_zero_int )
% 0.33/0.61        = zero_zero_rat ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_number_collapse(6)
% 0.33/0.61  thf(fact_5454_One__rat__def,axiom,
% 0.33/0.61      ( one_one_rat
% 0.33/0.61      = ( fract @ one_one_int @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % One_rat_def
% 0.33/0.61  thf(fact_5455_Fract__of__int__eq,axiom,
% 0.33/0.61      ! [K: int] :
% 0.33/0.61        ( ( fract @ K @ one_one_int )
% 0.33/0.61        = ( ring_1_of_int_rat @ K ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract_of_int_eq
% 0.33/0.61  thf(fact_5456_Zero__rat__def,axiom,
% 0.33/0.61      ( zero_zero_rat
% 0.33/0.61      = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Zero_rat_def
% 0.33/0.61  thf(fact_5457_rat__number__expand_I3_J,axiom,
% 0.33/0.61      ( numeral_numeral_rat
% 0.33/0.61      = ( ^ [K2: num] : ( fract @ ( numeral_numeral_int @ K2 ) @ one_one_int ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_number_expand(3)
% 0.33/0.61  thf(fact_5458_rat__number__collapse_I3_J,axiom,
% 0.33/0.61      ! [W2: num] :
% 0.33/0.61        ( ( fract @ ( numeral_numeral_int @ W2 ) @ one_one_int )
% 0.33/0.61        = ( numeral_numeral_rat @ W2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_number_collapse(3)
% 0.33/0.61  thf(fact_5459_zero__less__Fract__iff,axiom,
% 0.33/0.61      ! [B: int,A: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.33/0.61          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % zero_less_Fract_iff
% 0.33/0.61  thf(fact_5460_Fract__less__zero__iff,axiom,
% 0.33/0.61      ! [B: int,A: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.33/0.61          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract_less_zero_iff
% 0.33/0.61  thf(fact_5461_Fract__less__one__iff,axiom,
% 0.33/0.61      ! [B: int,A: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.33/0.61          = ( ord_less_int @ A @ B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract_less_one_iff
% 0.33/0.61  thf(fact_5462_one__less__Fract__iff,axiom,
% 0.33/0.61      ! [B: int,A: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.33/0.61          = ( ord_less_int @ B @ A ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % one_less_Fract_iff
% 0.33/0.61  thf(fact_5463_rat__number__collapse_I5_J,axiom,
% 0.33/0.61      ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.33/0.61      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_number_collapse(5)
% 0.33/0.61  thf(fact_5464_Fract__add__one,axiom,
% 0.33/0.61      ! [N: int,M: int] :
% 0.33/0.61        ( ( N != zero_zero_int )
% 0.33/0.61       => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 0.33/0.61          = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract_add_one
% 0.33/0.61  thf(fact_5465_Fract__le__zero__iff,axiom,
% 0.33/0.61      ! [B: int,A: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.33/0.61          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract_le_zero_iff
% 0.33/0.61  thf(fact_5466_zero__le__Fract__iff,axiom,
% 0.33/0.61      ! [B: int,A: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.33/0.61          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % zero_le_Fract_iff
% 0.33/0.61  thf(fact_5467_Fract__le__one__iff,axiom,
% 0.33/0.61      ! [B: int,A: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.33/0.61          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract_le_one_iff
% 0.33/0.61  thf(fact_5468_one__le__Fract__iff,axiom,
% 0.33/0.61      ! [B: int,A: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.33/0.61          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % one_le_Fract_iff
% 0.33/0.61  thf(fact_5469_rat__number__expand_I5_J,axiom,
% 0.33/0.61      ! [K: num] :
% 0.33/0.61        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 0.33/0.61        = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_number_expand(5)
% 0.33/0.61  thf(fact_5470_rat__number__collapse_I4_J,axiom,
% 0.33/0.61      ! [W2: num] :
% 0.33/0.61        ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ one_one_int )
% 0.33/0.61        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_number_collapse(4)
% 0.33/0.61  thf(fact_5471_pow_Osimps_I3_J,axiom,
% 0.33/0.61      ! [X2: num,Y: num] :
% 0.33/0.61        ( ( pow @ X2 @ ( bit1 @ Y ) )
% 0.33/0.61        = ( times_times_num @ ( sqr @ ( pow @ X2 @ Y ) ) @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % pow.simps(3)
% 0.33/0.61  thf(fact_5472_of__nat__eq__id,axiom,
% 0.33/0.61      semiri1316708129612266289at_nat = id_nat ).
% 0.33/0.61  
% 0.33/0.61  % of_nat_eq_id
% 0.33/0.61  thf(fact_5473_sqr_Osimps_I2_J,axiom,
% 0.33/0.61      ! [N: num] :
% 0.33/0.61        ( ( sqr @ ( bit0 @ N ) )
% 0.33/0.61        = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sqr.simps(2)
% 0.33/0.61  thf(fact_5474_sqr_Osimps_I1_J,axiom,
% 0.33/0.61      ( ( sqr @ one )
% 0.33/0.61      = one ) ).
% 0.33/0.61  
% 0.33/0.61  % sqr.simps(1)
% 0.33/0.61  thf(fact_5475_less__int__def,axiom,
% 0.33/0.61      ( ord_less_int
% 0.33/0.61      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.33/0.61        @ ( produc8739625826339149834_nat_o
% 0.33/0.61          @ ^ [X: nat,Y4: nat] :
% 0.33/0.61              ( produc6081775807080527818_nat_o
% 0.33/0.61              @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_int_def
% 0.33/0.61  thf(fact_5476_less__eq__int__def,axiom,
% 0.33/0.61      ( ord_less_eq_int
% 0.33/0.61      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.33/0.61        @ ( produc8739625826339149834_nat_o
% 0.33/0.61          @ ^ [X: nat,Y4: nat] :
% 0.33/0.61              ( produc6081775807080527818_nat_o
% 0.33/0.61              @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_eq_int_def
% 0.33/0.61  thf(fact_5477_sqr__conv__mult,axiom,
% 0.33/0.61      ( sqr
% 0.33/0.61      = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sqr_conv_mult
% 0.33/0.61  thf(fact_5478_nat__def,axiom,
% 0.33/0.61      ( nat2
% 0.33/0.61      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % nat_def
% 0.33/0.61  thf(fact_5479_pow_Osimps_I2_J,axiom,
% 0.33/0.61      ! [X2: num,Y: num] :
% 0.33/0.61        ( ( pow @ X2 @ ( bit0 @ Y ) )
% 0.33/0.61        = ( sqr @ ( pow @ X2 @ Y ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % pow.simps(2)
% 0.33/0.61  thf(fact_5480_sqr_Osimps_I3_J,axiom,
% 0.33/0.61      ! [N: num] :
% 0.33/0.61        ( ( sqr @ ( bit1 @ N ) )
% 0.33/0.61        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sqr.simps(3)
% 0.33/0.61  thf(fact_5481_positive__rat,axiom,
% 0.33/0.61      ! [A: int,B: int] :
% 0.33/0.61        ( ( positive @ ( fract @ A @ B ) )
% 0.33/0.61        = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % positive_rat
% 0.33/0.61  thf(fact_5482_less__eq__integer__def,axiom,
% 0.33/0.61      ( ord_le3102999989581377725nteger
% 0.33/0.61      = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_eq_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_eq_integer_def
% 0.33/0.61  thf(fact_5483_less__integer__def,axiom,
% 0.33/0.61      ( ord_le6747313008572928689nteger
% 0.33/0.61      = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_integer_def
% 0.33/0.61  thf(fact_5484_plus__integer__def,axiom,
% 0.33/0.61      ( plus_p5714425477246183910nteger
% 0.33/0.61      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ plus_plus_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_integer_def
% 0.33/0.61  thf(fact_5485_times__integer__def,axiom,
% 0.33/0.61      ( times_3573771949741848930nteger
% 0.33/0.61      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ times_times_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % times_integer_def
% 0.33/0.61  thf(fact_5486_minus__integer__def,axiom,
% 0.33/0.61      ( minus_8373710615458151222nteger
% 0.33/0.61      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ minus_minus_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % minus_integer_def
% 0.33/0.61  thf(fact_5487_divide__integer__def,axiom,
% 0.33/0.61      ( divide6298287555418463151nteger
% 0.33/0.61      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ divide_divide_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % divide_integer_def
% 0.33/0.61  thf(fact_5488_modulo__integer__def,axiom,
% 0.33/0.61      ( modulo364778990260209775nteger
% 0.33/0.61      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ modulo_modulo_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % modulo_integer_def
% 0.33/0.61  thf(fact_5489_positive__add,axiom,
% 0.33/0.61      ! [X2: rat,Y: rat] :
% 0.33/0.61        ( ( positive @ X2 )
% 0.33/0.61       => ( ( positive @ Y )
% 0.33/0.61         => ( positive @ ( plus_plus_rat @ X2 @ Y ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % positive_add
% 0.33/0.61  thf(fact_5490_and__integer__def,axiom,
% 0.33/0.61      ( bit_se3949692690581998587nteger
% 0.33/0.61      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se725231765392027082nd_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % and_integer_def
% 0.33/0.61  thf(fact_5491_or__integer__def,axiom,
% 0.33/0.61      ( bit_se1080825931792720795nteger
% 0.33/0.61      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se1409905431419307370or_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % or_integer_def
% 0.33/0.61  thf(fact_5492_take__bit__integer__def,axiom,
% 0.33/0.61      ( bit_se1745604003318907178nteger
% 0.33/0.61      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se2923211474154528505it_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % take_bit_integer_def
% 0.33/0.61  thf(fact_5493_xor__integer__def,axiom,
% 0.33/0.61      ( bit_se3222712562003087583nteger
% 0.33/0.61      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se6526347334894502574or_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % xor_integer_def
% 0.33/0.61  thf(fact_5494_drop__bit__integer__def,axiom,
% 0.33/0.61      ( bit_se3928097537394005634nteger
% 0.33/0.61      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se8568078237143864401it_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % drop_bit_integer_def
% 0.33/0.61  thf(fact_5495_push__bit__integer__def,axiom,
% 0.33/0.61      ( bit_se7788150548672797655nteger
% 0.33/0.61      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se545348938243370406it_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % push_bit_integer_def
% 0.33/0.61  thf(fact_5496_unset__bit__integer__def,axiom,
% 0.33/0.61      ( bit_se8260200283734997820nteger
% 0.33/0.61      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se4203085406695923979it_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % unset_bit_integer_def
% 0.33/0.61  thf(fact_5497_set__bit__integer__def,axiom,
% 0.33/0.61      ( bit_se2793503036327961859nteger
% 0.33/0.61      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se7879613467334960850it_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % set_bit_integer_def
% 0.33/0.61  thf(fact_5498_flip__bit__integer__def,axiom,
% 0.33/0.61      ( bit_se1345352211410354436nteger
% 0.33/0.61      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se2159334234014336723it_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % flip_bit_integer_def
% 0.33/0.61  thf(fact_5499_nat__of__integer__def,axiom,
% 0.33/0.61      ( code_nat_of_integer
% 0.33/0.61      = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ nat2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % nat_of_integer_def
% 0.33/0.61  thf(fact_5500_bit__integer__def,axiom,
% 0.33/0.61      ( bit_se9216721137139052372nteger
% 0.33/0.61      = ( map_fu186220595405829473_nat_o @ code_int_of_integer @ id_nat_o @ bit_se1146084159140164899it_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bit_integer_def
% 0.33/0.61  thf(fact_5501_uminus__integer__def,axiom,
% 0.33/0.61      ( uminus1351360451143612070nteger
% 0.33/0.61      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ uminus_uminus_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % uminus_integer_def
% 0.33/0.61  thf(fact_5502_abs__integer__def,axiom,
% 0.33/0.61      ( abs_abs_Code_integer
% 0.33/0.61      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ abs_abs_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % abs_integer_def
% 0.33/0.61  thf(fact_5503_mask__integer__def,axiom,
% 0.33/0.61      ( bit_se2119862282449309892nteger
% 0.33/0.61      = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ bit_se2000444600071755411sk_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % mask_integer_def
% 0.33/0.61  thf(fact_5504_sgn__integer__def,axiom,
% 0.33/0.61      ( sgn_sgn_Code_integer
% 0.33/0.61      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ sgn_sgn_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sgn_integer_def
% 0.33/0.61  thf(fact_5505_not__integer__def,axiom,
% 0.33/0.61      ( bit_ri7632146776885996613nteger
% 0.33/0.61      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ bit_ri7919022796975470100ot_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % not_integer_def
% 0.33/0.61  thf(fact_5506_num__of__integer__def,axiom,
% 0.33/0.61      ( code_num_of_integer
% 0.33/0.61      = ( map_fu1227494855608507351um_num @ code_int_of_integer @ id_num @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % num_of_integer_def
% 0.33/0.61  thf(fact_5507_min__0R,axiom,
% 0.33/0.61      ! [N: nat] :
% 0.33/0.61        ( ( ord_min_nat @ N @ zero_zero_nat )
% 0.33/0.61        = zero_zero_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % min_0R
% 0.33/0.61  thf(fact_5508_min__0L,axiom,
% 0.33/0.61      ! [N: nat] :
% 0.33/0.61        ( ( ord_min_nat @ zero_zero_nat @ N )
% 0.33/0.61        = zero_zero_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % min_0L
% 0.33/0.61  thf(fact_5509_min__Suc__Suc,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.33/0.61        = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % min_Suc_Suc
% 0.33/0.61  thf(fact_5510_min__Suc__gt_I2_J,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( ord_less_nat @ A @ B )
% 0.33/0.61       => ( ( ord_min_nat @ B @ ( suc @ A ) )
% 0.33/0.61          = ( suc @ A ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % min_Suc_gt(2)
% 0.33/0.61  thf(fact_5511_min__Suc__gt_I1_J,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( ord_less_nat @ A @ B )
% 0.33/0.61       => ( ( ord_min_nat @ ( suc @ A ) @ B )
% 0.33/0.61          = ( suc @ A ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % min_Suc_gt(1)
% 0.33/0.61  thf(fact_5512_min__numeral__Suc,axiom,
% 0.33/0.61      ! [K: num,N: nat] :
% 0.33/0.61        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.33/0.61        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % min_numeral_Suc
% 0.33/0.61  thf(fact_5513_min__Suc__numeral,axiom,
% 0.33/0.61      ! [N: nat,K: num] :
% 0.33/0.61        ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.33/0.61        = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % min_Suc_numeral
% 0.33/0.61  thf(fact_5514_nat__mult__min__left,axiom,
% 0.33/0.61      ! [M: nat,N: nat,Q2: nat] :
% 0.33/0.61        ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 0.33/0.61        = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % nat_mult_min_left
% 0.33/0.61  thf(fact_5515_nat__mult__min__right,axiom,
% 0.33/0.61      ! [M: nat,N: nat,Q2: nat] :
% 0.33/0.61        ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 0.33/0.61        = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % nat_mult_min_right
% 0.33/0.61  thf(fact_5516_inf__nat__def,axiom,
% 0.33/0.61      inf_inf_nat = ord_min_nat ).
% 0.33/0.61  
% 0.33/0.61  % inf_nat_def
% 0.33/0.61  thf(fact_5517_min__diff,axiom,
% 0.33/0.61      ! [M: nat,I: nat,N: nat] :
% 0.33/0.61        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 0.33/0.61        = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 0.33/0.61  
% 0.33/0.61  % min_diff
% 0.33/0.61  thf(fact_5518_min__Suc1,axiom,
% 0.33/0.61      ! [N: nat,M: nat] :
% 0.33/0.61        ( ( ord_min_nat @ ( suc @ N ) @ M )
% 0.33/0.61        = ( case_nat_nat @ zero_zero_nat
% 0.33/0.61          @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ N @ M7 ) )
% 0.33/0.61          @ M ) ) ).
% 0.33/0.61  
% 0.33/0.61  % min_Suc1
% 0.33/0.61  thf(fact_5519_min__Suc2,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( ord_min_nat @ M @ ( suc @ N ) )
% 0.33/0.61        = ( case_nat_nat @ zero_zero_nat
% 0.33/0.61          @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ M7 @ N ) )
% 0.33/0.61          @ M ) ) ).
% 0.33/0.61  
% 0.33/0.61  % min_Suc2
% 0.33/0.61  thf(fact_5520_integer__of__nat__def,axiom,
% 0.33/0.61      ( code_integer_of_nat
% 0.33/0.61      = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_nat_def
% 0.33/0.61  thf(fact_5521_nat__of__integer__integer__of__nat,axiom,
% 0.33/0.61      ! [N: nat] :
% 0.33/0.61        ( ( code_nat_of_integer @ ( code_integer_of_nat @ N ) )
% 0.33/0.61        = N ) ).
% 0.33/0.61  
% 0.33/0.61  % nat_of_integer_integer_of_nat
% 0.33/0.61  thf(fact_5522_fst__divmod__integer,axiom,
% 0.33/0.61      ! [K: code_integer,L: code_integer] :
% 0.33/0.61        ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L ) )
% 0.33/0.61        = ( divide6298287555418463151nteger @ K @ L ) ) ).
% 0.33/0.61  
% 0.33/0.61  % fst_divmod_integer
% 0.33/0.61  thf(fact_5523_int__of__integer__min,axiom,
% 0.33/0.61      ! [K: code_integer,L: code_integer] :
% 0.33/0.61        ( ( code_int_of_integer @ ( ord_min_Code_integer @ K @ L ) )
% 0.33/0.61        = ( ord_min_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % int_of_integer_min
% 0.33/0.61  thf(fact_5524_int__of__integer__integer__of__nat,axiom,
% 0.33/0.61      ! [N: nat] :
% 0.33/0.61        ( ( code_int_of_integer @ ( code_integer_of_nat @ N ) )
% 0.33/0.61        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % int_of_integer_integer_of_nat
% 0.33/0.61  thf(fact_5525_integer__of__nat_Orep__eq,axiom,
% 0.33/0.61      ! [X2: nat] :
% 0.33/0.61        ( ( code_int_of_integer @ ( code_integer_of_nat @ X2 ) )
% 0.33/0.61        = ( semiri1314217659103216013at_int @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_nat.rep_eq
% 0.33/0.61  thf(fact_5526_fst__divmod__abs,axiom,
% 0.33/0.61      ! [K: code_integer,L: code_integer] :
% 0.33/0.61        ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L ) )
% 0.33/0.61        = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % fst_divmod_abs
% 0.33/0.61  thf(fact_5527_Suc__0__div__numeral,axiom,
% 0.33/0.61      ! [K: num] :
% 0.33/0.61        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.33/0.61        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Suc_0_div_numeral
% 0.33/0.61  thf(fact_5528_inf__int__def,axiom,
% 0.33/0.61      inf_inf_int = ord_min_int ).
% 0.33/0.61  
% 0.33/0.61  % inf_int_def
% 0.33/0.61  thf(fact_5529_integer__of__nat__eq__of__nat,axiom,
% 0.33/0.61      code_integer_of_nat = semiri4939895301339042750nteger ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_nat_eq_of_nat
% 0.33/0.61  thf(fact_5530_integer__of__nat__0,axiom,
% 0.33/0.61      ( ( code_integer_of_nat @ zero_zero_nat )
% 0.33/0.61      = zero_z3403309356797280102nteger ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_nat_0
% 0.33/0.61  thf(fact_5531_integer__of__nat_Oabs__eq,axiom,
% 0.33/0.61      ( code_integer_of_nat
% 0.33/0.61      = ( ^ [X: nat] : ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_nat.abs_eq
% 0.33/0.61  thf(fact_5532_integer__of__nat__numeral,axiom,
% 0.33/0.61      ! [N: num] :
% 0.33/0.61        ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N ) )
% 0.33/0.61        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_nat_numeral
% 0.33/0.61  thf(fact_5533_integer__of__nat__1,axiom,
% 0.33/0.61      ( ( code_integer_of_nat @ one_one_nat )
% 0.33/0.61      = one_one_Code_integer ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_nat_1
% 0.33/0.61  thf(fact_5534_rat__sgn__code,axiom,
% 0.33/0.61      ! [P3: rat] :
% 0.33/0.61        ( ( quotient_of @ ( sgn_sgn_rat @ P3 ) )
% 0.33/0.61        = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P3 ) ) ) @ one_one_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % rat_sgn_code
% 0.33/0.61  thf(fact_5535_bezw_Oelims,axiom,
% 0.33/0.61      ! [X2: nat,Xa: nat,Y: product_prod_int_int] :
% 0.33/0.61        ( ( ( bezw @ X2 @ Xa )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( ( Xa = zero_zero_nat )
% 0.33/0.61           => ( Y
% 0.33/0.61              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.33/0.61          & ( ( Xa != zero_zero_nat )
% 0.33/0.61           => ( Y
% 0.33/0.61              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa ) ) ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bezw.elims
% 0.33/0.61  thf(fact_5536_bezw_Osimps,axiom,
% 0.33/0.61      ( bezw
% 0.33/0.61      = ( ^ [X: nat,Y4: nat] : ( if_Pro3027730157355071871nt_int @ ( Y4 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y4 ) ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bezw.simps
% 0.33/0.61  thf(fact_5537_quotient__of__denom__pos_H,axiom,
% 0.33/0.61      ! [R: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % quotient_of_denom_pos'
% 0.33/0.61  thf(fact_5538_bezw__non__0,axiom,
% 0.33/0.61      ! [Y: nat,X2: nat] :
% 0.33/0.61        ( ( ord_less_nat @ zero_zero_nat @ Y )
% 0.33/0.61       => ( ( bezw @ X2 @ Y )
% 0.33/0.61          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bezw_non_0
% 0.33/0.61  thf(fact_5539_minus__one__mod__numeral,axiom,
% 0.33/0.61      ! [N: num] :
% 0.33/0.61        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.33/0.61        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % minus_one_mod_numeral
% 0.33/0.61  thf(fact_5540_one__mod__minus__numeral,axiom,
% 0.33/0.61      ! [N: num] :
% 0.33/0.61        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.61        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % one_mod_minus_numeral
% 0.33/0.61  thf(fact_5541_snd__divmod__integer,axiom,
% 0.33/0.61      ! [K: code_integer,L: code_integer] :
% 0.33/0.61        ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 0.33/0.61        = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 0.33/0.61  
% 0.33/0.61  % snd_divmod_integer
% 0.33/0.61  thf(fact_5542_snd__divmod__abs,axiom,
% 0.33/0.61      ! [K: code_integer,L: code_integer] :
% 0.33/0.61        ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 0.33/0.61        = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % snd_divmod_abs
% 0.33/0.61  thf(fact_5543_Suc__0__mod__numeral,axiom,
% 0.33/0.61      ! [K: num] :
% 0.33/0.61        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.33/0.61        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Suc_0_mod_numeral
% 0.33/0.61  thf(fact_5544_Divides_Oadjust__mod__def,axiom,
% 0.33/0.61      ( adjust_mod
% 0.33/0.61      = ( ^ [L2: int,R2: int] : ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R2 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Divides.adjust_mod_def
% 0.33/0.61  thf(fact_5545_positive__def,axiom,
% 0.33/0.61      ( positive
% 0.33/0.61      = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 0.33/0.61        @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % positive_def
% 0.33/0.61  thf(fact_5546_bezw_Opelims,axiom,
% 0.33/0.61      ! [X2: nat,Xa: nat,Y: product_prod_int_int] :
% 0.33/0.61        ( ( ( bezw @ X2 @ Xa )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) )
% 0.33/0.61         => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.33/0.61                 => ( Y
% 0.33/0.61                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.33/0.61                & ( ( Xa != zero_zero_nat )
% 0.33/0.61                 => ( Y
% 0.33/0.61                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa ) ) ) ) ) ) ) )
% 0.33/0.61             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bezw.pelims
% 0.33/0.61  thf(fact_5547_positive_Orep__eq,axiom,
% 0.33/0.61      ( positive
% 0.33/0.61      = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % positive.rep_eq
% 0.33/0.61  thf(fact_5548_prod__decode__aux_Opelims,axiom,
% 0.33/0.61      ! [X2: nat,Xa: nat,Y: product_prod_nat_nat] :
% 0.33/0.61        ( ( ( nat_prod_decode_aux @ X2 @ Xa )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) )
% 0.33/0.61         => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X2 )
% 0.33/0.61                 => ( Y
% 0.33/0.61                    = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X2 @ Xa ) ) ) )
% 0.33/0.61                & ( ~ ( ord_less_eq_nat @ Xa @ X2 )
% 0.33/0.61                 => ( Y
% 0.33/0.61                    = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa @ ( suc @ X2 ) ) ) ) ) )
% 0.33/0.61             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % prod_decode_aux.pelims
% 0.33/0.61  thf(fact_5549_plus__rat__def,axiom,
% 0.33/0.61      ( plus_plus_rat
% 0.33/0.61      = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 0.33/0.61        @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_rat_def
% 0.33/0.61  thf(fact_5550_inverse__rat__def,axiom,
% 0.33/0.61      ( inverse_inverse_rat
% 0.33/0.61      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 0.33/0.61        @ ^ [X: product_prod_int_int] :
% 0.33/0.61            ( if_Pro3027730157355071871nt_int
% 0.33/0.61            @ ( ( product_fst_int_int @ X )
% 0.33/0.61              = zero_zero_int )
% 0.33/0.61            @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.61            @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % inverse_rat_def
% 0.33/0.61  thf(fact_5551_one__rat__def,axiom,
% 0.33/0.61      ( one_one_rat
% 0.33/0.61      = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % one_rat_def
% 0.33/0.61  thf(fact_5552_Fract_Oabs__eq,axiom,
% 0.33/0.61      ( fract
% 0.33/0.61      = ( ^ [Xa4: int,X: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract.abs_eq
% 0.33/0.61  thf(fact_5553_zero__rat__def,axiom,
% 0.33/0.61      ( zero_zero_rat
% 0.33/0.61      = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % zero_rat_def
% 0.33/0.61  thf(fact_5554_Fract__def,axiom,
% 0.33/0.61      ( fract
% 0.33/0.61      = ( map_fu7831380289885515383nt_rat @ id_int @ ( map_fu3424225382358772769nt_rat @ id_int @ abs_Rat )
% 0.33/0.61        @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract_def
% 0.33/0.61  thf(fact_5555_uminus__rat__def,axiom,
% 0.33/0.61      ( uminus_uminus_rat
% 0.33/0.61      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 0.33/0.61        @ ^ [X: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % uminus_rat_def
% 0.33/0.61  thf(fact_5556_times__rat__def,axiom,
% 0.33/0.61      ( times_times_rat
% 0.33/0.61      = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 0.33/0.61        @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % times_rat_def
% 0.33/0.61  thf(fact_5557_normalize__def,axiom,
% 0.33/0.61      ( normalize
% 0.33/0.61      = ( ^ [P6: product_prod_int_int] :
% 0.33/0.61            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P6 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) )
% 0.33/0.61            @ ( if_Pro3027730157355071871nt_int
% 0.33/0.61              @ ( ( product_snd_int_int @ P6 )
% 0.33/0.61                = zero_zero_int )
% 0.33/0.61              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.61              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % normalize_def
% 0.33/0.61  thf(fact_5558_of__int__eq__id,axiom,
% 0.33/0.61      ring_1_of_int_int = id_int ).
% 0.33/0.61  
% 0.33/0.61  % of_int_eq_id
% 0.33/0.61  thf(fact_5559_gcd__1__int,axiom,
% 0.33/0.61      ! [M: int] :
% 0.33/0.61        ( ( gcd_gcd_int @ M @ one_one_int )
% 0.33/0.61        = one_one_int ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_1_int
% 0.33/0.61  thf(fact_5560_gcd__neg1__int,axiom,
% 0.33/0.61      ! [X2: int,Y: int] :
% 0.33/0.61        ( ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ Y )
% 0.33/0.61        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_neg1_int
% 0.33/0.61  thf(fact_5561_gcd__neg2__int,axiom,
% 0.33/0.61      ! [X2: int,Y: int] :
% 0.33/0.61        ( ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ Y ) )
% 0.33/0.61        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_neg2_int
% 0.33/0.61  thf(fact_5562_gcd__abs2__int,axiom,
% 0.33/0.61      ! [X2: int,Y: int] :
% 0.33/0.61        ( ( gcd_gcd_int @ X2 @ ( abs_abs_int @ Y ) )
% 0.33/0.61        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_abs2_int
% 0.33/0.61  thf(fact_5563_gcd__abs1__int,axiom,
% 0.33/0.61      ! [X2: int,Y: int] :
% 0.33/0.61        ( ( gcd_gcd_int @ ( abs_abs_int @ X2 ) @ Y )
% 0.33/0.61        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_abs1_int
% 0.33/0.61  thf(fact_5564_abs__gcd__int,axiom,
% 0.33/0.61      ! [X2: int,Y: int] :
% 0.33/0.61        ( ( abs_abs_int @ ( gcd_gcd_int @ X2 @ Y ) )
% 0.33/0.61        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % abs_gcd_int
% 0.33/0.61  thf(fact_5565_gcd__pos__int,axiom,
% 0.33/0.61      ! [M: int,N: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 0.33/0.61        = ( ( M != zero_zero_int )
% 0.33/0.61          | ( N != zero_zero_int ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_pos_int
% 0.33/0.61  thf(fact_5566_gcd__neg__numeral__2__int,axiom,
% 0.33/0.61      ! [X2: int,N: num] :
% 0.33/0.61        ( ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.33/0.61        = ( gcd_gcd_int @ X2 @ ( numeral_numeral_int @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_neg_numeral_2_int
% 0.33/0.61  thf(fact_5567_gcd__neg__numeral__1__int,axiom,
% 0.33/0.61      ! [N: num,X2: int] :
% 0.33/0.61        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X2 )
% 0.33/0.61        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_neg_numeral_1_int
% 0.33/0.61  thf(fact_5568_gcd__0__int,axiom,
% 0.33/0.61      ! [X2: int] :
% 0.33/0.61        ( ( gcd_gcd_int @ X2 @ zero_zero_int )
% 0.33/0.61        = ( abs_abs_int @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_0_int
% 0.33/0.61  thf(fact_5569_gcd__0__left__int,axiom,
% 0.33/0.61      ! [X2: int] :
% 0.33/0.61        ( ( gcd_gcd_int @ zero_zero_int @ X2 )
% 0.33/0.61        = ( abs_abs_int @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_0_left_int
% 0.33/0.61  thf(fact_5570_gcd__proj2__if__dvd__int,axiom,
% 0.33/0.61      ! [Y: int,X2: int] :
% 0.33/0.61        ( ( dvd_dvd_int @ Y @ X2 )
% 0.33/0.61       => ( ( gcd_gcd_int @ X2 @ Y )
% 0.33/0.61          = ( abs_abs_int @ Y ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_proj2_if_dvd_int
% 0.33/0.61  thf(fact_5571_gcd__proj1__if__dvd__int,axiom,
% 0.33/0.61      ! [X2: int,Y: int] :
% 0.33/0.61        ( ( dvd_dvd_int @ X2 @ Y )
% 0.33/0.61       => ( ( gcd_gcd_int @ X2 @ Y )
% 0.33/0.61          = ( abs_abs_int @ X2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_proj1_if_dvd_int
% 0.33/0.61  thf(fact_5572_gcd__idem__int,axiom,
% 0.33/0.61      ! [X2: int] :
% 0.33/0.61        ( ( gcd_gcd_int @ X2 @ X2 )
% 0.33/0.61        = ( abs_abs_int @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_idem_int
% 0.33/0.61  thf(fact_5573_gcd__red__int,axiom,
% 0.33/0.61      ( gcd_gcd_int
% 0.33/0.61      = ( ^ [X: int,Y4: int] : ( gcd_gcd_int @ Y4 @ ( modulo_modulo_int @ X @ Y4 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_red_int
% 0.33/0.61  thf(fact_5574_gcd__ge__0__int,axiom,
% 0.33/0.61      ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X2 @ Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_ge_0_int
% 0.33/0.61  thf(fact_5575_bezout__int,axiom,
% 0.33/0.61      ! [X2: int,Y: int] :
% 0.33/0.61      ? [U4: int,V4: int] :
% 0.33/0.61        ( ( plus_plus_int @ ( times_times_int @ U4 @ X2 ) @ ( times_times_int @ V4 @ Y ) )
% 0.33/0.61        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bezout_int
% 0.33/0.61  thf(fact_5576_gcd__mult__distrib__int,axiom,
% 0.33/0.61      ! [K: int,M: int,N: int] :
% 0.33/0.61        ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 0.33/0.61        = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_mult_distrib_int
% 0.33/0.61  thf(fact_5577_gcd__le2__int,axiom,
% 0.33/0.61      ! [B: int,A: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.33/0.61       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_le2_int
% 0.33/0.61  thf(fact_5578_gcd__le1__int,axiom,
% 0.33/0.61      ! [A: int,B: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ A )
% 0.33/0.61       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_le1_int
% 0.33/0.61  thf(fact_5579_gcd__cases__int,axiom,
% 0.33/0.61      ! [X2: int,Y: int,P: int > $o] :
% 0.33/0.61        ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.33/0.61         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.61           => ( P @ ( gcd_gcd_int @ X2 @ Y ) ) ) )
% 0.33/0.61       => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.33/0.61           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.33/0.61             => ( P @ ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.33/0.61         => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 0.33/0.61             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.33/0.61               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ Y ) ) ) )
% 0.33/0.61           => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 0.33/0.61               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.33/0.61                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.33/0.61             => ( P @ ( gcd_gcd_int @ X2 @ Y ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_cases_int
% 0.33/0.61  thf(fact_5580_gcd__unique__int,axiom,
% 0.33/0.61      ! [D: int,A: int,B: int] :
% 0.33/0.61        ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 0.33/0.61          & ( dvd_dvd_int @ D @ A )
% 0.33/0.61          & ( dvd_dvd_int @ D @ B )
% 0.33/0.61          & ! [E4: int] :
% 0.33/0.61              ( ( ( dvd_dvd_int @ E4 @ A )
% 0.33/0.61                & ( dvd_dvd_int @ E4 @ B ) )
% 0.33/0.61             => ( dvd_dvd_int @ E4 @ D ) ) )
% 0.33/0.61        = ( D
% 0.33/0.61          = ( gcd_gcd_int @ A @ B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_unique_int
% 0.33/0.61  thf(fact_5581_gcd__non__0__int,axiom,
% 0.33/0.61      ! [Y: int,X2: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ Y )
% 0.33/0.61       => ( ( gcd_gcd_int @ X2 @ Y )
% 0.33/0.61          = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X2 @ Y ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_non_0_int
% 0.33/0.61  thf(fact_5582_gcd__code__int,axiom,
% 0.33/0.61      ( gcd_gcd_int
% 0.33/0.61      = ( ^ [K2: int,L2: int] : ( abs_abs_int @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( gcd_gcd_int @ L2 @ ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_code_int
% 0.33/0.61  thf(fact_5583_Code__Numeral_Odup__def,axiom,
% 0.33/0.61      ( code_dup
% 0.33/0.61      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int
% 0.33/0.61        @ ^ [K2: int] : ( plus_plus_int @ K2 @ K2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Code_Numeral.dup_def
% 0.33/0.61  thf(fact_5584_gcd__nat_Oeq__neutr__iff,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( ( gcd_gcd_nat @ A @ B )
% 0.33/0.61          = zero_zero_nat )
% 0.33/0.61        = ( ( A = zero_zero_nat )
% 0.33/0.61          & ( B = zero_zero_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.eq_neutr_iff
% 0.33/0.61  thf(fact_5585_gcd__nat_Oleft__neutral,axiom,
% 0.33/0.61      ! [A: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 0.33/0.61        = A ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.left_neutral
% 0.33/0.61  thf(fact_5586_gcd__nat_Oneutr__eq__iff,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( zero_zero_nat
% 0.33/0.61          = ( gcd_gcd_nat @ A @ B ) )
% 0.33/0.61        = ( ( A = zero_zero_nat )
% 0.33/0.61          & ( B = zero_zero_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.neutr_eq_iff
% 0.33/0.61  thf(fact_5587_gcd__nat_Oright__neutral,axiom,
% 0.33/0.61      ! [A: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 0.33/0.61        = A ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.right_neutral
% 0.33/0.61  thf(fact_5588_gcd__0__nat,axiom,
% 0.33/0.61      ! [X2: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ X2 @ zero_zero_nat )
% 0.33/0.61        = X2 ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_0_nat
% 0.33/0.61  thf(fact_5589_gcd__0__left__nat,axiom,
% 0.33/0.61      ! [X2: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ zero_zero_nat @ X2 )
% 0.33/0.61        = X2 ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_0_left_nat
% 0.33/0.61  thf(fact_5590_gcd__1__nat,axiom,
% 0.33/0.61      ! [M: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 0.33/0.61        = one_one_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_1_nat
% 0.33/0.61  thf(fact_5591_gcd__nat_Oabsorb1,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.61       => ( ( gcd_gcd_nat @ A @ B )
% 0.33/0.61          = A ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.absorb1
% 0.33/0.61  thf(fact_5592_gcd__nat_Oabsorb2,axiom,
% 0.33/0.61      ! [B: nat,A: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ B @ A )
% 0.33/0.61       => ( ( gcd_gcd_nat @ A @ B )
% 0.33/0.61          = B ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.absorb2
% 0.33/0.61  thf(fact_5593_gcd__nat_Obounded__iff,axiom,
% 0.33/0.61      ! [A: nat,B: nat,C: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) )
% 0.33/0.61        = ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.61          & ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.bounded_iff
% 0.33/0.61  thf(fact_5594_gcd__proj1__if__dvd__nat,axiom,
% 0.33/0.61      ! [X2: nat,Y: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ X2 @ Y )
% 0.33/0.61       => ( ( gcd_gcd_nat @ X2 @ Y )
% 0.33/0.61          = X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_proj1_if_dvd_nat
% 0.33/0.61  thf(fact_5595_gcd__proj2__if__dvd__nat,axiom,
% 0.33/0.61      ! [Y: nat,X2: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ Y @ X2 )
% 0.33/0.61       => ( ( gcd_gcd_nat @ X2 @ Y )
% 0.33/0.61          = Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_proj2_if_dvd_nat
% 0.33/0.61  thf(fact_5596_gcd__Suc__0,axiom,
% 0.33/0.61      ! [M: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.33/0.61        = ( suc @ zero_zero_nat ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_Suc_0
% 0.33/0.61  thf(fact_5597_gcd__pos__nat,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 0.33/0.61        = ( ( M != zero_zero_nat )
% 0.33/0.61          | ( N != zero_zero_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_pos_nat
% 0.33/0.61  thf(fact_5598_gcd__int__int__eq,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.33/0.61        = ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_int_int_eq
% 0.33/0.61  thf(fact_5599_gcd__nat__abs__left__eq,axiom,
% 0.33/0.61      ! [K: int,N: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 0.33/0.61        = ( nat2 @ ( gcd_gcd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat_abs_left_eq
% 0.33/0.61  thf(fact_5600_gcd__nat__abs__right__eq,axiom,
% 0.33/0.61      ! [N: nat,K: int] :
% 0.33/0.61        ( ( gcd_gcd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 0.33/0.61        = ( nat2 @ ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat_abs_right_eq
% 0.33/0.61  thf(fact_5601_gcd__mult__distrib__nat,axiom,
% 0.33/0.61      ! [K: nat,M: nat,N: nat] :
% 0.33/0.61        ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 0.33/0.61        = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_mult_distrib_nat
% 0.33/0.61  thf(fact_5602_gcd__nat_Omono,axiom,
% 0.33/0.61      ! [A: nat,C: nat,B: nat,D: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.61       => ( ( dvd_dvd_nat @ B @ D )
% 0.33/0.61         => ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ ( gcd_gcd_nat @ C @ D ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.mono
% 0.33/0.61  thf(fact_5603_gcd__nat_OorderE,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.61       => ( A
% 0.33/0.61          = ( gcd_gcd_nat @ A @ B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.orderE
% 0.33/0.61  thf(fact_5604_gcd__nat_OorderI,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( A
% 0.33/0.61          = ( gcd_gcd_nat @ A @ B ) )
% 0.33/0.61       => ( dvd_dvd_nat @ A @ B ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.orderI
% 0.33/0.61  thf(fact_5605_gcd__nat_Oabsorb3,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.61          & ( A != B ) )
% 0.33/0.61       => ( ( gcd_gcd_nat @ A @ B )
% 0.33/0.61          = A ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.absorb3
% 0.33/0.61  thf(fact_5606_gcd__nat_Oabsorb4,axiom,
% 0.33/0.61      ! [B: nat,A: nat] :
% 0.33/0.61        ( ( ( dvd_dvd_nat @ B @ A )
% 0.33/0.61          & ( B != A ) )
% 0.33/0.61       => ( ( gcd_gcd_nat @ A @ B )
% 0.33/0.61          = B ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.absorb4
% 0.33/0.61  thf(fact_5607_gcd__nat_OboundedE,axiom,
% 0.33/0.61      ! [A: nat,B: nat,C: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) )
% 0.33/0.61       => ~ ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.61           => ~ ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.boundedE
% 0.33/0.61  thf(fact_5608_gcd__nat_OboundedI,axiom,
% 0.33/0.61      ! [A: nat,B: nat,C: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.61       => ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.61         => ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.boundedI
% 0.33/0.61  thf(fact_5609_gcd__nat_Oorder__iff,axiom,
% 0.33/0.61      ( dvd_dvd_nat
% 0.33/0.61      = ( ^ [A2: nat,B2: nat] :
% 0.33/0.61            ( A2
% 0.33/0.61            = ( gcd_gcd_nat @ A2 @ B2 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.order_iff
% 0.33/0.61  thf(fact_5610_gcd__nat_Ocobounded1,axiom,
% 0.33/0.61      ! [A: nat,B: nat] : ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.cobounded1
% 0.33/0.61  thf(fact_5611_gcd__nat_Ocobounded2,axiom,
% 0.33/0.61      ! [A: nat,B: nat] : ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.cobounded2
% 0.33/0.61  thf(fact_5612_gcd__nat_Oabsorb__iff1,axiom,
% 0.33/0.61      ( dvd_dvd_nat
% 0.33/0.61      = ( ^ [A2: nat,B2: nat] :
% 0.33/0.61            ( ( gcd_gcd_nat @ A2 @ B2 )
% 0.33/0.61            = A2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.absorb_iff1
% 0.33/0.61  thf(fact_5613_gcd__nat_Oabsorb__iff2,axiom,
% 0.33/0.61      ( dvd_dvd_nat
% 0.33/0.61      = ( ^ [B2: nat,A2: nat] :
% 0.33/0.61            ( ( gcd_gcd_nat @ A2 @ B2 )
% 0.33/0.61            = B2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.absorb_iff2
% 0.33/0.61  thf(fact_5614_gcd__nat_OcoboundedI1,axiom,
% 0.33/0.61      ! [A: nat,C: nat,B: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.61       => ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.coboundedI1
% 0.33/0.61  thf(fact_5615_gcd__nat_OcoboundedI2,axiom,
% 0.33/0.61      ! [B: nat,C: nat,A: nat] :
% 0.33/0.61        ( ( dvd_dvd_nat @ B @ C )
% 0.33/0.61       => ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.coboundedI2
% 0.33/0.61  thf(fact_5616_gcd__nat_Ostrict__boundedE,axiom,
% 0.33/0.61      ! [A: nat,B: nat,C: nat] :
% 0.33/0.61        ( ( ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) )
% 0.33/0.61          & ( A
% 0.33/0.61           != ( gcd_gcd_nat @ B @ C ) ) )
% 0.33/0.61       => ~ ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.61              & ( A != B ) )
% 0.33/0.61           => ~ ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.61                & ( A != C ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.strict_boundedE
% 0.33/0.61  thf(fact_5617_gcd__nat_Ostrict__order__iff,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( ( dvd_dvd_nat @ A @ B )
% 0.33/0.61          & ( A != B ) )
% 0.33/0.61        = ( ( A
% 0.33/0.61            = ( gcd_gcd_nat @ A @ B ) )
% 0.33/0.61          & ( A != B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.strict_order_iff
% 0.33/0.61  thf(fact_5618_gcd__nat_Ostrict__coboundedI1,axiom,
% 0.33/0.61      ! [A: nat,C: nat,B: nat] :
% 0.33/0.61        ( ( ( dvd_dvd_nat @ A @ C )
% 0.33/0.61          & ( A != C ) )
% 0.33/0.61       => ( ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C )
% 0.33/0.61          & ( ( gcd_gcd_nat @ A @ B )
% 0.33/0.61           != C ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.strict_coboundedI1
% 0.33/0.61  thf(fact_5619_gcd__nat_Ostrict__coboundedI2,axiom,
% 0.33/0.61      ! [B: nat,C: nat,A: nat] :
% 0.33/0.61        ( ( ( dvd_dvd_nat @ B @ C )
% 0.33/0.61          & ( B != C ) )
% 0.33/0.61       => ( ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C )
% 0.33/0.61          & ( ( gcd_gcd_nat @ A @ B )
% 0.33/0.61           != C ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.strict_coboundedI2
% 0.33/0.61  thf(fact_5620_gcd__unique__nat,axiom,
% 0.33/0.61      ! [D: nat,A: nat,B: nat] :
% 0.33/0.61        ( ( ( dvd_dvd_nat @ D @ A )
% 0.33/0.61          & ( dvd_dvd_nat @ D @ B )
% 0.33/0.61          & ! [E4: nat] :
% 0.33/0.61              ( ( ( dvd_dvd_nat @ E4 @ A )
% 0.33/0.61                & ( dvd_dvd_nat @ E4 @ B ) )
% 0.33/0.61             => ( dvd_dvd_nat @ E4 @ D ) ) )
% 0.33/0.61        = ( D
% 0.33/0.61          = ( gcd_gcd_nat @ A @ B ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_unique_nat
% 0.33/0.61  thf(fact_5621_gcd__red__nat,axiom,
% 0.33/0.61      ( gcd_gcd_nat
% 0.33/0.61      = ( ^ [X: nat,Y4: nat] : ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_red_nat
% 0.33/0.61  thf(fact_5622_gcd__le1__nat,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( A != zero_zero_nat )
% 0.33/0.61       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_le1_nat
% 0.33/0.61  thf(fact_5623_gcd__le2__nat,axiom,
% 0.33/0.61      ! [B: nat,A: nat] :
% 0.33/0.61        ( ( B != zero_zero_nat )
% 0.33/0.61       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_le2_nat
% 0.33/0.61  thf(fact_5624_gcd__diff2__nat,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.33/0.61       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 0.33/0.61          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_diff2_nat
% 0.33/0.61  thf(fact_5625_gcd__diff1__nat,axiom,
% 0.33/0.61      ! [N: nat,M: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ N @ M )
% 0.33/0.61       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.33/0.61          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_diff1_nat
% 0.33/0.61  thf(fact_5626_gcd__non__0__nat,axiom,
% 0.33/0.61      ! [Y: nat,X2: nat] :
% 0.33/0.61        ( ( Y != zero_zero_nat )
% 0.33/0.61       => ( ( gcd_gcd_nat @ X2 @ Y )
% 0.33/0.61          = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_non_0_nat
% 0.33/0.61  thf(fact_5627_gcd__nat_Osimps,axiom,
% 0.33/0.61      ( gcd_gcd_nat
% 0.33/0.61      = ( ^ [X: nat,Y4: nat] : ( if_nat @ ( Y4 = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.simps
% 0.33/0.61  thf(fact_5628_gcd__nat_Oelims,axiom,
% 0.33/0.61      ! [X2: nat,Xa: nat,Y: nat] :
% 0.33/0.61        ( ( ( gcd_gcd_nat @ X2 @ Xa )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( ( Xa = zero_zero_nat )
% 0.33/0.61           => ( Y = X2 ) )
% 0.33/0.61          & ( ( Xa != zero_zero_nat )
% 0.33/0.61           => ( Y
% 0.33/0.61              = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.elims
% 0.33/0.61  thf(fact_5629_gcd__integer_Orep__eq,axiom,
% 0.33/0.61      ! [X2: code_integer,Xa: code_integer] :
% 0.33/0.61        ( ( code_int_of_integer @ ( gcd_gcd_Code_integer @ X2 @ Xa ) )
% 0.33/0.61        = ( gcd_gcd_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_integer.rep_eq
% 0.33/0.61  thf(fact_5630_gcd__integer_Oabs__eq,axiom,
% 0.33/0.61      ! [Xa: int,X2: int] :
% 0.33/0.61        ( ( gcd_gcd_Code_integer @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 0.33/0.61        = ( code_integer_of_int @ ( gcd_gcd_int @ Xa @ X2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_integer.abs_eq
% 0.33/0.61  thf(fact_5631_Code__Numeral_Odup__code_I1_J,axiom,
% 0.33/0.61      ( ( code_dup @ zero_z3403309356797280102nteger )
% 0.33/0.61      = zero_z3403309356797280102nteger ) ).
% 0.33/0.61  
% 0.33/0.61  % Code_Numeral.dup_code(1)
% 0.33/0.61  thf(fact_5632_Gcd__in,axiom,
% 0.33/0.61      ! [A4: set_nat] :
% 0.33/0.61        ( ! [A3: nat,B3: nat] :
% 0.33/0.61            ( ( member_nat @ A3 @ A4 )
% 0.33/0.61           => ( ( member_nat @ B3 @ A4 )
% 0.33/0.61             => ( member_nat @ ( gcd_gcd_nat @ A3 @ B3 ) @ A4 ) ) )
% 0.33/0.61       => ( ( A4 != bot_bot_set_nat )
% 0.33/0.61         => ( member_nat @ ( gcd_Gcd_nat @ A4 ) @ A4 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Gcd_in
% 0.33/0.61  thf(fact_5633_bezout__nat,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( A != zero_zero_nat )
% 0.33/0.61       => ? [X3: nat,Y2: nat] :
% 0.33/0.61            ( ( times_times_nat @ A @ X3 )
% 0.33/0.61            = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bezout_nat
% 0.33/0.61  thf(fact_5634_bezout__gcd__nat_H,axiom,
% 0.33/0.61      ! [B: nat,A: nat] :
% 0.33/0.61      ? [X3: nat,Y2: nat] :
% 0.33/0.61        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y2 ) @ ( times_times_nat @ A @ X3 ) )
% 0.33/0.61          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y2 ) )
% 0.33/0.61            = ( gcd_gcd_nat @ A @ B ) ) )
% 0.33/0.61        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y2 ) @ ( times_times_nat @ B @ X3 ) )
% 0.33/0.61          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y2 ) )
% 0.33/0.61            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bezout_gcd_nat'
% 0.33/0.61  thf(fact_5635_gcd__code__integer,axiom,
% 0.33/0.61      ( gcd_gcd_Code_integer
% 0.33/0.61      = ( ^ [K2: code_integer,L2: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L2 = zero_z3403309356797280102nteger ) @ K2 @ ( gcd_gcd_Code_integer @ L2 @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_code_integer
% 0.33/0.61  thf(fact_5636_dup_Orep__eq,axiom,
% 0.33/0.61      ! [X2: code_integer] :
% 0.33/0.61        ( ( code_int_of_integer @ ( code_dup @ X2 ) )
% 0.33/0.61        = ( plus_plus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ X2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % dup.rep_eq
% 0.33/0.61  thf(fact_5637_dup_Oabs__eq,axiom,
% 0.33/0.61      ! [X2: int] :
% 0.33/0.61        ( ( code_dup @ ( code_integer_of_int @ X2 ) )
% 0.33/0.61        = ( code_integer_of_int @ ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % dup.abs_eq
% 0.33/0.61  thf(fact_5638_gcd__int__def,axiom,
% 0.33/0.61      ( gcd_gcd_int
% 0.33/0.61      = ( ^ [X: int,Y4: int] : ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ X ) ) @ ( nat2 @ ( abs_abs_int @ Y4 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_int_def
% 0.33/0.61  thf(fact_5639_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.33/0.61      ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 0.33/0.61      @ ^ [M2: nat,N3: nat] :
% 0.33/0.61          ( ( dvd_dvd_nat @ M2 @ N3 )
% 0.33/0.61          & ( M2 != N3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.semilattice_neutr_order_axioms
% 0.33/0.61  thf(fact_5640_gcd__integer__def,axiom,
% 0.33/0.61      ( gcd_gcd_Code_integer
% 0.33/0.61      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ gcd_gcd_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_integer_def
% 0.33/0.61  thf(fact_5641_bezw__aux,axiom,
% 0.33/0.61      ! [X2: nat,Y: nat] :
% 0.33/0.61        ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X2 @ Y ) )
% 0.33/0.61        = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X2 @ Y ) ) @ ( semiri1314217659103216013at_int @ X2 ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X2 @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % bezw_aux
% 0.33/0.61  thf(fact_5642_gcd__nat_Opelims,axiom,
% 0.33/0.61      ! [X2: nat,Xa: nat,Y: nat] :
% 0.33/0.61        ( ( ( gcd_gcd_nat @ X2 @ Xa )
% 0.33/0.61          = Y )
% 0.33/0.61       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) )
% 0.33/0.61         => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.33/0.61                 => ( Y = X2 ) )
% 0.33/0.61                & ( ( Xa != zero_zero_nat )
% 0.33/0.61                 => ( Y
% 0.33/0.61                    = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) ) )
% 0.33/0.61             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.pelims
% 0.33/0.61  thf(fact_5643_plus__rat_Oabs__eq,axiom,
% 0.33/0.61      ! [Xa: product_prod_int_int,X2: product_prod_int_int] :
% 0.33/0.61        ( ( ratrel @ Xa @ Xa )
% 0.33/0.61       => ( ( ratrel @ X2 @ X2 )
% 0.33/0.61         => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X2 ) )
% 0.33/0.61            = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X2 ) ) @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_rat.abs_eq
% 0.33/0.61  thf(fact_5644_gcd__idem__nat,axiom,
% 0.33/0.61      ! [X2: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ X2 @ X2 )
% 0.33/0.61        = X2 ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_idem_nat
% 0.33/0.61  thf(fact_5645_gcd__nat_Oright__idem,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ ( gcd_gcd_nat @ A @ B ) @ B )
% 0.33/0.61        = ( gcd_gcd_nat @ A @ B ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.right_idem
% 0.33/0.61  thf(fact_5646_gcd__nat_Oleft__idem,axiom,
% 0.33/0.61      ! [A: nat,B: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ A @ ( gcd_gcd_nat @ A @ B ) )
% 0.33/0.61        = ( gcd_gcd_nat @ A @ B ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.left_idem
% 0.33/0.61  thf(fact_5647_gcd__nat_Oidem,axiom,
% 0.33/0.61      ! [A: nat] :
% 0.33/0.61        ( ( gcd_gcd_nat @ A @ A )
% 0.33/0.61        = A ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_nat.idem
% 0.33/0.61  thf(fact_5648_ratrel__iff,axiom,
% 0.33/0.61      ( ratrel
% 0.33/0.61      = ( ^ [X: product_prod_int_int,Y4: product_prod_int_int] :
% 0.33/0.61            ( ( ( product_snd_int_int @ X )
% 0.33/0.61             != zero_zero_int )
% 0.33/0.61            & ( ( product_snd_int_int @ Y4 )
% 0.33/0.61             != zero_zero_int )
% 0.33/0.61            & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) )
% 0.33/0.61              = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % ratrel_iff
% 0.33/0.61  thf(fact_5649_one__rat_Orsp,axiom,
% 0.33/0.61      ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 0.33/0.61  
% 0.33/0.61  % one_rat.rsp
% 0.33/0.61  thf(fact_5650_zero__rat_Orsp,axiom,
% 0.33/0.61      ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 0.33/0.61  
% 0.33/0.61  % zero_rat.rsp
% 0.33/0.61  thf(fact_5651_ratrel__def,axiom,
% 0.33/0.61      ( ratrel
% 0.33/0.61      = ( ^ [X: product_prod_int_int,Y4: product_prod_int_int] :
% 0.33/0.61            ( ( ( product_snd_int_int @ X )
% 0.33/0.61             != zero_zero_int )
% 0.33/0.61            & ( ( product_snd_int_int @ Y4 )
% 0.33/0.61             != zero_zero_int )
% 0.33/0.61            & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) )
% 0.33/0.61              = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % ratrel_def
% 0.33/0.61  thf(fact_5652_positive_Oabs__eq,axiom,
% 0.33/0.61      ! [X2: product_prod_int_int] :
% 0.33/0.61        ( ( ratrel @ X2 @ X2 )
% 0.33/0.61       => ( ( positive @ ( abs_Rat @ X2 ) )
% 0.33/0.61          = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % positive.abs_eq
% 0.33/0.61  thf(fact_5653_inverse__rat_Oabs__eq,axiom,
% 0.33/0.61      ! [X2: product_prod_int_int] :
% 0.33/0.61        ( ( ratrel @ X2 @ X2 )
% 0.33/0.61       => ( ( inverse_inverse_rat @ ( abs_Rat @ X2 ) )
% 0.33/0.61          = ( abs_Rat
% 0.33/0.61            @ ( if_Pro3027730157355071871nt_int
% 0.33/0.61              @ ( ( product_fst_int_int @ X2 )
% 0.33/0.61                = zero_zero_int )
% 0.33/0.61              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.61              @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % inverse_rat.abs_eq
% 0.33/0.61  thf(fact_5654_Code__Numeral_Osub__code_I9_J,axiom,
% 0.33/0.61      ! [M: num,N: num] :
% 0.33/0.61        ( ( code_sub @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.33/0.61        = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Code_Numeral.sub_code(9)
% 0.33/0.61  thf(fact_5655_Code__Numeral_Osub__code_I8_J,axiom,
% 0.33/0.61      ! [M: num,N: num] :
% 0.33/0.61        ( ( code_sub @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.33/0.61        = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Code_Numeral.sub_code(8)
% 0.33/0.61  thf(fact_5656_Code__Numeral_Osub__code_I1_J,axiom,
% 0.33/0.61      ( ( code_sub @ one @ one )
% 0.33/0.61      = zero_z3403309356797280102nteger ) ).
% 0.33/0.61  
% 0.33/0.61  % Code_Numeral.sub_code(1)
% 0.33/0.61  thf(fact_5657_Code__Numeral_Osub__code_I6_J,axiom,
% 0.33/0.61      ! [M: num,N: num] :
% 0.33/0.61        ( ( code_sub @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.33/0.61        = ( code_dup @ ( code_sub @ M @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Code_Numeral.sub_code(6)
% 0.33/0.61  thf(fact_5658_Code__Numeral_Osub__code_I7_J,axiom,
% 0.33/0.61      ! [M: num,N: num] :
% 0.33/0.61        ( ( code_sub @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.33/0.61        = ( code_dup @ ( code_sub @ M @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Code_Numeral.sub_code(7)
% 0.33/0.61  thf(fact_5659_sub_Orep__eq,axiom,
% 0.33/0.61      ! [X2: num,Xa: num] :
% 0.33/0.61        ( ( code_int_of_integer @ ( code_sub @ X2 @ Xa ) )
% 0.33/0.61        = ( minus_minus_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Xa ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sub.rep_eq
% 0.33/0.61  thf(fact_5660_sub_Oabs__eq,axiom,
% 0.33/0.61      ( code_sub
% 0.33/0.61      = ( ^ [Xa4: num,X: num] : ( code_integer_of_int @ ( minus_minus_int @ ( numeral_numeral_int @ Xa4 ) @ ( numeral_numeral_int @ X ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sub.abs_eq
% 0.33/0.61  thf(fact_5661_Code__Numeral_Osub__def,axiom,
% 0.33/0.61      ( code_sub
% 0.33/0.61      = ( map_fu6891787308814931657nteger @ id_num @ ( map_fu8638147718074629079nteger @ id_num @ code_integer_of_int )
% 0.33/0.61        @ ^ [M2: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Code_Numeral.sub_def
% 0.33/0.61  thf(fact_5662_cr__rat__def,axiom,
% 0.33/0.61      ( cr_rat
% 0.33/0.61      = ( ^ [X: product_prod_int_int,Y4: rat] :
% 0.33/0.61            ( ( ratrel @ X @ X )
% 0.33/0.61            & ( ( abs_Rat @ X )
% 0.33/0.61              = Y4 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % cr_rat_def
% 0.33/0.61  thf(fact_5663_card__UNIV__unit,axiom,
% 0.33/0.61      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 0.33/0.61      = one_one_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % card_UNIV_unit
% 0.33/0.61  thf(fact_5664_infinite__UNIV__int,axiom,
% 0.33/0.61      ~ ( finite_finite_int @ top_top_set_int ) ).
% 0.33/0.61  
% 0.33/0.61  % infinite_UNIV_int
% 0.33/0.61  thf(fact_5665_integer__of__int__cases,axiom,
% 0.33/0.61      ! [X2: code_integer] :
% 0.33/0.61        ~ ! [Y2: int] :
% 0.33/0.61            ( ( X2
% 0.33/0.61              = ( code_integer_of_int @ Y2 ) )
% 0.33/0.61           => ~ ( member_int @ Y2 @ top_top_set_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_int_cases
% 0.33/0.61  thf(fact_5666_integer__of__int__induct,axiom,
% 0.33/0.61      ! [P: code_integer > $o,X2: code_integer] :
% 0.33/0.61        ( ! [Y2: int] :
% 0.33/0.61            ( ( member_int @ Y2 @ top_top_set_int )
% 0.33/0.61           => ( P @ ( code_integer_of_int @ Y2 ) ) )
% 0.33/0.61       => ( P @ X2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_int_induct
% 0.33/0.61  thf(fact_5667_integer__of__int__inject,axiom,
% 0.33/0.61      ! [X2: int,Y: int] :
% 0.33/0.61        ( ( member_int @ X2 @ top_top_set_int )
% 0.33/0.61       => ( ( member_int @ Y @ top_top_set_int )
% 0.33/0.61         => ( ( ( code_integer_of_int @ X2 )
% 0.33/0.61              = ( code_integer_of_int @ Y ) )
% 0.33/0.61            = ( X2 = Y ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_int_inject
% 0.33/0.61  thf(fact_5668_int__of__integer,axiom,
% 0.33/0.61      ! [X2: code_integer] : ( member_int @ ( code_int_of_integer @ X2 ) @ top_top_set_int ) ).
% 0.33/0.61  
% 0.33/0.61  % int_of_integer
% 0.33/0.61  thf(fact_5669_int__of__integer__cases,axiom,
% 0.33/0.61      ! [Y: int] :
% 0.33/0.61        ( ( member_int @ Y @ top_top_set_int )
% 0.33/0.61       => ~ ! [X3: code_integer] :
% 0.33/0.61              ( Y
% 0.33/0.61             != ( code_int_of_integer @ X3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % int_of_integer_cases
% 0.33/0.61  thf(fact_5670_int__of__integer__induct,axiom,
% 0.33/0.61      ! [Y: int,P: int > $o] :
% 0.33/0.61        ( ( member_int @ Y @ top_top_set_int )
% 0.33/0.61       => ( ! [X3: code_integer] : ( P @ ( code_int_of_integer @ X3 ) )
% 0.33/0.61         => ( P @ Y ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % int_of_integer_induct
% 0.33/0.61  thf(fact_5671_integer__of__int__inverse,axiom,
% 0.33/0.61      ! [Y: int] :
% 0.33/0.61        ( ( member_int @ Y @ top_top_set_int )
% 0.33/0.61       => ( ( code_int_of_integer @ ( code_integer_of_int @ Y ) )
% 0.33/0.61          = Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_int_inverse
% 0.33/0.61  thf(fact_5672_int__in__range__abs,axiom,
% 0.33/0.61      ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 0.33/0.61  
% 0.33/0.61  % int_in_range_abs
% 0.33/0.61  thf(fact_5673_range__mod,axiom,
% 0.33/0.61      ! [N: nat] :
% 0.33/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.61       => ( ( image_nat_nat
% 0.33/0.61            @ ^ [M2: nat] : ( modulo_modulo_nat @ M2 @ N )
% 0.33/0.61            @ top_top_set_nat )
% 0.33/0.61          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % range_mod
% 0.33/0.61  thf(fact_5674_UN__atMost__UNIV,axiom,
% 0.33/0.61      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 0.33/0.61      = top_top_set_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % UN_atMost_UNIV
% 0.33/0.61  thf(fact_5675_UN__lessThan__UNIV,axiom,
% 0.33/0.61      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 0.33/0.61      = top_top_set_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % UN_lessThan_UNIV
% 0.33/0.61  thf(fact_5676_Sup__nat__empty,axiom,
% 0.33/0.61      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 0.33/0.61      = zero_zero_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % Sup_nat_empty
% 0.33/0.61  thf(fact_5677_natLess__def,axiom,
% 0.33/0.61      ( bNF_Ca8459412986667044542atLess
% 0.33/0.61      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % natLess_def
% 0.33/0.61  thf(fact_5678_Gcd__eq__Max,axiom,
% 0.33/0.61      ! [M3: set_nat] :
% 0.33/0.61        ( ( finite_finite_nat @ M3 )
% 0.33/0.61       => ( ( M3 != bot_bot_set_nat )
% 0.33/0.61         => ( ~ ( member_nat @ zero_zero_nat @ M3 )
% 0.33/0.61           => ( ( gcd_Gcd_nat @ M3 )
% 0.33/0.61              = ( lattic8265883725875713057ax_nat
% 0.33/0.61                @ ( comple7806235888213564991et_nat
% 0.33/0.61                  @ ( image_nat_set_nat
% 0.33/0.61                    @ ^ [M2: nat] :
% 0.33/0.61                        ( collect_nat
% 0.33/0.61                        @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M2 ) )
% 0.33/0.61                    @ M3 ) ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Gcd_eq_Max
% 0.33/0.61  thf(fact_5679_Max__divisors__self__nat,axiom,
% 0.33/0.61      ! [N: nat] :
% 0.33/0.61        ( ( N != zero_zero_nat )
% 0.33/0.61       => ( ( lattic8265883725875713057ax_nat
% 0.33/0.61            @ ( collect_nat
% 0.33/0.61              @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N ) ) )
% 0.33/0.61          = N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Max_divisors_self_nat
% 0.33/0.61  thf(fact_5680_Sup__nat__def,axiom,
% 0.33/0.61      ( complete_Sup_Sup_nat
% 0.33/0.61      = ( ^ [X5: set_nat] : ( if_nat @ ( X5 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X5 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Sup_nat_def
% 0.33/0.61  thf(fact_5681_card__le__Suc__Max,axiom,
% 0.33/0.61      ! [S3: set_nat] :
% 0.33/0.61        ( ( finite_finite_nat @ S3 )
% 0.33/0.61       => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % card_le_Suc_Max
% 0.33/0.61  thf(fact_5682_divide__nat__def,axiom,
% 0.33/0.61      ( divide_divide_nat
% 0.33/0.61      = ( ^ [M2: nat,N3: nat] :
% 0.33/0.61            ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 0.33/0.61            @ ( lattic8265883725875713057ax_nat
% 0.33/0.61              @ ( collect_nat
% 0.33/0.61                @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N3 ) @ M2 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % divide_nat_def
% 0.33/0.61  thf(fact_5683_gcd__is__Max__divisors__nat,axiom,
% 0.33/0.61      ! [N: nat,M: nat] :
% 0.33/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.61       => ( ( gcd_gcd_nat @ M @ N )
% 0.33/0.61          = ( lattic8265883725875713057ax_nat
% 0.33/0.61            @ ( collect_nat
% 0.33/0.61              @ ^ [D4: nat] :
% 0.33/0.61                  ( ( dvd_dvd_nat @ D4 @ M )
% 0.33/0.61                  & ( dvd_dvd_nat @ D4 @ N ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_is_Max_divisors_nat
% 0.33/0.61  thf(fact_5684_Max__divisors__self__int,axiom,
% 0.33/0.61      ! [N: int] :
% 0.33/0.61        ( ( N != zero_zero_int )
% 0.33/0.61       => ( ( lattic8263393255366662781ax_int
% 0.33/0.61            @ ( collect_int
% 0.33/0.61              @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N ) ) )
% 0.33/0.61          = ( abs_abs_int @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Max_divisors_self_int
% 0.33/0.61  thf(fact_5685_gcd__is__Max__divisors__int,axiom,
% 0.33/0.61      ! [N: int,M: int] :
% 0.33/0.61        ( ( N != zero_zero_int )
% 0.33/0.61       => ( ( gcd_gcd_int @ M @ N )
% 0.33/0.61          = ( lattic8263393255366662781ax_int
% 0.33/0.61            @ ( collect_int
% 0.33/0.61              @ ^ [D4: int] :
% 0.33/0.61                  ( ( dvd_dvd_int @ D4 @ M )
% 0.33/0.61                  & ( dvd_dvd_int @ D4 @ N ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_is_Max_divisors_int
% 0.33/0.61  thf(fact_5686_INT__greaterThan__UNIV,axiom,
% 0.33/0.61      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 0.33/0.61      = bot_bot_set_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % INT_greaterThan_UNIV
% 0.33/0.61  thf(fact_5687_atLeastLessThan__add__Un,axiom,
% 0.33/0.61      ! [I: nat,J: nat,K: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ I @ J )
% 0.33/0.61       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 0.33/0.61          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % atLeastLessThan_add_Un
% 0.33/0.61  thf(fact_5688_greaterThan__0,axiom,
% 0.33/0.61      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.33/0.61      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.33/0.61  
% 0.33/0.61  % greaterThan_0
% 0.33/0.61  thf(fact_5689_greaterThan__Suc,axiom,
% 0.33/0.61      ! [K: nat] :
% 0.33/0.61        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 0.33/0.61        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % greaterThan_Suc
% 0.33/0.61  thf(fact_5690_atLeast__0,axiom,
% 0.33/0.61      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 0.33/0.61      = top_top_set_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % atLeast_0
% 0.33/0.61  thf(fact_5691_sup__nat__def,axiom,
% 0.33/0.61      sup_sup_nat = ord_max_nat ).
% 0.33/0.61  
% 0.33/0.61  % sup_nat_def
% 0.33/0.61  thf(fact_5692_sup__int__def,axiom,
% 0.33/0.61      sup_sup_int = ord_max_int ).
% 0.33/0.61  
% 0.33/0.61  % sup_int_def
% 0.33/0.61  thf(fact_5693_atLeast__Suc__greaterThan,axiom,
% 0.33/0.61      ! [K: nat] :
% 0.33/0.61        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.33/0.61        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 0.33/0.61  
% 0.33/0.61  % atLeast_Suc_greaterThan
% 0.33/0.61  thf(fact_5694_atLeast__Suc,axiom,
% 0.33/0.61      ! [K: nat] :
% 0.33/0.61        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.33/0.61        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % atLeast_Suc
% 0.33/0.61  thf(fact_5695_UN__atLeast__UNIV,axiom,
% 0.33/0.61      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 0.33/0.61      = top_top_set_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % UN_atLeast_UNIV
% 0.33/0.61  thf(fact_5696_range__abs__Nats,axiom,
% 0.33/0.61      ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 0.33/0.61      = semiring_1_Nats_int ) ).
% 0.33/0.61  
% 0.33/0.61  % range_abs_Nats
% 0.33/0.61  thf(fact_5697_binomial__def,axiom,
% 0.33/0.61      ( binomial
% 0.33/0.61      = ( ^ [N3: nat,K2: nat] :
% 0.33/0.61            ( finite_card_set_nat
% 0.33/0.61            @ ( collect_set_nat
% 0.33/0.61              @ ^ [K6: set_nat] :
% 0.33/0.61                  ( ( member_set_nat @ K6 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) )
% 0.33/0.61                  & ( ( finite_card_nat @ K6 )
% 0.33/0.61                    = K2 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % binomial_def
% 0.33/0.61  thf(fact_5698_pred__nat__def,axiom,
% 0.33/0.61      ( pred_nat
% 0.33/0.61      = ( collec3392354462482085612at_nat
% 0.33/0.61        @ ( produc6081775807080527818_nat_o
% 0.33/0.61          @ ^ [M2: nat,N3: nat] :
% 0.33/0.61              ( N3
% 0.33/0.61              = ( suc @ M2 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % pred_nat_def
% 0.33/0.61  thf(fact_5699_pred__nat__trancl__eq__le,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 0.33/0.61        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % pred_nat_trancl_eq_le
% 0.33/0.61  thf(fact_5700_vimage__Suc__insert__0,axiom,
% 0.33/0.61      ! [A4: set_nat] :
% 0.33/0.61        ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A4 ) )
% 0.33/0.61        = ( vimage_nat_nat @ suc @ A4 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % vimage_Suc_insert_0
% 0.33/0.61  thf(fact_5701_mono__Suc,axiom,
% 0.33/0.61      order_mono_nat_nat @ suc ).
% 0.33/0.61  
% 0.33/0.61  % mono_Suc
% 0.33/0.61  thf(fact_5702_mono__times__nat,axiom,
% 0.33/0.61      ! [N: nat] :
% 0.33/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.61       => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % mono_times_nat
% 0.33/0.61  thf(fact_5703_mono__ge2__power__minus__self,axiom,
% 0.33/0.61      ! [K: nat] :
% 0.33/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.33/0.61       => ( order_mono_nat_nat
% 0.33/0.61          @ ^ [M2: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ M2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % mono_ge2_power_minus_self
% 0.33/0.61  thf(fact_5704_quotient__of__def,axiom,
% 0.33/0.61      ( quotient_of
% 0.33/0.61      = ( ^ [X: rat] :
% 0.33/0.61            ( the_Pr4378521158711661632nt_int
% 0.33/0.61            @ ^ [Pair: product_prod_int_int] :
% 0.33/0.61                ( ( X
% 0.33/0.61                  = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 0.33/0.61                & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 0.33/0.61                & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % quotient_of_def
% 0.33/0.61  thf(fact_5705_normalize__stable,axiom,
% 0.33/0.61      ! [Q2: int,P3: int] :
% 0.33/0.61        ( ( ord_less_int @ zero_zero_int @ Q2 )
% 0.33/0.61       => ( ( algebr932160517623751201me_int @ P3 @ Q2 )
% 0.33/0.61         => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q2 ) )
% 0.33/0.61            = ( product_Pair_int_int @ P3 @ Q2 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % normalize_stable
% 0.33/0.61  thf(fact_5706_inj__on__diff__nat,axiom,
% 0.33/0.61      ! [N4: set_nat,K: nat] :
% 0.33/0.61        ( ! [N2: nat] :
% 0.33/0.61            ( ( member_nat @ N2 @ N4 )
% 0.33/0.61           => ( ord_less_eq_nat @ K @ N2 ) )
% 0.33/0.61       => ( inj_on_nat_nat
% 0.33/0.61          @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ K )
% 0.33/0.61          @ N4 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % inj_on_diff_nat
% 0.33/0.61  thf(fact_5707_coprime__crossproduct__int,axiom,
% 0.33/0.61      ! [A: int,D: int,B: int,C: int] :
% 0.33/0.61        ( ( algebr932160517623751201me_int @ A @ D )
% 0.33/0.61       => ( ( algebr932160517623751201me_int @ B @ C )
% 0.33/0.61         => ( ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ C ) )
% 0.33/0.61              = ( times_times_int @ ( abs_abs_int @ B ) @ ( abs_abs_int @ D ) ) )
% 0.33/0.61            = ( ( ( abs_abs_int @ A )
% 0.33/0.61                = ( abs_abs_int @ B ) )
% 0.33/0.61              & ( ( abs_abs_int @ C )
% 0.33/0.61                = ( abs_abs_int @ D ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_crossproduct_int
% 0.33/0.61  thf(fact_5708_inj__Suc,axiom,
% 0.33/0.61      ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 0.33/0.61  
% 0.33/0.61  % inj_Suc
% 0.33/0.61  thf(fact_5709_Rat__cases,axiom,
% 0.33/0.61      ! [Q2: rat] :
% 0.33/0.61        ~ ! [A3: int,B3: int] :
% 0.33/0.61            ( ( Q2
% 0.33/0.61              = ( fract @ A3 @ B3 ) )
% 0.33/0.61           => ( ( ord_less_int @ zero_zero_int @ B3 )
% 0.33/0.61             => ~ ( algebr932160517623751201me_int @ A3 @ B3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Rat_cases
% 0.33/0.61  thf(fact_5710_Rat__induct,axiom,
% 0.33/0.61      ! [P: rat > $o,Q2: rat] :
% 0.33/0.61        ( ! [A3: int,B3: int] :
% 0.33/0.61            ( ( ord_less_int @ zero_zero_int @ B3 )
% 0.33/0.61           => ( ( algebr932160517623751201me_int @ A3 @ B3 )
% 0.33/0.61             => ( P @ ( fract @ A3 @ B3 ) ) ) )
% 0.33/0.61       => ( P @ Q2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Rat_induct
% 0.33/0.61  thf(fact_5711_coprime__common__divisor__int,axiom,
% 0.33/0.61      ! [A: int,B: int,X2: int] :
% 0.33/0.61        ( ( algebr932160517623751201me_int @ A @ B )
% 0.33/0.61       => ( ( dvd_dvd_int @ X2 @ A )
% 0.33/0.61         => ( ( dvd_dvd_int @ X2 @ B )
% 0.33/0.61           => ( ( abs_abs_int @ X2 )
% 0.33/0.61              = one_one_int ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_common_divisor_int
% 0.33/0.61  thf(fact_5712_Rat__cases__nonzero,axiom,
% 0.33/0.61      ! [Q2: rat] :
% 0.33/0.61        ( ! [A3: int,B3: int] :
% 0.33/0.61            ( ( Q2
% 0.33/0.61              = ( fract @ A3 @ B3 ) )
% 0.33/0.61           => ( ( ord_less_int @ zero_zero_int @ B3 )
% 0.33/0.61             => ( ( A3 != zero_zero_int )
% 0.33/0.61               => ~ ( algebr932160517623751201me_int @ A3 @ B3 ) ) ) )
% 0.33/0.61       => ( Q2 = zero_zero_rat ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Rat_cases_nonzero
% 0.33/0.61  thf(fact_5713_quotient__of__unique,axiom,
% 0.33/0.61      ! [R: rat] :
% 0.33/0.61      ? [X3: product_prod_int_int] :
% 0.33/0.61        ( ( R
% 0.33/0.61          = ( fract @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 0.33/0.61        & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X3 ) )
% 0.33/0.61        & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) )
% 0.33/0.61        & ! [Y5: product_prod_int_int] :
% 0.33/0.61            ( ( ( R
% 0.33/0.61                = ( fract @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 0.33/0.61              & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y5 ) )
% 0.33/0.61              & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 0.33/0.61           => ( Y5 = X3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % quotient_of_unique
% 0.33/0.61  thf(fact_5714_coprime__int__iff,axiom,
% 0.33/0.61      ! [M: nat,N: nat] :
% 0.33/0.61        ( ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.33/0.61        = ( algebr934650988132801477me_nat @ M @ N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_int_iff
% 0.33/0.61  thf(fact_5715_coprime__nat__abs__left__iff,axiom,
% 0.33/0.61      ! [K: int,N: nat] :
% 0.33/0.61        ( ( algebr934650988132801477me_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 0.33/0.61        = ( algebr932160517623751201me_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_nat_abs_left_iff
% 0.33/0.61  thf(fact_5716_coprime__nat__abs__right__iff,axiom,
% 0.33/0.61      ! [N: nat,K: int] :
% 0.33/0.61        ( ( algebr934650988132801477me_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 0.33/0.61        = ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_nat_abs_right_iff
% 0.33/0.61  thf(fact_5717_coprime__common__divisor__nat,axiom,
% 0.33/0.61      ! [A: nat,B: nat,X2: nat] :
% 0.33/0.61        ( ( algebr934650988132801477me_nat @ A @ B )
% 0.33/0.61       => ( ( dvd_dvd_nat @ X2 @ A )
% 0.33/0.61         => ( ( dvd_dvd_nat @ X2 @ B )
% 0.33/0.61           => ( X2 = one_one_nat ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_common_divisor_nat
% 0.33/0.61  thf(fact_5718_coprime__Suc__right__nat,axiom,
% 0.33/0.61      ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_Suc_right_nat
% 0.33/0.61  thf(fact_5719_coprime__Suc__left__nat,axiom,
% 0.33/0.61      ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_Suc_left_nat
% 0.33/0.61  thf(fact_5720_coprime__crossproduct__nat,axiom,
% 0.33/0.61      ! [A: nat,D: nat,B: nat,C: nat] :
% 0.33/0.61        ( ( algebr934650988132801477me_nat @ A @ D )
% 0.33/0.61       => ( ( algebr934650988132801477me_nat @ B @ C )
% 0.33/0.61         => ( ( ( times_times_nat @ A @ C )
% 0.33/0.61              = ( times_times_nat @ B @ D ) )
% 0.33/0.61            = ( ( A = B )
% 0.33/0.61              & ( C = D ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_crossproduct_nat
% 0.33/0.61  thf(fact_5721_coprime__Suc__0__left,axiom,
% 0.33/0.61      ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_Suc_0_left
% 0.33/0.61  thf(fact_5722_coprime__Suc__0__right,axiom,
% 0.33/0.61      ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_Suc_0_right
% 0.33/0.61  thf(fact_5723_coprime__diff__one__left__nat,axiom,
% 0.33/0.61      ! [N: nat] :
% 0.33/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.61       => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_diff_one_left_nat
% 0.33/0.61  thf(fact_5724_coprime__diff__one__right__nat,axiom,
% 0.33/0.61      ! [N: nat] :
% 0.33/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.33/0.61       => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % coprime_diff_one_right_nat
% 0.33/0.61  thf(fact_5725_positive_Orsp,axiom,
% 0.33/0.61      ( bNF_re8699439704749558557nt_o_o @ ratrel
% 0.33/0.61      @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.33/0.61      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 0.33/0.61      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % positive.rsp
% 0.33/0.61  thf(fact_5726_Fract_Orsp,axiom,
% 0.33/0.61      ( bNF_re157797125943740599nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re6250860962936578807nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ratrel )
% 0.33/0.61      @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) )
% 0.33/0.61      @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract.rsp
% 0.33/0.61  thf(fact_5727_less__eq__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re3403563459893282935_int_o
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5089333283451836215nt_o_o
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.61      @ ord_less_eq_int
% 0.33/0.61      @ ord_less_eq_int ) ).
% 0.33/0.61  
% 0.33/0.61  % less_eq_integer.rsp
% 0.33/0.61  thf(fact_5728_less__eq__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re578469030762574527_nat_o
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4705727531993890431at_o_o
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.61      @ ord_less_eq_nat
% 0.33/0.61      @ ord_less_eq_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % less_eq_natural.rsp
% 0.33/0.61  thf(fact_5729_uminus__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4712519889275205905nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ uminus_uminus_int
% 0.33/0.61      @ uminus_uminus_int ) ).
% 0.33/0.61  
% 0.33/0.61  % uminus_integer.rsp
% 0.33/0.61  thf(fact_5730_minus__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ minus_minus_nat
% 0.33/0.61      @ minus_minus_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % minus_natural.rsp
% 0.33/0.61  thf(fact_5731_minus__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re711492959462206631nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ minus_minus_int
% 0.33/0.61      @ minus_minus_int ) ).
% 0.33/0.61  
% 0.33/0.61  % minus_integer.rsp
% 0.33/0.61  thf(fact_5732_sub_Orsp,axiom,
% 0.33/0.61      ( bNF_re8402795839162346335um_int
% 0.33/0.61      @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re1822329894187522285nt_int
% 0.33/0.61        @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ ^ [M2: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N3 ) )
% 0.33/0.61      @ ^ [M2: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N3 ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % sub.rsp
% 0.33/0.61  thf(fact_5733_gcd__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re711492959462206631nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ gcd_gcd_int
% 0.33/0.61      @ gcd_gcd_int ) ).
% 0.33/0.61  
% 0.33/0.61  % gcd_integer.rsp
% 0.33/0.61  thf(fact_5734_integer__of__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re6650684261131312217nt_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ semiri1314217659103216013at_int
% 0.33/0.61      @ semiri1314217659103216013at_int ) ).
% 0.33/0.61  
% 0.33/0.61  % integer_of_natural.rsp
% 0.33/0.61  thf(fact_5735_dup_Orsp,axiom,
% 0.33/0.61      ( bNF_re4712519889275205905nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ^ [K2: int] : ( plus_plus_int @ K2 @ K2 )
% 0.33/0.61      @ ^ [K2: int] : ( plus_plus_int @ K2 @ K2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % dup.rsp
% 0.33/0.61  thf(fact_5736_sgn__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4712519889275205905nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ sgn_sgn_int
% 0.33/0.61      @ sgn_sgn_int ) ).
% 0.33/0.61  
% 0.33/0.61  % sgn_integer.rsp
% 0.33/0.61  thf(fact_5737_plus__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ plus_plus_nat
% 0.33/0.61      @ plus_plus_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_natural.rsp
% 0.33/0.61  thf(fact_5738_plus__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re711492959462206631nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ plus_plus_int
% 0.33/0.61      @ plus_plus_int ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_integer.rsp
% 0.33/0.61  thf(fact_5739_bit__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re578469030762574527_nat_o
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: nat > $o,Z: nat > $o] : ( Y3 = Z )
% 0.33/0.61      @ bit_se1148574629649215175it_nat
% 0.33/0.61      @ bit_se1148574629649215175it_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % bit_natural.rsp
% 0.33/0.61  thf(fact_5740_Suc_Orsp,axiom,
% 0.33/0.61      ( bNF_re5653821019739307937at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ suc
% 0.33/0.61      @ suc ) ).
% 0.33/0.61  
% 0.33/0.61  % Suc.rsp
% 0.33/0.61  thf(fact_5741_natural__of__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re3715656647883201625at_nat
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ nat2
% 0.33/0.61      @ nat2 ) ).
% 0.33/0.61  
% 0.33/0.61  % natural_of_integer.rsp
% 0.33/0.61  thf(fact_5742_not__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4712519889275205905nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ bit_ri7919022796975470100ot_int
% 0.33/0.61      @ bit_ri7919022796975470100ot_int ) ).
% 0.33/0.61  
% 0.33/0.61  % not_integer.rsp
% 0.33/0.61  thf(fact_5743_and__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se727722235901077358nd_nat
% 0.33/0.61      @ bit_se727722235901077358nd_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % and_natural.rsp
% 0.33/0.61  thf(fact_5744_and__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re711492959462206631nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se725231765392027082nd_int
% 0.33/0.61      @ bit_se725231765392027082nd_int ) ).
% 0.33/0.61  
% 0.33/0.61  % and_integer.rsp
% 0.33/0.61  thf(fact_5745_take__bit__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se2925701944663578781it_nat
% 0.33/0.61      @ bit_se2925701944663578781it_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % take_bit_natural.rsp
% 0.33/0.61  thf(fact_5746_take__bit__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4785983289428654063nt_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se2923211474154528505it_int
% 0.33/0.61      @ bit_se2923211474154528505it_int ) ).
% 0.33/0.61  
% 0.33/0.61  % take_bit_integer.rsp
% 0.33/0.61  thf(fact_5747_modulo__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ modulo_modulo_nat
% 0.33/0.61      @ modulo_modulo_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % modulo_natural.rsp
% 0.33/0.61  thf(fact_5748_modulo__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re711492959462206631nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ modulo_modulo_int
% 0.33/0.61      @ modulo_modulo_int ) ).
% 0.33/0.61  
% 0.33/0.61  % modulo_integer.rsp
% 0.33/0.61  thf(fact_5749_unset__bit__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se4205575877204974255it_nat
% 0.33/0.61      @ bit_se4205575877204974255it_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % unset_bit_natural.rsp
% 0.33/0.61  thf(fact_5750_unset__bit__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4785983289428654063nt_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se4203085406695923979it_int
% 0.33/0.61      @ bit_se4203085406695923979it_int ) ).
% 0.33/0.61  
% 0.33/0.61  % unset_bit_integer.rsp
% 0.33/0.61  thf(fact_5751_set__bit__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se7882103937844011126it_nat
% 0.33/0.61      @ bit_se7882103937844011126it_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % set_bit_natural.rsp
% 0.33/0.61  thf(fact_5752_set__bit__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4785983289428654063nt_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se7879613467334960850it_int
% 0.33/0.61      @ bit_se7879613467334960850it_int ) ).
% 0.33/0.61  
% 0.33/0.61  % set_bit_integer.rsp
% 0.33/0.61  thf(fact_5753_flip__bit__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4785983289428654063nt_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se2159334234014336723it_int
% 0.33/0.61      @ bit_se2159334234014336723it_int ) ).
% 0.33/0.61  
% 0.33/0.61  % flip_bit_integer.rsp
% 0.33/0.61  thf(fact_5754_flip__bit__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se2161824704523386999it_nat
% 0.33/0.61      @ bit_se2161824704523386999it_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % flip_bit_natural.rsp
% 0.33/0.61  thf(fact_5755_push__bit__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se547839408752420682it_nat
% 0.33/0.61      @ bit_se547839408752420682it_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % push_bit_natural.rsp
% 0.33/0.61  thf(fact_5756_push__bit__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4785983289428654063nt_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se545348938243370406it_int
% 0.33/0.61      @ bit_se545348938243370406it_int ) ).
% 0.33/0.61  
% 0.33/0.61  % push_bit_integer.rsp
% 0.33/0.61  thf(fact_5757_xor__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se6528837805403552850or_nat
% 0.33/0.61      @ bit_se6528837805403552850or_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % xor_natural.rsp
% 0.33/0.61  thf(fact_5758_xor__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re711492959462206631nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se6526347334894502574or_int
% 0.33/0.61      @ bit_se6526347334894502574or_int ) ).
% 0.33/0.61  
% 0.33/0.61  % xor_integer.rsp
% 0.33/0.61  thf(fact_5759_bit__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re3376528473927230327_nat_o
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: nat > $o,Z: nat > $o] : ( Y3 = Z )
% 0.33/0.61      @ bit_se1146084159140164899it_int
% 0.33/0.61      @ bit_se1146084159140164899it_int ) ).
% 0.33/0.61  
% 0.33/0.61  % bit_integer.rsp
% 0.33/0.61  thf(fact_5760_or__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re711492959462206631nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se1409905431419307370or_int
% 0.33/0.61      @ bit_se1409905431419307370or_int ) ).
% 0.33/0.61  
% 0.33/0.61  % or_integer.rsp
% 0.33/0.61  thf(fact_5761_or__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se1412395901928357646or_nat
% 0.33/0.61      @ bit_se1412395901928357646or_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % or_natural.rsp
% 0.33/0.61  thf(fact_5762_drop__bit__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4785983289428654063nt_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se8568078237143864401it_int
% 0.33/0.61      @ bit_se8568078237143864401it_int ) ).
% 0.33/0.61  
% 0.33/0.61  % drop_bit_integer.rsp
% 0.33/0.61  thf(fact_5763_drop__bit__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ bit_se8570568707652914677it_nat
% 0.33/0.61      @ bit_se8570568707652914677it_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % drop_bit_natural.rsp
% 0.33/0.61  thf(fact_5764_mask__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re6650684261131312217nt_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ bit_se2000444600071755411sk_int
% 0.33/0.61      @ bit_se2000444600071755411sk_int ) ).
% 0.33/0.61  
% 0.33/0.61  % mask_integer.rsp
% 0.33/0.61  thf(fact_5765_mask__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re5653821019739307937at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ bit_se2002935070580805687sk_nat
% 0.33/0.61      @ bit_se2002935070580805687sk_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % mask_natural.rsp
% 0.33/0.61  thf(fact_5766_abs__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re4712519889275205905nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ abs_abs_int
% 0.33/0.61      @ abs_abs_int ) ).
% 0.33/0.61  
% 0.33/0.61  % abs_integer.rsp
% 0.33/0.61  thf(fact_5767_divide__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re711492959462206631nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ divide_divide_int
% 0.33/0.61      @ divide_divide_int ) ).
% 0.33/0.61  
% 0.33/0.61  % divide_integer.rsp
% 0.33/0.61  thf(fact_5768_divide__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ divide_divide_nat
% 0.33/0.61      @ divide_divide_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % divide_natural.rsp
% 0.33/0.61  thf(fact_5769_times__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re1345281282404953727at_nat
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5653821019739307937at_nat
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.61      @ times_times_nat
% 0.33/0.61      @ times_times_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % times_natural.rsp
% 0.33/0.61  thf(fact_5770_times__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re711492959462206631nt_int
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4712519889275205905nt_int
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.61      @ times_times_int
% 0.33/0.61      @ times_times_int ) ).
% 0.33/0.61  
% 0.33/0.61  % times_integer.rsp
% 0.33/0.61  thf(fact_5771_less__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re3403563459893282935_int_o
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re5089333283451836215nt_o_o
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.61      @ ord_less_int
% 0.33/0.61      @ ord_less_int ) ).
% 0.33/0.61  
% 0.33/0.61  % less_integer.rsp
% 0.33/0.61  thf(fact_5772_less__natural_Orsp,axiom,
% 0.33/0.61      ( bNF_re578469030762574527_nat_o
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re4705727531993890431at_o_o
% 0.33/0.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.61      @ ord_less_nat
% 0.33/0.61      @ ord_less_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % less_natural.rsp
% 0.33/0.61  thf(fact_5773_times__rat_Orsp,axiom,
% 0.33/0.61      ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 0.33/0.61      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) )
% 0.33/0.61      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % times_rat.rsp
% 0.33/0.61  thf(fact_5774_plus__rat_Orsp,axiom,
% 0.33/0.61      ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 0.33/0.61      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) )
% 0.33/0.61      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_rat.rsp
% 0.33/0.61  thf(fact_5775_num__of__integer_Orsp,axiom,
% 0.33/0.61      ( bNF_re7626690874201225453um_num
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 0.33/0.61      @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 0.33/0.61      @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ).
% 0.33/0.61  
% 0.33/0.61  % num_of_integer.rsp
% 0.33/0.61  thf(fact_5776_uminus__rat_Orsp,axiom,
% 0.33/0.61      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 0.33/0.61      @ ^ [X: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) )
% 0.33/0.61      @ ^ [X: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % uminus_rat.rsp
% 0.33/0.61  thf(fact_5777_inverse__rat_Orsp,axiom,
% 0.33/0.61      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 0.33/0.61      @ ^ [X: product_prod_int_int] :
% 0.33/0.61          ( if_Pro3027730157355071871nt_int
% 0.33/0.61          @ ( ( product_fst_int_int @ X )
% 0.33/0.61            = zero_zero_int )
% 0.33/0.61          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.61          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) )
% 0.33/0.61      @ ^ [X: product_prod_int_int] :
% 0.33/0.61          ( if_Pro3027730157355071871nt_int
% 0.33/0.61          @ ( ( product_fst_int_int @ X )
% 0.33/0.61            = zero_zero_int )
% 0.33/0.61          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.61          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % inverse_rat.rsp
% 0.33/0.61  thf(fact_5778_plus__rat_Otransfer,axiom,
% 0.33/0.61      ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 0.33/0.61      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) )
% 0.33/0.61      @ plus_plus_rat ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_rat.transfer
% 0.33/0.61  thf(fact_5779_inverse__rat_Otransfer,axiom,
% 0.33/0.61      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 0.33/0.61      @ ^ [X: product_prod_int_int] :
% 0.33/0.61          ( if_Pro3027730157355071871nt_int
% 0.33/0.61          @ ( ( product_fst_int_int @ X )
% 0.33/0.61            = zero_zero_int )
% 0.33/0.61          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.33/0.61          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) )
% 0.33/0.61      @ inverse_inverse_rat ) ).
% 0.33/0.61  
% 0.33/0.61  % inverse_rat.transfer
% 0.33/0.61  thf(fact_5780_one__rat_Otransfer,axiom,
% 0.33/0.61      pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 0.33/0.61  
% 0.33/0.61  % one_rat.transfer
% 0.33/0.61  thf(fact_5781_zero__rat_Otransfer,axiom,
% 0.33/0.61      pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 0.33/0.61  
% 0.33/0.61  % zero_rat.transfer
% 0.33/0.61  thf(fact_5782_Fract_Otransfer,axiom,
% 0.33/0.61      ( bNF_re3461391660133120880nt_rat
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61      @ ( bNF_re2214769303045360666nt_rat
% 0.33/0.61        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.61        @ pcr_rat )
% 0.33/0.61      @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) )
% 0.33/0.61      @ fract ) ).
% 0.33/0.61  
% 0.33/0.61  % Fract.transfer
% 0.33/0.61  thf(fact_5783_uminus__rat_Otransfer,axiom,
% 0.33/0.61      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 0.33/0.61      @ ^ [X: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) )
% 0.33/0.61      @ uminus_uminus_rat ) ).
% 0.33/0.61  
% 0.33/0.61  % uminus_rat.transfer
% 0.33/0.61  thf(fact_5784_times__rat_Otransfer,axiom,
% 0.33/0.61      ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 0.33/0.61      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) )
% 0.33/0.61      @ times_times_rat ) ).
% 0.33/0.61  
% 0.33/0.61  % times_rat.transfer
% 0.33/0.61  thf(fact_5785_positive_Otransfer,axiom,
% 0.33/0.61      ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 0.33/0.61      @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.33/0.61      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 0.33/0.61      @ positive ) ).
% 0.33/0.61  
% 0.33/0.61  % positive.transfer
% 0.33/0.61  thf(fact_5786_times__int_Otransfer,axiom,
% 0.33/0.61      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.33/0.61      @ ( produc27273713700761075at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 0.33/0.61      @ times_times_int ) ).
% 0.33/0.61  
% 0.33/0.61  % times_int.transfer
% 0.33/0.61  thf(fact_5787_zero__int_Otransfer,axiom,
% 0.33/0.61      pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 0.33/0.61  
% 0.33/0.61  % zero_int.transfer
% 0.33/0.61  thf(fact_5788_int__transfer,axiom,
% 0.33/0.61      ( bNF_re6830278522597306478at_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ pcr_int
% 0.33/0.61      @ ^ [N3: nat] : ( product_Pair_nat_nat @ N3 @ zero_zero_nat )
% 0.33/0.61      @ semiri1314217659103216013at_int ) ).
% 0.33/0.61  
% 0.33/0.61  % int_transfer
% 0.33/0.61  thf(fact_5789_uminus__int_Otransfer,axiom,
% 0.33/0.61      ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 0.33/0.61      @ ( produc2626176000494625587at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X ) )
% 0.33/0.61      @ uminus_uminus_int ) ).
% 0.33/0.61  
% 0.33/0.61  % uminus_int.transfer
% 0.33/0.61  thf(fact_5790_nat_Otransfer,axiom,
% 0.33/0.61      ( bNF_re4555766996558763186at_nat @ pcr_int
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 0.33/0.61      @ nat2 ) ).
% 0.33/0.61  
% 0.33/0.61  % nat.transfer
% 0.33/0.61  thf(fact_5791_one__int_Otransfer,axiom,
% 0.33/0.61      pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 0.33/0.61  
% 0.33/0.61  % one_int.transfer
% 0.33/0.61  thf(fact_5792_less__int_Otransfer,axiom,
% 0.33/0.61      ( bNF_re717283939379294677_int_o @ pcr_int
% 0.33/0.61      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.33/0.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.61      @ ( produc8739625826339149834_nat_o
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc6081775807080527818_nat_o
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 0.33/0.61      @ ord_less_int ) ).
% 0.33/0.61  
% 0.33/0.61  % less_int.transfer
% 0.33/0.61  thf(fact_5793_less__eq__int_Otransfer,axiom,
% 0.33/0.61      ( bNF_re717283939379294677_int_o @ pcr_int
% 0.33/0.61      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.33/0.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.61      @ ( produc8739625826339149834_nat_o
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc6081775807080527818_nat_o
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 0.33/0.61      @ ord_less_eq_int ) ).
% 0.33/0.61  
% 0.33/0.61  % less_eq_int.transfer
% 0.33/0.61  thf(fact_5794_plus__int_Otransfer,axiom,
% 0.33/0.61      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.33/0.61      @ ( produc27273713700761075at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 0.33/0.61      @ plus_plus_int ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_int.transfer
% 0.33/0.61  thf(fact_5795_minus__int_Otransfer,axiom,
% 0.33/0.61      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.33/0.61      @ ( produc27273713700761075at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 0.33/0.61      @ minus_minus_int ) ).
% 0.33/0.61  
% 0.33/0.61  % minus_int.transfer
% 0.33/0.61  thf(fact_5796_times__int_Orsp,axiom,
% 0.33/0.61      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.33/0.61      @ ( produc27273713700761075at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 0.33/0.61      @ ( produc27273713700761075at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % times_int.rsp
% 0.33/0.61  thf(fact_5797_intrel__iff,axiom,
% 0.33/0.61      ! [X2: nat,Y: nat,U: nat,V: nat] :
% 0.33/0.61        ( ( intrel @ ( product_Pair_nat_nat @ X2 @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 0.33/0.61        = ( ( plus_plus_nat @ X2 @ V )
% 0.33/0.61          = ( plus_plus_nat @ U @ Y ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % intrel_iff
% 0.33/0.61  thf(fact_5798_int_Orel__eq__transfer,axiom,
% 0.33/0.61      ( bNF_re717283939379294677_int_o @ pcr_int
% 0.33/0.61      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.33/0.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.61      @ intrel
% 0.33/0.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z ) ) ).
% 0.33/0.61  
% 0.33/0.61  % int.rel_eq_transfer
% 0.33/0.61  thf(fact_5799_zero__int_Orsp,axiom,
% 0.33/0.61      intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % zero_int.rsp
% 0.33/0.61  thf(fact_5800_int_Oabs__eq__iff,axiom,
% 0.33/0.61      ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.33/0.61        ( ( ( abs_Integ @ X2 )
% 0.33/0.61          = ( abs_Integ @ Y ) )
% 0.33/0.61        = ( intrel @ X2 @ Y ) ) ).
% 0.33/0.61  
% 0.33/0.61  % int.abs_eq_iff
% 0.33/0.61  thf(fact_5801_uminus__int_Orsp,axiom,
% 0.33/0.61      ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 0.33/0.61      @ ( produc2626176000494625587at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X ) )
% 0.33/0.61      @ ( produc2626176000494625587at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % uminus_int.rsp
% 0.33/0.61  thf(fact_5802_nat_Orsp,axiom,
% 0.33/0.61      ( bNF_re8246922863344978751at_nat @ intrel
% 0.33/0.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.61      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 0.33/0.61      @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 0.33/0.61  
% 0.33/0.61  % nat.rsp
% 0.33/0.61  thf(fact_5803_one__int_Orsp,axiom,
% 0.33/0.61      intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.33/0.61  
% 0.33/0.61  % one_int.rsp
% 0.33/0.61  thf(fact_5804_intrel__def,axiom,
% 0.33/0.61      ( intrel
% 0.33/0.61      = ( produc8739625826339149834_nat_o
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc6081775807080527818_nat_o
% 0.33/0.61            @ ^ [U2: nat,V3: nat] :
% 0.33/0.61                ( ( plus_plus_nat @ X @ V3 )
% 0.33/0.61                = ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % intrel_def
% 0.33/0.61  thf(fact_5805_less__int_Orsp,axiom,
% 0.33/0.61      ( bNF_re4202695980764964119_nat_o @ intrel
% 0.33/0.61      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.33/0.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.61      @ ( produc8739625826339149834_nat_o
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc6081775807080527818_nat_o
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 0.33/0.61      @ ( produc8739625826339149834_nat_o
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc6081775807080527818_nat_o
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_int.rsp
% 0.33/0.61  thf(fact_5806_less__eq__int_Orsp,axiom,
% 0.33/0.61      ( bNF_re4202695980764964119_nat_o @ intrel
% 0.33/0.61      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.33/0.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.61      @ ( produc8739625826339149834_nat_o
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc6081775807080527818_nat_o
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 0.33/0.61      @ ( produc8739625826339149834_nat_o
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc6081775807080527818_nat_o
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % less_eq_int.rsp
% 0.33/0.61  thf(fact_5807_minus__int_Orsp,axiom,
% 0.33/0.61      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.33/0.61      @ ( produc27273713700761075at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 0.33/0.61      @ ( produc27273713700761075at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % minus_int.rsp
% 0.33/0.61  thf(fact_5808_plus__int_Orsp,axiom,
% 0.33/0.61      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.33/0.61      @ ( produc27273713700761075at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 0.33/0.61      @ ( produc27273713700761075at_nat
% 0.33/0.61        @ ^ [X: nat,Y4: nat] :
% 0.33/0.61            ( produc2626176000494625587at_nat
% 0.33/0.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ).
% 0.33/0.61  
% 0.33/0.61  % plus_int.rsp
% 0.33/0.61  thf(fact_5809_le__enumerate,axiom,
% 0.33/0.61      ! [S3: set_nat,N: nat] :
% 0.33/0.62        ( ~ ( finite_finite_nat @ S3 )
% 0.33/0.62       => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % le_enumerate
% 0.33/0.62  thf(fact_5810_finite__le__enumerate,axiom,
% 0.33/0.62      ! [S3: set_nat,N: nat] :
% 0.33/0.62        ( ( finite_finite_nat @ S3 )
% 0.33/0.62       => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 0.33/0.62         => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % finite_le_enumerate
% 0.33/0.62  thf(fact_5811_Least__eq__0,axiom,
% 0.33/0.62      ! [P: nat > $o] :
% 0.33/0.62        ( ( P @ zero_zero_nat )
% 0.33/0.62       => ( ( ord_Least_nat @ P )
% 0.33/0.62          = zero_zero_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Least_eq_0
% 0.33/0.62  thf(fact_5812_Least__Suc2,axiom,
% 0.33/0.62      ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 0.33/0.62        ( ( P @ N )
% 0.33/0.62       => ( ( Q @ M )
% 0.33/0.62         => ( ~ ( P @ zero_zero_nat )
% 0.33/0.62           => ( ! [K3: nat] :
% 0.33/0.62                  ( ( P @ ( suc @ K3 ) )
% 0.33/0.62                  = ( Q @ K3 ) )
% 0.33/0.62             => ( ( ord_Least_nat @ P )
% 0.33/0.62                = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Least_Suc2
% 0.33/0.62  thf(fact_5813_Least__Suc,axiom,
% 0.33/0.62      ! [P: nat > $o,N: nat] :
% 0.33/0.62        ( ( P @ N )
% 0.33/0.62       => ( ~ ( P @ zero_zero_nat )
% 0.33/0.62         => ( ( ord_Least_nat @ P )
% 0.33/0.62            = ( suc
% 0.33/0.62              @ ( ord_Least_nat
% 0.33/0.62                @ ^ [M2: nat] : ( P @ ( suc @ M2 ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Least_Suc
% 0.33/0.62  thf(fact_5814_Inf__nat__def,axiom,
% 0.33/0.62      ( complete_Inf_Inf_nat
% 0.33/0.62      = ( ^ [X5: set_nat] :
% 0.33/0.62            ( ord_Least_nat
% 0.33/0.62            @ ^ [N3: nat] : ( member_nat @ N3 @ X5 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Inf_nat_def
% 0.33/0.62  thf(fact_5815_type__definition__integer,axiom,
% 0.33/0.62      type_d8366093980585677751er_int @ code_int_of_integer @ code_integer_of_int @ top_top_set_int ).
% 0.33/0.62  
% 0.33/0.62  % type_definition_integer
% 0.33/0.62  thf(fact_5816_mset__set__upto__eq__mset__upto,axiom,
% 0.33/0.62      ! [N: nat] :
% 0.33/0.62        ( ( mset_set_nat @ ( set_ord_lessThan_nat @ N ) )
% 0.33/0.62        = ( mset_nat @ ( upt @ zero_zero_nat @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % mset_set_upto_eq_mset_upto
% 0.33/0.62  thf(fact_5817_filterlim__lessThan__at__top,axiom,
% 0.33/0.62      filter3212408913953519116et_nat @ set_ord_lessThan_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 0.33/0.62  
% 0.33/0.62  % filterlim_lessThan_at_top
% 0.33/0.62  thf(fact_5818_filterlim__atMost__at__top,axiom,
% 0.33/0.62      filter3212408913953519116et_nat @ set_ord_atMost_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 0.33/0.62  
% 0.33/0.62  % filterlim_atMost_at_top
% 0.33/0.62  thf(fact_5819_bij__betw__Suc,axiom,
% 0.33/0.62      ! [M3: set_nat,N4: set_nat] :
% 0.33/0.62        ( ( bij_betw_nat_nat @ suc @ M3 @ N4 )
% 0.33/0.62        = ( ( image_nat_nat @ suc @ M3 )
% 0.33/0.62          = N4 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % bij_betw_Suc
% 0.33/0.62  thf(fact_5820_Sup__int__def,axiom,
% 0.33/0.62      ( complete_Sup_Sup_int
% 0.33/0.62      = ( ^ [X5: set_int] :
% 0.33/0.62            ( the_int
% 0.33/0.62            @ ^ [X: int] :
% 0.33/0.62                ( ( member_int @ X @ X5 )
% 0.33/0.62                & ! [Y4: int] :
% 0.33/0.62                    ( ( member_int @ Y4 @ X5 )
% 0.33/0.62                   => ( ord_less_eq_int @ Y4 @ X ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Sup_int_def
% 0.33/0.62  thf(fact_5821_and__not__num_Opelims,axiom,
% 0.33/0.62      ! [X2: num,Xa: num,Y: option_num] :
% 0.33/0.62        ( ( ( bit_and_not_num @ X2 @ Xa )
% 0.33/0.62          = Y )
% 0.33/0.62       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X2 @ Xa ) )
% 0.33/0.62         => ( ( ( X2 = one )
% 0.33/0.62             => ( ( Xa = one )
% 0.33/0.62               => ( ( Y = none_num )
% 0.33/0.62                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.33/0.62           => ( ( ( X2 = one )
% 0.33/0.62               => ! [N2: num] :
% 0.33/0.62                    ( ( Xa
% 0.33/0.62                      = ( bit0 @ N2 ) )
% 0.33/0.62                   => ( ( Y
% 0.33/0.62                        = ( some_num @ one ) )
% 0.33/0.62                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 0.33/0.62             => ( ( ( X2 = one )
% 0.33/0.62                 => ! [N2: num] :
% 0.33/0.62                      ( ( Xa
% 0.33/0.62                        = ( bit1 @ N2 ) )
% 0.33/0.62                     => ( ( Y = none_num )
% 0.33/0.62                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 0.33/0.62               => ( ! [M4: num] :
% 0.33/0.62                      ( ( X2
% 0.33/0.62                        = ( bit0 @ M4 ) )
% 0.33/0.62                     => ( ( Xa = one )
% 0.33/0.62                       => ( ( Y
% 0.33/0.62                            = ( some_num @ ( bit0 @ M4 ) ) )
% 0.33/0.62                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 0.33/0.62                 => ( ! [M4: num] :
% 0.33/0.62                        ( ( X2
% 0.33/0.62                          = ( bit0 @ M4 ) )
% 0.33/0.62                       => ! [N2: num] :
% 0.33/0.62                            ( ( Xa
% 0.33/0.62                              = ( bit0 @ N2 ) )
% 0.33/0.62                           => ( ( Y
% 0.33/0.62                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 0.33/0.62                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.33/0.62                   => ( ! [M4: num] :
% 0.33/0.62                          ( ( X2
% 0.33/0.62                            = ( bit0 @ M4 ) )
% 0.33/0.62                         => ! [N2: num] :
% 0.33/0.62                              ( ( Xa
% 0.33/0.62                                = ( bit1 @ N2 ) )
% 0.33/0.62                             => ( ( Y
% 0.33/0.62                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 0.33/0.62                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 0.33/0.62                     => ( ! [M4: num] :
% 0.33/0.62                            ( ( X2
% 0.33/0.62                              = ( bit1 @ M4 ) )
% 0.33/0.62                           => ( ( Xa = one )
% 0.33/0.62                             => ( ( Y
% 0.33/0.62                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 0.33/0.62                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 0.33/0.62                       => ( ! [M4: num] :
% 0.33/0.62                              ( ( X2
% 0.33/0.62                                = ( bit1 @ M4 ) )
% 0.33/0.62                             => ! [N2: num] :
% 0.33/0.62                                  ( ( Xa
% 0.33/0.62                                    = ( bit0 @ N2 ) )
% 0.33/0.62                                 => ( ( Y
% 0.33/0.62                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.62                                        @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 0.33/0.62                                        @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 0.33/0.62                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.33/0.62                         => ~ ! [M4: num] :
% 0.33/0.62                                ( ( X2
% 0.33/0.62                                  = ( bit1 @ M4 ) )
% 0.33/0.62                               => ! [N2: num] :
% 0.33/0.62                                    ( ( Xa
% 0.33/0.62                                      = ( bit1 @ N2 ) )
% 0.33/0.62                                   => ( ( Y
% 0.33/0.62                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 0.33/0.62                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % and_not_num.pelims
% 0.33/0.62  thf(fact_5822_and__num_Opelims,axiom,
% 0.33/0.62      ! [X2: num,Xa: num,Y: option_num] :
% 0.33/0.62        ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa )
% 0.33/0.62          = Y )
% 0.33/0.62       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X2 @ Xa ) )
% 0.33/0.62         => ( ( ( X2 = one )
% 0.33/0.62             => ( ( Xa = one )
% 0.33/0.62               => ( ( Y
% 0.33/0.62                    = ( some_num @ one ) )
% 0.33/0.62                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.33/0.62           => ( ( ( X2 = one )
% 0.33/0.62               => ! [N2: num] :
% 0.33/0.62                    ( ( Xa
% 0.33/0.62                      = ( bit0 @ N2 ) )
% 0.33/0.62                   => ( ( Y = none_num )
% 0.33/0.62                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 0.33/0.62             => ( ( ( X2 = one )
% 0.33/0.62                 => ! [N2: num] :
% 0.33/0.62                      ( ( Xa
% 0.33/0.62                        = ( bit1 @ N2 ) )
% 0.33/0.62                     => ( ( Y
% 0.33/0.62                          = ( some_num @ one ) )
% 0.33/0.62                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 0.33/0.62               => ( ! [M4: num] :
% 0.33/0.62                      ( ( X2
% 0.33/0.62                        = ( bit0 @ M4 ) )
% 0.33/0.62                     => ( ( Xa = one )
% 0.33/0.62                       => ( ( Y = none_num )
% 0.33/0.62                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 0.33/0.62                 => ( ! [M4: num] :
% 0.33/0.62                        ( ( X2
% 0.33/0.62                          = ( bit0 @ M4 ) )
% 0.33/0.62                       => ! [N2: num] :
% 0.33/0.62                            ( ( Xa
% 0.33/0.62                              = ( bit0 @ N2 ) )
% 0.33/0.62                           => ( ( Y
% 0.33/0.62                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 0.33/0.62                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.33/0.62                   => ( ! [M4: num] :
% 0.33/0.62                          ( ( X2
% 0.33/0.62                            = ( bit0 @ M4 ) )
% 0.33/0.62                         => ! [N2: num] :
% 0.33/0.62                              ( ( Xa
% 0.33/0.62                                = ( bit1 @ N2 ) )
% 0.33/0.62                             => ( ( Y
% 0.33/0.62                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 0.33/0.62                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 0.33/0.62                     => ( ! [M4: num] :
% 0.33/0.62                            ( ( X2
% 0.33/0.62                              = ( bit1 @ M4 ) )
% 0.33/0.62                           => ( ( Xa = one )
% 0.33/0.62                             => ( ( Y
% 0.33/0.62                                  = ( some_num @ one ) )
% 0.33/0.62                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 0.33/0.62                       => ( ! [M4: num] :
% 0.33/0.62                              ( ( X2
% 0.33/0.62                                = ( bit1 @ M4 ) )
% 0.33/0.62                             => ! [N2: num] :
% 0.33/0.62                                  ( ( Xa
% 0.33/0.62                                    = ( bit0 @ N2 ) )
% 0.33/0.62                                 => ( ( Y
% 0.33/0.62                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 0.33/0.62                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 0.33/0.62                         => ~ ! [M4: num] :
% 0.33/0.62                                ( ( X2
% 0.33/0.62                                  = ( bit1 @ M4 ) )
% 0.33/0.62                               => ! [N2: num] :
% 0.33/0.62                                    ( ( Xa
% 0.33/0.62                                      = ( bit1 @ N2 ) )
% 0.33/0.62                                   => ( ( Y
% 0.33/0.62                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.33/0.62                                          @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 0.33/0.62                                          @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 0.33/0.62                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % and_num.pelims
% 0.33/0.62  thf(fact_5823_int_Obi__total,axiom,
% 0.33/0.62      bi_tot896582865486249351at_int @ pcr_int ).
% 0.33/0.62  
% 0.33/0.62  % int.bi_total
% 0.33/0.62  thf(fact_5824_Domainp__cr__rat,axiom,
% 0.33/0.62      ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 0.33/0.62      = ( ^ [X: product_prod_int_int] :
% 0.33/0.62            ( ( product_snd_int_int @ X )
% 0.33/0.62           != zero_zero_int ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Domainp_cr_rat
% 0.33/0.62  thf(fact_5825_eventually__sequentially__Suc,axiom,
% 0.33/0.62      ! [P: nat > $o] :
% 0.33/0.62        ( ( eventually_nat
% 0.33/0.62          @ ^ [I2: nat] : ( P @ ( suc @ I2 ) )
% 0.33/0.62          @ at_top_nat )
% 0.33/0.62        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % eventually_sequentially_Suc
% 0.33/0.62  thf(fact_5826_eventually__sequentially__seg,axiom,
% 0.33/0.62      ! [P: nat > $o,K: nat] :
% 0.33/0.62        ( ( eventually_nat
% 0.33/0.62          @ ^ [N3: nat] : ( P @ ( plus_plus_nat @ N3 @ K ) )
% 0.33/0.62          @ at_top_nat )
% 0.33/0.62        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % eventually_sequentially_seg
% 0.33/0.62  thf(fact_5827_eventually__sequentially,axiom,
% 0.33/0.62      ! [P: nat > $o] :
% 0.33/0.62        ( ( eventually_nat @ P @ at_top_nat )
% 0.33/0.62        = ( ? [N8: nat] :
% 0.33/0.62            ! [N3: nat] :
% 0.33/0.62              ( ( ord_less_eq_nat @ N8 @ N3 )
% 0.33/0.62             => ( P @ N3 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % eventually_sequentially
% 0.33/0.62  thf(fact_5828_eventually__sequentiallyI,axiom,
% 0.33/0.62      ! [C: nat,P: nat > $o] :
% 0.33/0.62        ( ! [X3: nat] :
% 0.33/0.62            ( ( ord_less_eq_nat @ C @ X3 )
% 0.33/0.62           => ( P @ X3 ) )
% 0.33/0.62       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % eventually_sequentiallyI
% 0.33/0.62  thf(fact_5829_le__sequentially,axiom,
% 0.33/0.62      ! [F4: filter_nat] :
% 0.33/0.62        ( ( ord_le2510731241096832064er_nat @ F4 @ at_top_nat )
% 0.33/0.62        = ( ! [N8: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N8 ) @ F4 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % le_sequentially
% 0.33/0.62  thf(fact_5830_eventually__False__sequentially,axiom,
% 0.33/0.62      ~ ( eventually_nat
% 0.33/0.62        @ ^ [N3: nat] : $false
% 0.33/0.62        @ at_top_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % eventually_False_sequentially
% 0.33/0.62  thf(fact_5831_int_Oright__total,axiom,
% 0.33/0.62      right_1157779049177982926at_int @ pcr_int ).
% 0.33/0.62  
% 0.33/0.62  % int.right_total
% 0.33/0.62  thf(fact_5832_pair__lessI2,axiom,
% 0.33/0.62      ! [A: nat,B: nat,S: nat,T: nat] :
% 0.33/0.62        ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.62       => ( ( ord_less_nat @ S @ T )
% 0.33/0.62         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % pair_lessI2
% 0.33/0.62  thf(fact_5833_pair__leqI2,axiom,
% 0.33/0.62      ! [A: nat,B: nat,S: nat,T: nat] :
% 0.33/0.62        ( ( ord_less_eq_nat @ A @ B )
% 0.33/0.62       => ( ( ord_less_eq_nat @ S @ T )
% 0.33/0.62         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % pair_leqI2
% 0.33/0.62  thf(fact_5834_euclidean__size__integer_Orep__eq,axiom,
% 0.33/0.62      ( euclid6377331345833325938nteger
% 0.33/0.62      = ( ^ [X: code_integer] : ( euclid4774559944035922753ze_int @ ( code_int_of_integer @ X ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % euclidean_size_integer.rep_eq
% 0.33/0.62  thf(fact_5835_euclidean__size__integer__def,axiom,
% 0.33/0.62      ( euclid6377331345833325938nteger
% 0.33/0.62      = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ euclid4774559944035922753ze_int ) ) ).
% 0.33/0.62  
% 0.33/0.62  % euclidean_size_integer_def
% 0.33/0.62  thf(fact_5836_euclidean__size__integer_Oabs__eq,axiom,
% 0.33/0.62      ! [X2: int] :
% 0.33/0.62        ( ( euclid6377331345833325938nteger @ ( code_integer_of_int @ X2 ) )
% 0.33/0.62        = ( euclid4774559944035922753ze_int @ X2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % euclidean_size_integer.abs_eq
% 0.33/0.62  thf(fact_5837_euclidean__size__natural_Orsp,axiom,
% 0.33/0.62      ( bNF_re5653821019739307937at_nat
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ euclid4777050414544973029ze_nat
% 0.33/0.62      @ euclid4777050414544973029ze_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % euclidean_size_natural.rsp
% 0.33/0.62  thf(fact_5838_euclidean__size__integer_Orsp,axiom,
% 0.33/0.62      ( bNF_re3715656647883201625at_nat
% 0.33/0.62      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ euclid4774559944035922753ze_int
% 0.33/0.62      @ euclid4774559944035922753ze_int ) ).
% 0.33/0.62  
% 0.33/0.62  % euclidean_size_integer.rsp
% 0.33/0.62  thf(fact_5839_division__segment__integer_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_integer] :
% 0.33/0.62        ( ( code_int_of_integer @ ( euclid6289375185220004616nteger @ X2 ) )
% 0.33/0.62        = ( euclid3395696857347342551nt_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_integer.rep_eq
% 0.33/0.62  thf(fact_5840_abs__division__segment,axiom,
% 0.33/0.62      ! [K: int] :
% 0.33/0.62        ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 0.33/0.62        = one_one_int ) ).
% 0.33/0.62  
% 0.33/0.62  % abs_division_segment
% 0.33/0.62  thf(fact_5841_division__segment__integer_Orsp,axiom,
% 0.33/0.62      ( bNF_re4712519889275205905nt_int
% 0.33/0.62      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62      @ euclid3395696857347342551nt_int
% 0.33/0.62      @ euclid3395696857347342551nt_int ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_integer.rsp
% 0.33/0.62  thf(fact_5842_division__segment__natural_Orsp,axiom,
% 0.33/0.62      ( bNF_re5653821019739307937at_nat
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ euclid3398187327856392827nt_nat
% 0.33/0.62      @ euclid3398187327856392827nt_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_natural.rsp
% 0.33/0.62  thf(fact_5843_division__segment__nat__def,axiom,
% 0.33/0.62      ( euclid3398187327856392827nt_nat
% 0.33/0.62      = ( ^ [N3: nat] : one_one_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_nat_def
% 0.33/0.62  thf(fact_5844_division__segment__integer_Oabs__eq,axiom,
% 0.33/0.62      ! [X2: int] :
% 0.33/0.62        ( ( euclid6289375185220004616nteger @ ( code_integer_of_int @ X2 ) )
% 0.33/0.62        = ( code_integer_of_int @ ( euclid3395696857347342551nt_int @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_integer.abs_eq
% 0.33/0.62  thf(fact_5845_division__segment__eq__sgn,axiom,
% 0.33/0.62      ! [K: int] :
% 0.33/0.62        ( ( K != zero_zero_int )
% 0.33/0.62       => ( ( euclid3395696857347342551nt_int @ K )
% 0.33/0.62          = ( sgn_sgn_int @ K ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_eq_sgn
% 0.33/0.62  thf(fact_5846_division__segment__integer__def,axiom,
% 0.33/0.62      ( euclid6289375185220004616nteger
% 0.33/0.62      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ euclid3395696857347342551nt_int ) ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_integer_def
% 0.33/0.62  thf(fact_5847_division__segment__int__def,axiom,
% 0.33/0.62      ( euclid3395696857347342551nt_int
% 0.33/0.62      = ( ^ [K2: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_int_def
% 0.33/0.62  thf(fact_5848_wf__int__ge__less__than2,axiom,
% 0.33/0.62      ! [D: int] : ( wf_int @ ( int_ge_less_than2 @ D ) ) ).
% 0.33/0.62  
% 0.33/0.62  % wf_int_ge_less_than2
% 0.33/0.62  thf(fact_5849_wf__int__ge__less__than,axiom,
% 0.33/0.62      ! [D: int] : ( wf_int @ ( int_ge_less_than @ D ) ) ).
% 0.33/0.62  
% 0.33/0.62  % wf_int_ge_less_than
% 0.33/0.62  thf(fact_5850_wf__less,axiom,
% 0.33/0.62      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % wf_less
% 0.33/0.62  thf(fact_5851_num__of__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re6718328864250387230um_num @ code_pcr_integer
% 0.33/0.62      @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 0.33/0.62      @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 0.33/0.62      @ code_num_of_integer ) ).
% 0.33/0.62  
% 0.33/0.62  % num_of_integer.transfer
% 0.33/0.62  thf(fact_5852_euclidean__size__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ euclid4774559944035922753ze_int
% 0.33/0.62      @ euclid6377331345833325938nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % euclidean_size_integer.transfer
% 0.33/0.62  thf(fact_5853_integer_Oleft__unique,axiom,
% 0.33/0.62      left_u6795595883297946906nteger @ code_pcr_integer ).
% 0.33/0.62  
% 0.33/0.62  % integer.left_unique
% 0.33/0.62  thf(fact_5854_zero__integer_Otransfer,axiom,
% 0.33/0.62      code_pcr_integer @ zero_zero_int @ zero_z3403309356797280102nteger ).
% 0.33/0.62  
% 0.33/0.62  % zero_integer.transfer
% 0.33/0.62  thf(fact_5855_one__integer_Otransfer,axiom,
% 0.33/0.62      code_pcr_integer @ one_one_int @ one_one_Code_integer ).
% 0.33/0.62  
% 0.33/0.62  % one_integer.transfer
% 0.33/0.62  thf(fact_5856_integer_Obi__unique,axiom,
% 0.33/0.62      bi_uni8663861020805155098nteger @ code_pcr_integer ).
% 0.33/0.62  
% 0.33/0.62  % integer.bi_unique
% 0.33/0.62  thf(fact_5857_integer_Odomain,axiom,
% 0.33/0.62      ! [P: int > $o] :
% 0.33/0.62        ( ( ( domainp_int_int
% 0.33/0.62            @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.62          = P )
% 0.33/0.62       => ( ( domain452967906960104687nteger @ code_pcr_integer )
% 0.33/0.62          = P ) ) ).
% 0.33/0.62  
% 0.33/0.62  % integer.domain
% 0.33/0.62  thf(fact_5858_integer_Obi__total,axiom,
% 0.33/0.62      bi_tot1331153423839324337nteger @ code_pcr_integer ).
% 0.33/0.62  
% 0.33/0.62  % integer.bi_total
% 0.33/0.62  thf(fact_5859_flip__bit__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re4935368626670024657nteger
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.62      @ bit_se2159334234014336723it_int
% 0.33/0.62      @ bit_se1345352211410354436nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % flip_bit_integer.transfer
% 0.33/0.62  thf(fact_5860_push__bit__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re4935368626670024657nteger
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.62      @ bit_se545348938243370406it_int
% 0.33/0.62      @ bit_se7788150548672797655nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % push_bit_integer.transfer
% 0.33/0.62  thf(fact_5861_drop__bit__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re4935368626670024657nteger
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.62      @ bit_se8568078237143864401it_int
% 0.33/0.62      @ bit_se3928097537394005634nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % drop_bit_integer.transfer
% 0.33/0.62  thf(fact_5862_xor__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se6526347334894502574or_int @ bit_se3222712562003087583nteger ).
% 0.33/0.62  
% 0.33/0.62  % xor_integer.transfer
% 0.33/0.62  thf(fact_5863_bit__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re4711666741709854504_nat_o @ code_pcr_integer
% 0.33/0.62      @ ^ [Y3: nat > $o,Z: nat > $o] : ( Y3 = Z )
% 0.33/0.62      @ bit_se1146084159140164899it_int
% 0.33/0.62      @ bit_se9216721137139052372nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % bit_integer.transfer
% 0.33/0.62  thf(fact_5864_or__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se1409905431419307370or_int @ bit_se1080825931792720795nteger ).
% 0.33/0.62  
% 0.33/0.62  % or_integer.transfer
% 0.33/0.62  thf(fact_5865_take__bit__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re4935368626670024657nteger
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.62      @ bit_se2923211474154528505it_int
% 0.33/0.62      @ bit_se1745604003318907178nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % take_bit_integer.transfer
% 0.33/0.62  thf(fact_5866_not__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ bit_ri7919022796975470100ot_int @ bit_ri7632146776885996613nteger ).
% 0.33/0.62  
% 0.33/0.62  % not_integer.transfer
% 0.33/0.62  thf(fact_5867_and__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se725231765392027082nd_int @ bit_se3949692690581998587nteger ).
% 0.33/0.62  
% 0.33/0.62  % and_integer.transfer
% 0.33/0.62  thf(fact_5868_dup_Otransfer,axiom,
% 0.33/0.62      ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer
% 0.33/0.62      @ ^ [K2: int] : ( plus_plus_int @ K2 @ K2 )
% 0.33/0.62      @ code_dup ) ).
% 0.33/0.62  
% 0.33/0.62  % dup.transfer
% 0.33/0.62  thf(fact_5869_integer__of__nat_Otransfer,axiom,
% 0.33/0.62      ( bNF_re4153400068438556298nteger
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ code_pcr_integer
% 0.33/0.62      @ semiri1314217659103216013at_int
% 0.33/0.62      @ code_integer_of_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % integer_of_nat.transfer
% 0.33/0.62  thf(fact_5870_less__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 0.33/0.62      @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 0.33/0.62        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.62      @ ord_less_int
% 0.33/0.62      @ ord_le6747313008572928689nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % less_integer.transfer
% 0.33/0.62  thf(fact_5871_times__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ times_times_int @ times_3573771949741848930nteger ).
% 0.33/0.62  
% 0.33/0.62  % times_integer.transfer
% 0.33/0.62  thf(fact_5872_divide__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ divide_divide_int @ divide6298287555418463151nteger ).
% 0.33/0.62  
% 0.33/0.62  % divide_integer.transfer
% 0.33/0.62  thf(fact_5873_abs__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ abs_abs_int @ abs_abs_Code_integer ).
% 0.33/0.62  
% 0.33/0.62  % abs_integer.transfer
% 0.33/0.62  thf(fact_5874_nat__of__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ nat2
% 0.33/0.62      @ code_nat_of_integer ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_integer.transfer
% 0.33/0.62  thf(fact_5875_modulo__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ modulo_modulo_int @ modulo364778990260209775nteger ).
% 0.33/0.62  
% 0.33/0.62  % modulo_integer.transfer
% 0.33/0.62  thf(fact_5876_plus__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ plus_plus_int @ plus_p5714425477246183910nteger ).
% 0.33/0.62  
% 0.33/0.62  % plus_integer.transfer
% 0.33/0.62  thf(fact_5877_sgn__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ sgn_sgn_int @ sgn_sgn_Code_integer ).
% 0.33/0.62  
% 0.33/0.62  % sgn_integer.transfer
% 0.33/0.62  thf(fact_5878_integer_Orep__transfer,axiom,
% 0.33/0.62      ( bNF_re3804157879324367682nt_int @ code_pcr_integer
% 0.33/0.62      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62      @ ^ [X: int] : X
% 0.33/0.62      @ code_int_of_integer ) ).
% 0.33/0.62  
% 0.33/0.62  % integer.rep_transfer
% 0.33/0.62  thf(fact_5879_integer_Oid__abs__transfer,axiom,
% 0.33/0.62      ( bNF_re982302072995117890nteger
% 0.33/0.62      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62      @ code_pcr_integer
% 0.33/0.62      @ ^ [X: int] : X
% 0.33/0.62      @ code_integer_of_int ) ).
% 0.33/0.62  
% 0.33/0.62  % integer.id_abs_transfer
% 0.33/0.62  thf(fact_5880_gcd__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ gcd_gcd_int @ gcd_gcd_Code_integer ).
% 0.33/0.62  
% 0.33/0.62  % gcd_integer.transfer
% 0.33/0.62  thf(fact_5881_minus__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ minus_minus_int @ minus_8373710615458151222nteger ).
% 0.33/0.62  
% 0.33/0.62  % minus_integer.transfer
% 0.33/0.62  thf(fact_5882_uminus__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ uminus_uminus_int @ uminus1351360451143612070nteger ).
% 0.33/0.62  
% 0.33/0.62  % uminus_integer.transfer
% 0.33/0.62  thf(fact_5883_mask__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re4153400068438556298nteger
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ code_pcr_integer
% 0.33/0.62      @ bit_se2000444600071755411sk_int
% 0.33/0.62      @ bit_se2119862282449309892nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % mask_integer.transfer
% 0.33/0.62  thf(fact_5884_unset__bit__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re4935368626670024657nteger
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.62      @ bit_se4203085406695923979it_int
% 0.33/0.62      @ bit_se8260200283734997820nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % unset_bit_integer.transfer
% 0.33/0.62  thf(fact_5885_set__bit__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re4935368626670024657nteger
% 0.33/0.62      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 0.33/0.62      @ bit_se7879613467334960850it_int
% 0.33/0.62      @ bit_se2793503036327961859nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % set_bit_integer.transfer
% 0.33/0.62  thf(fact_5886_integer_Oright__total,axiom,
% 0.33/0.62      right_7281159819619925802nteger @ code_pcr_integer ).
% 0.33/0.62  
% 0.33/0.62  % integer.right_total
% 0.33/0.62  thf(fact_5887_less__eq__integer_Otransfer,axiom,
% 0.33/0.62      ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 0.33/0.62      @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 0.33/0.62        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.33/0.62      @ ord_less_eq_int
% 0.33/0.62      @ ord_le3102999989581377725nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % less_eq_integer.transfer
% 0.33/0.62  thf(fact_5888_division__segment__integer_Otransfer,axiom,
% 0.33/0.62      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ euclid3395696857347342551nt_int @ euclid6289375185220004616nteger ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_integer.transfer
% 0.33/0.62  thf(fact_5889_sub_Otransfer,axiom,
% 0.33/0.62      ( bNF_re7876454716742015248nteger
% 0.33/0.62      @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 0.33/0.62      @ ( bNF_re6501075790457514782nteger
% 0.33/0.62        @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 0.33/0.62        @ code_pcr_integer )
% 0.33/0.62      @ ^ [M2: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N3 ) )
% 0.33/0.62      @ code_sub ) ).
% 0.33/0.62  
% 0.33/0.62  % sub.transfer
% 0.33/0.62  thf(fact_5890_eventually__prod__sequentially,axiom,
% 0.33/0.62      ! [P: product_prod_nat_nat > $o] :
% 0.33/0.62        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 0.33/0.62        = ( ? [N8: nat] :
% 0.33/0.62            ! [M2: nat] :
% 0.33/0.62              ( ( ord_less_eq_nat @ N8 @ M2 )
% 0.33/0.62             => ! [N3: nat] :
% 0.33/0.62                  ( ( ord_less_eq_nat @ N8 @ N3 )
% 0.33/0.62                 => ( P @ ( product_Pair_nat_nat @ N3 @ M2 ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % eventually_prod_sequentially
% 0.33/0.62  thf(fact_5891_UNIV__char__of__nat,axiom,
% 0.33/0.62      ( top_top_set_char
% 0.33/0.62      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % UNIV_char_of_nat
% 0.33/0.62  thf(fact_5892_inj__on__char__of__nat,axiom,
% 0.33/0.62      inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % inj_on_char_of_nat
% 0.33/0.62  thf(fact_5893_range__nat__of__char,axiom,
% 0.33/0.62      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 0.33/0.62      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % range_nat_of_char
% 0.33/0.62  thf(fact_5894_char_Osize_I2_J,axiom,
% 0.33/0.62      ! [X12: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X8: $o] :
% 0.33/0.62        ( ( size_size_char @ ( char2 @ X12 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X8 ) )
% 0.33/0.62        = zero_zero_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % char.size(2)
% 0.33/0.62  thf(fact_5895_integer__of__char__code,axiom,
% 0.33/0.62      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B6: $o,B7: $o] :
% 0.33/0.62        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B6 @ B7 ) )
% 0.33/0.62        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B7 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B6 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % integer_of_char_code
% 0.33/0.62  thf(fact_5896_char_Osize__gen,axiom,
% 0.33/0.62      ! [X12: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X8: $o] :
% 0.33/0.62        ( ( size_char @ ( char2 @ X12 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X8 ) )
% 0.33/0.62        = zero_zero_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % char.size_gen
% 0.33/0.62  thf(fact_5897_char__of__integer__code,axiom,
% 0.33/0.62      ( char_of_integer
% 0.33/0.62      = ( ^ [K2: code_integer] :
% 0.33/0.62            ( produc4188289175737317920o_char
% 0.33/0.62            @ ^ [Q0: code_integer,B02: $o] :
% 0.33/0.62                ( produc4188289175737317920o_char
% 0.33/0.62                @ ^ [Q1: code_integer,B12: $o] :
% 0.33/0.62                    ( produc4188289175737317920o_char
% 0.33/0.62                    @ ^ [Q22: code_integer,B23: $o] :
% 0.33/0.62                        ( produc4188289175737317920o_char
% 0.33/0.62                        @ ^ [Q32: code_integer,B33: $o] :
% 0.33/0.62                            ( produc4188289175737317920o_char
% 0.33/0.62                            @ ^ [Q42: code_integer,B43: $o] :
% 0.33/0.62                                ( produc4188289175737317920o_char
% 0.33/0.62                                @ ^ [Q52: code_integer,B53: $o] :
% 0.33/0.62                                    ( produc4188289175737317920o_char
% 0.33/0.62                                    @ ^ [Q62: code_integer,B62: $o] :
% 0.33/0.62                                        ( produc4188289175737317920o_char
% 0.33/0.62                                        @ ^ [Uu: code_integer] : ( char2 @ B02 @ B12 @ B23 @ B33 @ B43 @ B53 @ B62 )
% 0.33/0.62                                        @ ( code_bit_cut_integer @ Q62 ) )
% 0.33/0.62                                    @ ( code_bit_cut_integer @ Q52 ) )
% 0.33/0.62                                @ ( code_bit_cut_integer @ Q42 ) )
% 0.33/0.62                            @ ( code_bit_cut_integer @ Q32 ) )
% 0.33/0.62                        @ ( code_bit_cut_integer @ Q22 ) )
% 0.33/0.62                    @ ( code_bit_cut_integer @ Q1 ) )
% 0.33/0.62                @ ( code_bit_cut_integer @ Q0 ) )
% 0.33/0.62            @ ( code_bit_cut_integer @ K2 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % char_of_integer_code
% 0.33/0.62  thf(fact_5898_assert_H__def,axiom,
% 0.33/0.62      ( refine_Imp_assert
% 0.33/0.62      = ( ^ [P5: $o] : ( if_Hea8138950348631371857t_unit @ P5 @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % assert'_def
% 0.33/0.62  thf(fact_5899_wait__def,axiom,
% 0.33/0.62      ( heap_Time_wait
% 0.33/0.62      = ( ^ [N3: nat] :
% 0.33/0.62            ( heap_T6183433275982383450t_unit
% 0.33/0.62            @ ^ [H3: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H3 @ N3 ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % wait_def
% 0.33/0.62  thf(fact_5900_unit__all__impI,axiom,
% 0.33/0.62      ! [P: product_unit > $o,Q: product_unit > $o] :
% 0.33/0.62        ( ( ( P @ product_Unity )
% 0.33/0.62         => ( Q @ product_Unity ) )
% 0.33/0.62       => ! [X4: product_unit] :
% 0.33/0.62            ( ( P @ X4 )
% 0.33/0.62           => ( Q @ X4 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % unit_all_impI
% 0.33/0.62  thf(fact_5901_eq__sym__Unity__conv,axiom,
% 0.33/0.62      ! [X2: $o] :
% 0.33/0.62        ( ( X2
% 0.33/0.62          = ( product_Unity = product_Unity ) )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  % eq_sym_Unity_conv
% 0.33/0.62  thf(fact_5902_refines__assert_H,axiom,
% 0.33/0.62      ! [Phi: $o] : ( refine451278484176762712t_unit @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( refine_Imp_assert @ Phi ) ) ).
% 0.33/0.62  
% 0.33/0.62  % refines_assert'
% 0.33/0.62  thf(fact_5903_execute__assert_H,axiom,
% 0.33/0.62      ! [P: $o,H: heap_e7401611519738050253t_unit] :
% 0.33/0.62        ( ( P
% 0.33/0.62         => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H )
% 0.33/0.62            = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H @ zero_zero_nat ) ) ) ) )
% 0.33/0.62        & ( ~ P
% 0.33/0.62         => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H )
% 0.33/0.62            = none_P9117596204409417319it_nat ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % execute_assert'
% 0.33/0.62  thf(fact_5904_natural__zero__minus__one,axiom,
% 0.33/0.62      ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 0.33/0.62      = zero_z2226904508553997617atural ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_zero_minus_one
% 0.33/0.62  thf(fact_5905_minus__shift__def,axiom,
% 0.33/0.62      ( minus_shift
% 0.33/0.62      = ( ^ [R2: code_natural,K2: code_natural,L2: code_natural] : ( if_Code_natural @ ( ord_le5570908160329646204atural @ K2 @ L2 ) @ ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ R2 @ K2 ) @ L2 ) @ ( minus_7197305767214868737atural @ K2 @ L2 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % minus_shift_def
% 0.33/0.62  thf(fact_5906_next_Osimps,axiom,
% 0.33/0.62      ! [V: code_natural,W2: code_natural] :
% 0.33/0.62        ( ( next @ ( produc3574140220909816553atural @ V @ W2 ) )
% 0.33/0.62        = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % next.simps
% 0.33/0.62  thf(fact_5907_log_Oelims,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural,Y: code_natural] :
% 0.33/0.62        ( ( ( log @ X2 @ Xa )
% 0.33/0.62          = Y )
% 0.33/0.62       => ( ( ( ( ord_le1926595141338095240atural @ X2 @ one_one_Code_natural )
% 0.33/0.62              | ( ord_le5570908160329646204atural @ Xa @ X2 ) )
% 0.33/0.62           => ( Y = one_one_Code_natural ) )
% 0.33/0.62          & ( ~ ( ( ord_le1926595141338095240atural @ X2 @ one_one_Code_natural )
% 0.33/0.62                | ( ord_le5570908160329646204atural @ Xa @ X2 ) )
% 0.33/0.62           => ( Y
% 0.33/0.62              = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X2 @ ( divide5121882707175180666atural @ Xa @ X2 ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % log.elims
% 0.33/0.62  thf(fact_5908_log_Osimps,axiom,
% 0.33/0.62      ( log
% 0.33/0.62      = ( ^ [B2: code_natural,I2: code_natural] :
% 0.33/0.62            ( if_Code_natural
% 0.33/0.62            @ ( ( ord_le1926595141338095240atural @ B2 @ one_one_Code_natural )
% 0.33/0.62              | ( ord_le5570908160329646204atural @ I2 @ B2 ) )
% 0.33/0.62            @ one_one_Code_natural
% 0.33/0.62            @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B2 @ ( divide5121882707175180666atural @ I2 @ B2 ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % log.simps
% 0.33/0.62  thf(fact_5909_split__seed__def,axiom,
% 0.33/0.62      ( split_seed
% 0.33/0.62      = ( ^ [S4: produc7822875418678951345atural] :
% 0.33/0.62            ( produc8282080750456430313atural
% 0.33/0.62            @ ^ [V3: code_natural,W: code_natural] :
% 0.33/0.62                ( produc8282080750456430313atural
% 0.33/0.62                @ ^ [V5: code_natural,W4: code_natural] : ( produc4480994950612372183atural @ ( produc3574140220909816553atural @ ( inc_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ V3 ) @ W4 ) @ ( produc3574140220909816553atural @ V5 @ ( inc_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ W ) ) )
% 0.33/0.62                @ ( produc6591912806276919810atural @ ( next @ S4 ) ) )
% 0.33/0.62            @ S4 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % split_seed_def
% 0.33/0.62  thf(fact_5910_Random_Orange__def,axiom,
% 0.33/0.62      ( range
% 0.33/0.62      = ( ^ [K2: code_natural] :
% 0.33/0.62            ( produc5538323210962509403atural
% 0.33/0.62            @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K2 )
% 0.33/0.62              @ ^ [L2: code_natural] :
% 0.33/0.62                  ( produc5538323210962509403atural @ next
% 0.33/0.62                  @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V3 @ ( times_2397367101498566445atural @ L2 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.33/0.62              @ one_one_Code_natural )
% 0.33/0.62            @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V3 @ K2 ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Random.range_def
% 0.33/0.62  thf(fact_5911_inc__shift__def,axiom,
% 0.33/0.62      ( inc_shift
% 0.33/0.62      = ( ^ [V3: code_natural,K2: code_natural] : ( if_Code_natural @ ( V3 = K2 ) @ one_one_Code_natural @ ( plus_p4538020629002901425atural @ K2 @ one_one_Code_natural ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % inc_shift_def
% 0.33/0.62  thf(fact_5912_log_Opelims,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural,Y: code_natural] :
% 0.33/0.62        ( ( ( log @ X2 @ Xa )
% 0.33/0.62          = Y )
% 0.33/0.62       => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X2 @ Xa ) )
% 0.33/0.62         => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X2 @ one_one_Code_natural )
% 0.33/0.62                    | ( ord_le5570908160329646204atural @ Xa @ X2 ) )
% 0.33/0.62                 => ( Y = one_one_Code_natural ) )
% 0.33/0.62                & ( ~ ( ( ord_le1926595141338095240atural @ X2 @ one_one_Code_natural )
% 0.33/0.62                      | ( ord_le5570908160329646204atural @ Xa @ X2 ) )
% 0.33/0.62                 => ( Y
% 0.33/0.62                    = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X2 @ ( divide5121882707175180666atural @ Xa @ X2 ) ) ) ) ) )
% 0.33/0.62             => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X2 @ Xa ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % log.pelims
% 0.33/0.62  thf(fact_5913_natural__of__nat__of__nat,axiom,
% 0.33/0.62      code_natural_of_nat = semiri3763490453095760265atural ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_nat_of_nat
% 0.33/0.62  thf(fact_5914_divide__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( divide5121882707175180666atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( divide_divide_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % divide_natural.abs_eq
% 0.33/0.62  thf(fact_5915_less__eq__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( ord_le1926595141338095240atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( ord_less_eq_nat @ Xa @ X2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_eq_natural.abs_eq
% 0.33/0.62  thf(fact_5916_minus__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( minus_7197305767214868737atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( minus_minus_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % minus_natural.abs_eq
% 0.33/0.62  thf(fact_5917_zero__natural__def,axiom,
% 0.33/0.62      ( zero_z2226904508553997617atural
% 0.33/0.62      = ( code_natural_of_nat @ zero_zero_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % zero_natural_def
% 0.33/0.62  thf(fact_5918_one__natural__def,axiom,
% 0.33/0.62      ( one_one_Code_natural
% 0.33/0.62      = ( code_natural_of_nat @ one_one_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % one_natural_def
% 0.33/0.62  thf(fact_5919_euclidean__size__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [X2: nat] :
% 0.33/0.62        ( ( euclid5200926497590043453atural @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( euclid4777050414544973029ze_nat @ X2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % euclidean_size_natural.abs_eq
% 0.33/0.62  thf(fact_5920_mask__natural__def,axiom,
% 0.33/0.62      ( bit_se943457434206027407atural
% 0.33/0.62      = ( map_fu4742413587575543474atural @ id_nat @ code_natural_of_nat @ bit_se2002935070580805687sk_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % mask_natural_def
% 0.33/0.62  thf(fact_5921_drop__bit__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( bit_se2751692689150723149atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( bit_se8570568707652914677it_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % drop_bit_natural.abs_eq
% 0.33/0.62  thf(fact_5922_and__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( bit_se2773287842338716102atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( bit_se727722235901077358nd_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % and_natural.abs_eq
% 0.33/0.62  thf(fact_5923_bit__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [X2: nat] :
% 0.33/0.62        ( ( bit_se8040316288895769887atural @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( bit_se1148574629649215175it_nat @ X2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % bit_natural.abs_eq
% 0.33/0.62  thf(fact_5924_take__bit__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( bit_se569199155075624693atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( bit_se2925701944663578781it_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % take_bit_natural.abs_eq
% 0.33/0.62  thf(fact_5925_xor__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( bit_se2046307713759805098atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( bit_se6528837805403552850or_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % xor_natural.abs_eq
% 0.33/0.62  thf(fact_5926_or__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( bit_se9127793120404214118atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( bit_se1412395901928357646or_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % or_natural.abs_eq
% 0.33/0.62  thf(fact_5927_push__bit__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( bit_se6611745700429515170atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( bit_se547839408752420682it_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % push_bit_natural.abs_eq
% 0.33/0.62  thf(fact_5928_mask__natural_Oabs__eq,axiom,
% 0.33/0.62      ( bit_se943457434206027407atural
% 0.33/0.62      = ( ^ [X: nat] : ( code_natural_of_nat @ ( bit_se2002935070580805687sk_nat @ X ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % mask_natural.abs_eq
% 0.33/0.62  thf(fact_5929_flip__bit__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( bit_se168947363167071951atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( bit_se2161824704523386999it_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % flip_bit_natural.abs_eq
% 0.33/0.62  thf(fact_5930_unset__bit__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( bit_se7083795435491715335atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( bit_se4205575877204974255it_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % unset_bit_natural.abs_eq
% 0.33/0.62  thf(fact_5931_set__bit__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( bit_se1617098188084679374atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( bit_se7882103937844011126it_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % set_bit_natural.abs_eq
% 0.33/0.62  thf(fact_5932_division__segment__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [X2: nat] :
% 0.33/0.62        ( ( euclid5112970336976722131atural @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( euclid3398187327856392827nt_nat @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_natural.abs_eq
% 0.33/0.62  thf(fact_5933_natural__of__nat__cases,axiom,
% 0.33/0.62      ! [X2: code_natural] :
% 0.33/0.62        ~ ! [Y2: nat] :
% 0.33/0.62            ( ( X2
% 0.33/0.62              = ( code_natural_of_nat @ Y2 ) )
% 0.33/0.62           => ~ ( member_nat @ Y2 @ top_top_set_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_nat_cases
% 0.33/0.62  thf(fact_5934_natural__of__nat__induct,axiom,
% 0.33/0.62      ! [P: code_natural > $o,X2: code_natural] :
% 0.33/0.62        ( ! [Y2: nat] :
% 0.33/0.62            ( ( member_nat @ Y2 @ top_top_set_nat )
% 0.33/0.62           => ( P @ ( code_natural_of_nat @ Y2 ) ) )
% 0.33/0.62       => ( P @ X2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_nat_induct
% 0.33/0.62  thf(fact_5935_natural__of__nat__inject,axiom,
% 0.33/0.62      ! [X2: nat,Y: nat] :
% 0.33/0.62        ( ( member_nat @ X2 @ top_top_set_nat )
% 0.33/0.62       => ( ( member_nat @ Y @ top_top_set_nat )
% 0.33/0.62         => ( ( ( code_natural_of_nat @ X2 )
% 0.33/0.62              = ( code_natural_of_nat @ Y ) )
% 0.33/0.62            = ( X2 = Y ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_nat_inject
% 0.33/0.62  thf(fact_5936_less__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( ord_le5570908160329646204atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( ord_less_nat @ Xa @ X2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_natural.abs_eq
% 0.33/0.62  thf(fact_5937_plus__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( plus_p4538020629002901425atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( plus_plus_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % plus_natural.abs_eq
% 0.33/0.62  thf(fact_5938_times__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( times_2397367101498566445atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( times_times_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % times_natural.abs_eq
% 0.33/0.62  thf(fact_5939_modulo__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [Xa: nat,X2: nat] :
% 0.33/0.62        ( ( modulo8411746178871703098atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( modulo_modulo_nat @ Xa @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % modulo_natural.abs_eq
% 0.33/0.62  thf(fact_5940_Nat_Oabs__eq,axiom,
% 0.33/0.62      ! [X2: int] :
% 0.33/0.62        ( ( code_Nat @ ( code_integer_of_int @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( nat2 @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Nat.abs_eq
% 0.33/0.62  thf(fact_5941_nat__of__natural__inverse,axiom,
% 0.33/0.62      ! [X2: code_natural] :
% 0.33/0.62        ( ( code_natural_of_nat @ ( code_nat_of_natural @ X2 ) )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural_inverse
% 0.33/0.62  thf(fact_5942_nat__of__natural__of__nat__inverse,axiom,
% 0.33/0.62      ! [N: nat] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( code_natural_of_nat @ N ) )
% 0.33/0.62        = N ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural_of_nat_inverse
% 0.33/0.62  thf(fact_5943_natural__of__nat__of__natural__inverse,axiom,
% 0.33/0.62      ! [N: code_natural] :
% 0.33/0.62        ( ( code_natural_of_nat @ ( code_nat_of_natural @ N ) )
% 0.33/0.62        = N ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_nat_of_natural_inverse
% 0.33/0.62  thf(fact_5944_nat__of__natural__min,axiom,
% 0.33/0.62      ! [K: code_natural,L: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( ord_min_Code_natural @ K @ L ) )
% 0.33/0.62        = ( ord_min_nat @ ( code_nat_of_natural @ K ) @ ( code_nat_of_natural @ L ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural_min
% 0.33/0.62  thf(fact_5945_nat__of__natural__max,axiom,
% 0.33/0.62      ! [K: code_natural,L: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( ord_max_Code_natural @ K @ L ) )
% 0.33/0.62        = ( ord_max_nat @ ( code_nat_of_natural @ K ) @ ( code_nat_of_natural @ L ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural_max
% 0.33/0.62  thf(fact_5946_nat__of__natural__of__nat,axiom,
% 0.33/0.62      ! [N: nat] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( semiri3763490453095760265atural @ N ) )
% 0.33/0.62        = N ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural_of_nat
% 0.33/0.62  thf(fact_5947_of__nat__of__natural,axiom,
% 0.33/0.62      ! [N: code_natural] :
% 0.33/0.62        ( ( semiri3763490453095760265atural @ ( code_nat_of_natural @ N ) )
% 0.33/0.62        = N ) ).
% 0.33/0.62  
% 0.33/0.62  % of_nat_of_natural
% 0.33/0.62  thf(fact_5948_zero__natural_Orep__eq,axiom,
% 0.33/0.62      ( ( code_nat_of_natural @ zero_z2226904508553997617atural )
% 0.33/0.62      = zero_zero_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % zero_natural.rep_eq
% 0.33/0.62  thf(fact_5949_one__natural_Orep__eq,axiom,
% 0.33/0.62      ( ( code_nat_of_natural @ one_one_Code_natural )
% 0.33/0.62      = one_one_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % one_natural.rep_eq
% 0.33/0.62  thf(fact_5950_plus__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( plus_p4538020629002901425atural @ X2 @ Xa ) )
% 0.33/0.62        = ( plus_plus_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % plus_natural.rep_eq
% 0.33/0.62  thf(fact_5951_minus__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( minus_7197305767214868737atural @ X2 @ Xa ) )
% 0.33/0.62        = ( minus_minus_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % minus_natural.rep_eq
% 0.33/0.62  thf(fact_5952_nat__of__natural__numeral,axiom,
% 0.33/0.62      ! [K: num] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( numera5444537566228673987atural @ K ) )
% 0.33/0.62        = ( numeral_numeral_nat @ K ) ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural_numeral
% 0.33/0.62  thf(fact_5953_times__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( times_2397367101498566445atural @ X2 @ Xa ) )
% 0.33/0.62        = ( times_times_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % times_natural.rep_eq
% 0.33/0.62  thf(fact_5954_divide__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( divide5121882707175180666atural @ X2 @ Xa ) )
% 0.33/0.62        = ( divide_divide_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % divide_natural.rep_eq
% 0.33/0.62  thf(fact_5955_modulo__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( modulo8411746178871703098atural @ X2 @ Xa ) )
% 0.33/0.62        = ( modulo_modulo_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % modulo_natural.rep_eq
% 0.33/0.62  thf(fact_5956_division__segment__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( euclid5112970336976722131atural @ X2 ) )
% 0.33/0.62        = ( euclid3398187327856392827nt_nat @ ( code_nat_of_natural @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_natural.rep_eq
% 0.33/0.62  thf(fact_5957_euclidean__size__natural_Orep__eq,axiom,
% 0.33/0.62      ( euclid5200926497590043453atural
% 0.33/0.62      = ( ^ [X: code_natural] : ( euclid4777050414544973029ze_nat @ ( code_nat_of_natural @ X ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % euclidean_size_natural.rep_eq
% 0.33/0.62  thf(fact_5958_minus__natural__def,axiom,
% 0.33/0.62      ( minus_7197305767214868737atural
% 0.33/0.62      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ minus_minus_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % minus_natural_def
% 0.33/0.62  thf(fact_5959_or__natural__def,axiom,
% 0.33/0.62      ( bit_se9127793120404214118atural
% 0.33/0.62      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se1412395901928357646or_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % or_natural_def
% 0.33/0.62  thf(fact_5960_xor__natural__def,axiom,
% 0.33/0.62      ( bit_se2046307713759805098atural
% 0.33/0.62      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se6528837805403552850or_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % xor_natural_def
% 0.33/0.62  thf(fact_5961_and__natural__def,axiom,
% 0.33/0.62      ( bit_se2773287842338716102atural
% 0.33/0.62      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se727722235901077358nd_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % and_natural_def
% 0.33/0.62  thf(fact_5962_division__segment__natural__def,axiom,
% 0.33/0.62      ( euclid5112970336976722131atural
% 0.33/0.62      = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ euclid3398187327856392827nt_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % division_segment_natural_def
% 0.33/0.62  thf(fact_5963_natural__of__nat__inverse,axiom,
% 0.33/0.62      ! [Y: nat] :
% 0.33/0.62        ( ( member_nat @ Y @ top_top_set_nat )
% 0.33/0.62       => ( ( code_nat_of_natural @ ( code_natural_of_nat @ Y ) )
% 0.33/0.62          = Y ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_nat_inverse
% 0.33/0.62  thf(fact_5964_type__definition__natural,axiom,
% 0.33/0.62      type_d4410041424927559462al_nat @ code_nat_of_natural @ code_natural_of_nat @ top_top_set_nat ).
% 0.33/0.62  
% 0.33/0.62  % type_definition_natural
% 0.33/0.62  thf(fact_5965_plus__natural__def,axiom,
% 0.33/0.62      ( plus_p4538020629002901425atural
% 0.33/0.62      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ plus_plus_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % plus_natural_def
% 0.33/0.62  thf(fact_5966_less__natural__def,axiom,
% 0.33/0.62      ( ord_le5570908160329646204atural
% 0.33/0.62      = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_natural_def
% 0.33/0.62  thf(fact_5967_less__natural_Orep__eq,axiom,
% 0.33/0.62      ( ord_le5570908160329646204atural
% 0.33/0.62      = ( ^ [X: code_natural,Xa4: code_natural] : ( ord_less_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_natural.rep_eq
% 0.33/0.62  thf(fact_5968_nat__of__natural__induct,axiom,
% 0.33/0.62      ! [Y: nat,P: nat > $o] :
% 0.33/0.62        ( ( member_nat @ Y @ top_top_set_nat )
% 0.33/0.62       => ( ! [X3: code_natural] : ( P @ ( code_nat_of_natural @ X3 ) )
% 0.33/0.62         => ( P @ Y ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural_induct
% 0.33/0.62  thf(fact_5969_nat__of__natural__cases,axiom,
% 0.33/0.62      ! [Y: nat] :
% 0.33/0.62        ( ( member_nat @ Y @ top_top_set_nat )
% 0.33/0.62       => ~ ! [X3: code_natural] :
% 0.33/0.62              ( Y
% 0.33/0.62             != ( code_nat_of_natural @ X3 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural_cases
% 0.33/0.62  thf(fact_5970_nat__of__natural,axiom,
% 0.33/0.62      ! [X2: code_natural] : ( member_nat @ ( code_nat_of_natural @ X2 ) @ top_top_set_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural
% 0.33/0.62  thf(fact_5971_drop__bit__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: nat,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se2751692689150723149atural @ X2 @ Xa ) )
% 0.33/0.62        = ( bit_se8570568707652914677it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % drop_bit_natural.rep_eq
% 0.33/0.62  thf(fact_5972_bit__natural_Orep__eq,axiom,
% 0.33/0.62      ( bit_se8040316288895769887atural
% 0.33/0.62      = ( ^ [X: code_natural] : ( bit_se1148574629649215175it_nat @ ( code_nat_of_natural @ X ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % bit_natural.rep_eq
% 0.33/0.62  thf(fact_5973_or__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se9127793120404214118atural @ X2 @ Xa ) )
% 0.33/0.62        = ( bit_se1412395901928357646or_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % or_natural.rep_eq
% 0.33/0.62  thf(fact_5974_xor__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se2046307713759805098atural @ X2 @ Xa ) )
% 0.33/0.62        = ( bit_se6528837805403552850or_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % xor_natural.rep_eq
% 0.33/0.62  thf(fact_5975_natural__eq__iff,axiom,
% 0.33/0.62      ( ( ^ [Y3: code_natural,Z: code_natural] : ( Y3 = Z ) )
% 0.33/0.62      = ( ^ [M2: code_natural,N3: code_natural] :
% 0.33/0.62            ( ( code_nat_of_natural @ M2 )
% 0.33/0.62            = ( code_nat_of_natural @ N3 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_eq_iff
% 0.33/0.62  thf(fact_5976_natural__eqI,axiom,
% 0.33/0.62      ! [M: code_natural,N: code_natural] :
% 0.33/0.62        ( ( ( code_nat_of_natural @ M )
% 0.33/0.62          = ( code_nat_of_natural @ N ) )
% 0.33/0.62       => ( M = N ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_eqI
% 0.33/0.62  thf(fact_5977_nat__of__natural__inject,axiom,
% 0.33/0.62      ! [X2: code_natural,Y: code_natural] :
% 0.33/0.62        ( ( ( code_nat_of_natural @ X2 )
% 0.33/0.62          = ( code_nat_of_natural @ Y ) )
% 0.33/0.62        = ( X2 = Y ) ) ).
% 0.33/0.62  
% 0.33/0.62  % nat_of_natural_inject
% 0.33/0.62  thf(fact_5978_take__bit__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: nat,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se569199155075624693atural @ X2 @ Xa ) )
% 0.33/0.62        = ( bit_se2925701944663578781it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % take_bit_natural.rep_eq
% 0.33/0.62  thf(fact_5979_and__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se2773287842338716102atural @ X2 @ Xa ) )
% 0.33/0.62        = ( bit_se727722235901077358nd_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % and_natural.rep_eq
% 0.33/0.62  thf(fact_5980_mask__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: nat] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se943457434206027407atural @ X2 ) )
% 0.33/0.62        = ( bit_se2002935070580805687sk_nat @ X2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % mask_natural.rep_eq
% 0.33/0.62  thf(fact_5981_push__bit__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: nat,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se6611745700429515170atural @ X2 @ Xa ) )
% 0.33/0.62        = ( bit_se547839408752420682it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % push_bit_natural.rep_eq
% 0.33/0.62  thf(fact_5982_set__bit__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: nat,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se1617098188084679374atural @ X2 @ Xa ) )
% 0.33/0.62        = ( bit_se7882103937844011126it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % set_bit_natural.rep_eq
% 0.33/0.62  thf(fact_5983_unset__bit__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: nat,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se7083795435491715335atural @ X2 @ Xa ) )
% 0.33/0.62        = ( bit_se4205575877204974255it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % unset_bit_natural.rep_eq
% 0.33/0.62  thf(fact_5984_flip__bit__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: nat,Xa: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( bit_se168947363167071951atural @ X2 @ Xa ) )
% 0.33/0.62        = ( bit_se2161824704523386999it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % flip_bit_natural.rep_eq
% 0.33/0.62  thf(fact_5985_Nat_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_integer] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( code_Nat @ X2 ) )
% 0.33/0.62        = ( nat2 @ ( code_int_of_integer @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Nat.rep_eq
% 0.33/0.62  thf(fact_5986_euclidean__size__natural__def,axiom,
% 0.33/0.62      ( euclid5200926497590043453atural
% 0.33/0.62      = ( map_fu226235371393106610at_nat @ code_nat_of_natural @ id_nat @ euclid4777050414544973029ze_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % euclidean_size_natural_def
% 0.33/0.62  thf(fact_5987_bit__natural__def,axiom,
% 0.33/0.62      ( bit_se8040316288895769887atural
% 0.33/0.62      = ( map_fu6244533035418998608_nat_o @ code_nat_of_natural @ id_nat_o @ bit_se1148574629649215175it_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % bit_natural_def
% 0.33/0.62  thf(fact_5988_less__eq__natural_Orep__eq,axiom,
% 0.33/0.62      ( ord_le1926595141338095240atural
% 0.33/0.62      = ( ^ [X: code_natural,Xa4: code_natural] : ( ord_less_eq_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_eq_natural.rep_eq
% 0.33/0.62  thf(fact_5989_times__natural__def,axiom,
% 0.33/0.62      ( times_2397367101498566445atural
% 0.33/0.62      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ times_times_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % times_natural_def
% 0.33/0.62  thf(fact_5990_divide__natural__def,axiom,
% 0.33/0.62      ( divide5121882707175180666atural
% 0.33/0.62      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ divide_divide_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % divide_natural_def
% 0.33/0.62  thf(fact_5991_take__bit__natural__def,axiom,
% 0.33/0.62      ( bit_se569199155075624693atural
% 0.33/0.62      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se2925701944663578781it_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % take_bit_natural_def
% 0.33/0.62  thf(fact_5992_push__bit__natural__def,axiom,
% 0.33/0.62      ( bit_se6611745700429515170atural
% 0.33/0.62      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se547839408752420682it_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % push_bit_natural_def
% 0.33/0.62  thf(fact_5993_less__eq__natural__def,axiom,
% 0.33/0.62      ( ord_le1926595141338095240atural
% 0.33/0.62      = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_eq_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_eq_natural_def
% 0.33/0.62  thf(fact_5994_modulo__natural__def,axiom,
% 0.33/0.62      ( modulo8411746178871703098atural
% 0.33/0.62      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ modulo_modulo_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % modulo_natural_def
% 0.33/0.62  thf(fact_5995_drop__bit__natural__def,axiom,
% 0.33/0.62      ( bit_se2751692689150723149atural
% 0.33/0.62      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se8570568707652914677it_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % drop_bit_natural_def
% 0.33/0.62  thf(fact_5996_flip__bit__natural__def,axiom,
% 0.33/0.62      ( bit_se168947363167071951atural
% 0.33/0.62      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se2161824704523386999it_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % flip_bit_natural_def
% 0.33/0.62  thf(fact_5997_set__bit__natural__def,axiom,
% 0.33/0.62      ( bit_se1617098188084679374atural
% 0.33/0.62      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se7882103937844011126it_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % set_bit_natural_def
% 0.33/0.62  thf(fact_5998_unset__bit__natural__def,axiom,
% 0.33/0.62      ( bit_se7083795435491715335atural
% 0.33/0.62      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se4205575877204974255it_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % unset_bit_natural_def
% 0.33/0.62  thf(fact_5999_natural__decr,axiom,
% 0.33/0.62      ! [N: code_natural] :
% 0.33/0.62        ( ( N != zero_z2226904508553997617atural )
% 0.33/0.62       => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_decr
% 0.33/0.62  thf(fact_6000_Nat__def,axiom,
% 0.33/0.62      ( code_Nat
% 0.33/0.62      = ( map_fu1051355602067684763atural @ code_int_of_integer @ code_natural_of_nat @ nat2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Nat_def
% 0.33/0.62  thf(fact_6001_integer__of__natural_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural] :
% 0.33/0.62        ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ X2 ) )
% 0.33/0.62        = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % integer_of_natural.rep_eq
% 0.33/0.62  thf(fact_6002_int__of__integer__of__natural,axiom,
% 0.33/0.62      ! [N: code_natural] :
% 0.33/0.62        ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ N ) )
% 0.33/0.62        = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % int_of_integer_of_natural
% 0.33/0.62  thf(fact_6003_integer__of__natural__of__nat,axiom,
% 0.33/0.62      ! [N: nat] :
% 0.33/0.62        ( ( code_i5400310926305786745atural @ ( semiri3763490453095760265atural @ N ) )
% 0.33/0.62        = ( semiri4939895301339042750nteger @ N ) ) ).
% 0.33/0.62  
% 0.33/0.62  % integer_of_natural_of_nat
% 0.33/0.62  thf(fact_6004_integer__of__natural__def,axiom,
% 0.33/0.62      ( code_i5400310926305786745atural
% 0.33/0.62      = ( map_fu2787874002554666395nteger @ code_nat_of_natural @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 0.33/0.62  
% 0.33/0.62  % integer_of_natural_def
% 0.33/0.62  thf(fact_6005_integer__of__natural_Oabs__eq,axiom,
% 0.33/0.62      ! [X2: nat] :
% 0.33/0.62        ( ( code_i5400310926305786745atural @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % integer_of_natural.abs_eq
% 0.33/0.62  thf(fact_6006_integer__of__natural__of__integer,axiom,
% 0.33/0.62      ! [K: code_integer] :
% 0.33/0.62        ( ( code_i5400310926305786745atural @ ( code_n4118661773612635043nteger @ K ) )
% 0.33/0.62        = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 0.33/0.62  
% 0.33/0.62  % integer_of_natural_of_integer
% 0.33/0.62  thf(fact_6007_natural__of__integer__def,axiom,
% 0.33/0.62      ( code_n4118661773612635043nteger
% 0.33/0.62      = ( map_fu1051355602067684763atural @ code_int_of_integer @ code_natural_of_nat @ nat2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_integer_def
% 0.33/0.62  thf(fact_6008_natural__of__integer__of__natural,axiom,
% 0.33/0.62      ! [N: code_natural] :
% 0.33/0.62        ( ( code_n4118661773612635043nteger @ ( code_i5400310926305786745atural @ N ) )
% 0.33/0.62        = N ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_integer_of_natural
% 0.33/0.62  thf(fact_6009_natural__of__integer_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_integer] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( code_n4118661773612635043nteger @ X2 ) )
% 0.33/0.62        = ( nat2 @ ( code_int_of_integer @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_integer.rep_eq
% 0.33/0.62  thf(fact_6010_natural__of__integer_Oabs__eq,axiom,
% 0.33/0.62      ! [X2: int] :
% 0.33/0.62        ( ( code_n4118661773612635043nteger @ ( code_integer_of_int @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( nat2 @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural_of_integer.abs_eq
% 0.33/0.62  thf(fact_6011_Code__Numeral_Osize__nat__def,axiom,
% 0.33/0.62      code_size_nat = code_nat_of_natural ).
% 0.33/0.62  
% 0.33/0.62  % Code_Numeral.size_nat_def
% 0.33/0.62  thf(fact_6012_Code__Numeral_OSuc__def,axiom,
% 0.33/0.62      ( code_Suc
% 0.33/0.62      = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ suc ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Code_Numeral.Suc_def
% 0.33/0.62  thf(fact_6013_natural_Oinject,axiom,
% 0.33/0.62      ! [Natural: code_natural,Natural2: code_natural] :
% 0.33/0.62        ( ( ( code_Suc @ Natural )
% 0.33/0.62          = ( code_Suc @ Natural2 ) )
% 0.33/0.62        = ( Natural = Natural2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural.inject
% 0.33/0.62  thf(fact_6014_Suc_Orep__eq,axiom,
% 0.33/0.62      ! [X2: code_natural] :
% 0.33/0.62        ( ( code_nat_of_natural @ ( code_Suc @ X2 ) )
% 0.33/0.62        = ( suc @ ( code_nat_of_natural @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Suc.rep_eq
% 0.33/0.62  thf(fact_6015_natural_Odistinct_I2_J,axiom,
% 0.33/0.62      ! [Natural2: code_natural] :
% 0.33/0.62        ( ( code_Suc @ Natural2 )
% 0.33/0.62       != zero_z2226904508553997617atural ) ).
% 0.33/0.62  
% 0.33/0.62  % natural.distinct(2)
% 0.33/0.62  thf(fact_6016_natural_Odistinct_I1_J,axiom,
% 0.33/0.62      ! [Natural2: code_natural] :
% 0.33/0.62        ( zero_z2226904508553997617atural
% 0.33/0.62       != ( code_Suc @ Natural2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural.distinct(1)
% 0.33/0.62  thf(fact_6017_natural_Oexhaust,axiom,
% 0.33/0.62      ! [Y: code_natural] :
% 0.33/0.62        ( ( Y != zero_z2226904508553997617atural )
% 0.33/0.62       => ~ ! [Natural3: code_natural] :
% 0.33/0.62              ( Y
% 0.33/0.62             != ( code_Suc @ Natural3 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % natural.exhaust
% 0.33/0.62  thf(fact_6018_Suc_Oabs__eq,axiom,
% 0.33/0.62      ! [X2: nat] :
% 0.33/0.62        ( ( code_Suc @ ( code_natural_of_nat @ X2 ) )
% 0.33/0.62        = ( code_natural_of_nat @ ( suc @ X2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Suc.abs_eq
% 0.33/0.62  thf(fact_6019_Suc__natural__minus__one,axiom,
% 0.33/0.62      ! [N: code_natural] :
% 0.33/0.62        ( ( minus_7197305767214868737atural @ ( code_Suc @ N ) @ one_one_Code_natural )
% 0.33/0.62        = N ) ).
% 0.33/0.62  
% 0.33/0.62  % Suc_natural_minus_one
% 0.33/0.62  thf(fact_6020_prod__decode__triangle__add,axiom,
% 0.33/0.62      ! [K: nat,M: nat] :
% 0.33/0.62        ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) )
% 0.33/0.62        = ( nat_prod_decode_aux @ K @ M ) ) ).
% 0.33/0.62  
% 0.33/0.62  % prod_decode_triangle_add
% 0.33/0.62  thf(fact_6021_prod__decode__def,axiom,
% 0.33/0.62      ( nat_prod_decode
% 0.33/0.62      = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % prod_decode_def
% 0.33/0.62  thf(fact_6022_list__decode_Oelims,axiom,
% 0.33/0.62      ! [X2: nat,Y: list_nat] :
% 0.33/0.62        ( ( ( nat_list_decode @ X2 )
% 0.33/0.62          = Y )
% 0.33/0.62       => ( ( ( X2 = zero_zero_nat )
% 0.33/0.62           => ( Y != nil_nat ) )
% 0.33/0.62         => ~ ! [N2: nat] :
% 0.33/0.62                ( ( X2
% 0.33/0.62                  = ( suc @ N2 ) )
% 0.33/0.62               => ( Y
% 0.33/0.62                 != ( produc2761476792215241774st_nat
% 0.33/0.62                    @ ^ [X: nat,Y4: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y4 ) )
% 0.33/0.62                    @ ( nat_prod_decode @ N2 ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % list_decode.elims
% 0.33/0.62  thf(fact_6023_list__decode_Osimps_I2_J,axiom,
% 0.33/0.62      ! [N: nat] :
% 0.33/0.62        ( ( nat_list_decode @ ( suc @ N ) )
% 0.33/0.62        = ( produc2761476792215241774st_nat
% 0.33/0.62          @ ^ [X: nat,Y4: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y4 ) )
% 0.33/0.62          @ ( nat_prod_decode @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % list_decode.simps(2)
% 0.33/0.62  thf(fact_6024_list__decode_Osimps_I1_J,axiom,
% 0.33/0.62      ( ( nat_list_decode @ zero_zero_nat )
% 0.33/0.62      = nil_nat ) ).
% 0.33/0.62  
% 0.33/0.62  % list_decode.simps(1)
% 0.33/0.62  thf(fact_6025_list__decode_Opelims,axiom,
% 0.33/0.62      ! [X2: nat,Y: list_nat] :
% 0.33/0.62        ( ( ( nat_list_decode @ X2 )
% 0.33/0.62          = Y )
% 0.33/0.62       => ( ( accp_nat @ nat_list_decode_rel @ X2 )
% 0.33/0.62         => ( ( ( X2 = zero_zero_nat )
% 0.33/0.62             => ( ( Y = nil_nat )
% 0.33/0.62               => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 0.33/0.62           => ~ ! [N2: nat] :
% 0.33/0.62                  ( ( X2
% 0.33/0.62                    = ( suc @ N2 ) )
% 0.33/0.62                 => ( ( Y
% 0.33/0.62                      = ( produc2761476792215241774st_nat
% 0.33/0.62                        @ ^ [X: nat,Y4: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y4 ) )
% 0.33/0.62                        @ ( nat_prod_decode @ N2 ) ) )
% 0.33/0.62                   => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % list_decode.pelims
% 0.33/0.62  thf(fact_6026_list__decode_Opsimps_I1_J,axiom,
% 0.33/0.62      ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 0.33/0.62     => ( ( nat_list_decode @ zero_zero_nat )
% 0.33/0.62        = nil_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % list_decode.psimps(1)
% 0.33/0.62  thf(fact_6027_list__decode_Opinduct,axiom,
% 0.33/0.62      ! [A0: nat,P: nat > $o] :
% 0.33/0.62        ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 0.33/0.62       => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 0.33/0.62           => ( P @ zero_zero_nat ) )
% 0.33/0.62         => ( ! [N2: nat] :
% 0.33/0.62                ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 0.33/0.62               => ( ! [X4: nat,Y5: nat] :
% 0.33/0.62                      ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 0.33/0.62                        = ( nat_prod_decode @ N2 ) )
% 0.33/0.62                     => ( P @ Y5 ) )
% 0.33/0.62                 => ( P @ ( suc @ N2 ) ) ) )
% 0.33/0.62           => ( P @ A0 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % list_decode.pinduct
% 0.33/0.62  thf(fact_6028_list__decode_Opsimps_I2_J,axiom,
% 0.33/0.62      ! [N: nat] :
% 0.33/0.62        ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 0.33/0.62       => ( ( nat_list_decode @ ( suc @ N ) )
% 0.33/0.62          = ( produc2761476792215241774st_nat
% 0.33/0.62            @ ^ [X: nat,Y4: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y4 ) )
% 0.33/0.62            @ ( nat_prod_decode @ N ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % list_decode.psimps(2)
% 0.33/0.62  thf(fact_6029_Code__Numeral_Osub__code_I4_J,axiom,
% 0.33/0.62      ! [N: num] :
% 0.33/0.62        ( ( code_sub @ one @ ( bit0 @ N ) )
% 0.33/0.62        = ( code_Neg @ ( bitM @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Code_Numeral.sub_code(4)
% 0.33/0.62  thf(fact_6030_less__eq__integer__code_I9_J,axiom,
% 0.33/0.62      ! [K: num,L: num] :
% 0.33/0.62        ( ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 0.33/0.62        = ( ord_less_eq_num @ L @ K ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_eq_integer_code(9)
% 0.33/0.62  thf(fact_6031_less__eq__integer__code_I3_J,axiom,
% 0.33/0.62      ! [L: num] :
% 0.33/0.62        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_eq_integer_code(3)
% 0.33/0.62  thf(fact_6032_less__eq__integer__code_I7_J,axiom,
% 0.33/0.62      ! [K: num] : ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % less_eq_integer_code(7)
% 0.33/0.62  thf(fact_6033_minus__integer__code_I6_J,axiom,
% 0.33/0.62      ! [M: num,N: num] :
% 0.33/0.62        ( ( minus_8373710615458151222nteger @ ( code_Neg @ M ) @ ( code_Neg @ N ) )
% 0.33/0.62        = ( code_sub @ N @ M ) ) ).
% 0.33/0.62  
% 0.33/0.62  % minus_integer_code(6)
% 0.33/0.62  thf(fact_6034_Code__Numeral_Odup__code_I3_J,axiom,
% 0.33/0.62      ! [N: num] :
% 0.33/0.62        ( ( code_dup @ ( code_Neg @ N ) )
% 0.33/0.62        = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Code_Numeral.dup_code(3)
% 0.33/0.62  thf(fact_6035_less__integer__code_I9_J,axiom,
% 0.33/0.62      ! [K: num,L: num] :
% 0.33/0.62        ( ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 0.33/0.62        = ( ord_less_num @ L @ K ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_integer_code(9)
% 0.33/0.62  thf(fact_6036_plus__integer__code_I6_J,axiom,
% 0.33/0.62      ! [M: num,N: num] :
% 0.33/0.62        ( ( plus_p5714425477246183910nteger @ ( code_Neg @ M ) @ ( code_Neg @ N ) )
% 0.33/0.62        = ( code_Neg @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % plus_integer_code(6)
% 0.33/0.62  thf(fact_6037_less__integer__code_I7_J,axiom,
% 0.33/0.62      ! [K: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 0.33/0.62  
% 0.33/0.62  % less_integer_code(7)
% 0.33/0.62  thf(fact_6038_less__integer__code_I3_J,axiom,
% 0.33/0.62      ! [L: num] :
% 0.33/0.62        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 0.33/0.62  
% 0.33/0.62  % less_integer_code(3)
% 0.33/0.62  thf(fact_6039_divmod__abs__code_I2_J,axiom,
% 0.33/0.62      ! [K: num,L: num] :
% 0.33/0.62        ( ( code_divmod_abs @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 0.33/0.62        = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 0.33/0.62  
% 0.33/0.62  % divmod_abs_code(2)
% 0.33/0.62  thf(fact_6040_Code__Numeral_Osub__code_I5_J,axiom,
% 0.33/0.62      ! [N: num] :
% 0.33/0.62        ( ( code_sub @ one @ ( bit1 @ N ) )
% 0.33/0.62        = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Code_Numeral.sub_code(5)
% 0.33/0.62  thf(fact_6041_Gcd__int__set__eq__fold,axiom,
% 0.33/0.62      ! [Xs: list_int] :
% 0.33/0.62        ( ( gcd_Gcd_int @ ( set_int2 @ Xs ) )
% 0.33/0.62        = ( fold_int_int @ gcd_gcd_int @ Xs @ zero_zero_int ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Gcd_int_set_eq_fold
% 0.33/0.62  thf(fact_6042_int_Oid__abs__transfer,axiom,
% 0.33/0.62      ( bNF_re7934895593101944656at_int
% 0.33/0.62      @ ( basic_5328504652464829177at_nat
% 0.33/0.62        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.62      @ pcr_int
% 0.33/0.62      @ ^ [X: product_prod_nat_nat] : X
% 0.33/0.62      @ abs_Integ ) ).
% 0.33/0.62  
% 0.33/0.62  % int.id_abs_transfer
% 0.33/0.62  thf(fact_6043_rat_Odomain,axiom,
% 0.33/0.62      ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 0.33/0.62      = ( ^ [X: product_prod_int_int] :
% 0.33/0.62          ? [Y4: product_prod_int_int] :
% 0.33/0.62            ( ( basic_4387203522000727145nt_int
% 0.33/0.62              @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62              @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62              @ X
% 0.33/0.62              @ Y4 )
% 0.33/0.62            & ( ratrel @ Y4 @ Y4 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % rat.domain
% 0.33/0.62  thf(fact_6044_rat_Odomain__par,axiom,
% 0.33/0.62      ! [DR1: int > $o,DR2: int > $o,P22: product_prod_int_int > $o] :
% 0.33/0.62        ( ( ( domainp_int_int
% 0.33/0.62            @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.62          = DR1 )
% 0.33/0.62       => ( ( ( domainp_int_int
% 0.33/0.62              @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.62            = DR2 )
% 0.33/0.62         => ( ( bNF_re8699439704749558557nt_o_o
% 0.33/0.62              @ ( basic_4387203522000727145nt_int
% 0.33/0.62                @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62                @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.62              @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.33/0.62              @ P22
% 0.33/0.62              @ ^ [X: product_prod_int_int] : ( ratrel @ X @ X ) )
% 0.33/0.62           => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 0.33/0.62              = ( inf_in3604695632404883862_int_o @ ( basic_1567116559311922317nt_int @ DR1 @ DR2 ) @ P22 ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % rat.domain_par
% 0.33/0.62  thf(fact_6045_rat_Odomain__par__left__total,axiom,
% 0.33/0.62      ! [P2: product_prod_int_int > $o] :
% 0.33/0.62        ( ( left_t3131394472396969446nt_int
% 0.33/0.62          @ ( basic_4387203522000727145nt_int
% 0.33/0.62            @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62            @ ^ [Y3: int,Z: int] : ( Y3 = Z ) ) )
% 0.33/0.62       => ( ( bNF_re8699439704749558557nt_o_o
% 0.33/0.62            @ ( basic_4387203522000727145nt_int
% 0.33/0.62              @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62              @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 0.33/0.62            @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.33/0.62            @ P2
% 0.33/0.62            @ ^ [X: product_prod_int_int] : ( ratrel @ X @ X ) )
% 0.33/0.62         => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 0.33/0.62            = P2 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % rat.domain_par_left_total
% 0.33/0.62  thf(fact_6046_Gcd__nat__set__eq__fold,axiom,
% 0.33/0.62      ! [Xs: list_nat] :
% 0.33/0.62        ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs ) )
% 0.33/0.62        = ( fold_nat_nat @ gcd_gcd_nat @ Xs @ zero_zero_nat ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Gcd_nat_set_eq_fold
% 0.33/0.62  thf(fact_6047_Abs__rat__cases,axiom,
% 0.33/0.62      ! [X2: rat] :
% 0.33/0.62        ~ ! [Y2: set_Pr958786334691620121nt_int] :
% 0.33/0.62            ( ( X2
% 0.33/0.62              = ( abs_rat @ Y2 ) )
% 0.33/0.62           => ~ ( member2340774599025711042nt_int @ Y2
% 0.33/0.62                @ ( collec5210948495886036740nt_int
% 0.33/0.62                  @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.33/0.62                    ? [X: product_prod_int_int] :
% 0.33/0.62                      ( ( ratrel @ X @ X )
% 0.33/0.62                      & ( C4
% 0.33/0.62                        = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Abs_rat_cases
% 0.33/0.62  thf(fact_6048_Abs__rat__induct,axiom,
% 0.33/0.62      ! [P: rat > $o,X2: rat] :
% 0.33/0.62        ( ! [Y2: set_Pr958786334691620121nt_int] :
% 0.33/0.62            ( ( member2340774599025711042nt_int @ Y2
% 0.33/0.62              @ ( collec5210948495886036740nt_int
% 0.33/0.62                @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.33/0.62                  ? [X: product_prod_int_int] :
% 0.33/0.62                    ( ( ratrel @ X @ X )
% 0.33/0.62                    & ( C4
% 0.33/0.62                      = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 0.33/0.62           => ( P @ ( abs_rat @ Y2 ) ) )
% 0.33/0.62       => ( P @ X2 ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Abs_rat_induct
% 0.33/0.62  thf(fact_6049_int_Odomain,axiom,
% 0.33/0.62      ! [DR1: nat > $o,DR2: nat > $o] :
% 0.33/0.62        ( ( ( domainp_nat_nat
% 0.33/0.62            @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.62          = DR1 )
% 0.33/0.62       => ( ( ( domainp_nat_nat
% 0.33/0.62              @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.62            = DR2 )
% 0.33/0.62         => ( ( domain7287725470393535433at_int @ pcr_int )
% 0.33/0.62            = ( basic_570253317919918037at_nat @ DR1 @ DR2 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % int.domain
% 0.33/0.62  thf(fact_6050_Abs__rat__inject,axiom,
% 0.33/0.62      ! [X2: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
% 0.33/0.62        ( ( member2340774599025711042nt_int @ X2
% 0.33/0.62          @ ( collec5210948495886036740nt_int
% 0.33/0.62            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.33/0.62              ? [X: product_prod_int_int] :
% 0.33/0.62                ( ( ratrel @ X @ X )
% 0.33/0.62                & ( C4
% 0.33/0.62                  = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 0.33/0.62       => ( ( member2340774599025711042nt_int @ Y
% 0.33/0.62            @ ( collec5210948495886036740nt_int
% 0.33/0.62              @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.33/0.62                ? [X: product_prod_int_int] :
% 0.33/0.62                  ( ( ratrel @ X @ X )
% 0.33/0.62                  & ( C4
% 0.33/0.62                    = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 0.33/0.62         => ( ( ( abs_rat @ X2 )
% 0.33/0.62              = ( abs_rat @ Y ) )
% 0.33/0.62            = ( X2 = Y ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Abs_rat_inject
% 0.33/0.62  thf(fact_6051_Abs__rat__inverse,axiom,
% 0.33/0.62      ! [Y: set_Pr958786334691620121nt_int] :
% 0.33/0.62        ( ( member2340774599025711042nt_int @ Y
% 0.33/0.62          @ ( collec5210948495886036740nt_int
% 0.33/0.62            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.33/0.62              ? [X: product_prod_int_int] :
% 0.33/0.62                ( ( ratrel @ X @ X )
% 0.33/0.62                & ( C4
% 0.33/0.62                  = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 0.33/0.62       => ( ( rep_rat @ ( abs_rat @ Y ) )
% 0.33/0.62          = Y ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Abs_rat_inverse
% 0.33/0.62  thf(fact_6052_type__definition__rat,axiom,
% 0.33/0.62      ( type_d8554052265237484179nt_int @ rep_rat @ abs_rat
% 0.33/0.62      @ ( collec5210948495886036740nt_int
% 0.33/0.62        @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.33/0.62          ? [X: product_prod_int_int] :
% 0.33/0.62            ( ( ratrel @ X @ X )
% 0.33/0.62            & ( C4
% 0.33/0.62              = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % type_definition_rat
% 0.33/0.62  thf(fact_6053_Rep__rat,axiom,
% 0.33/0.62      ! [X2: rat] :
% 0.33/0.62        ( member2340774599025711042nt_int @ ( rep_rat @ X2 )
% 0.33/0.62        @ ( collec5210948495886036740nt_int
% 0.33/0.62          @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.33/0.62            ? [X: product_prod_int_int] :
% 0.33/0.62              ( ( ratrel @ X @ X )
% 0.33/0.62              & ( C4
% 0.33/0.62                = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Rep_rat
% 0.33/0.62  thf(fact_6054_Rep__rat__cases,axiom,
% 0.33/0.62      ! [Y: set_Pr958786334691620121nt_int] :
% 0.33/0.62        ( ( member2340774599025711042nt_int @ Y
% 0.33/0.62          @ ( collec5210948495886036740nt_int
% 0.33/0.62            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.33/0.62              ? [X: product_prod_int_int] :
% 0.33/0.62                ( ( ratrel @ X @ X )
% 0.33/0.62                & ( C4
% 0.33/0.62                  = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 0.33/0.62       => ~ ! [X3: rat] :
% 0.33/0.62              ( Y
% 0.33/0.62             != ( rep_rat @ X3 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Rep_rat_cases
% 0.33/0.62  thf(fact_6055_Rep__rat__induct,axiom,
% 0.33/0.62      ! [Y: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.33/0.62        ( ( member2340774599025711042nt_int @ Y
% 0.33/0.62          @ ( collec5210948495886036740nt_int
% 0.33/0.62            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.33/0.62              ? [X: product_prod_int_int] :
% 0.33/0.62                ( ( ratrel @ X @ X )
% 0.33/0.62                & ( C4
% 0.33/0.62                  = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 0.33/0.62       => ( ! [X3: rat] : ( P @ ( rep_rat @ X3 ) )
% 0.33/0.62         => ( P @ Y ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % Rep_rat_induct
% 0.33/0.62  thf(fact_6056_pcr__int__def,axiom,
% 0.33/0.62      ( pcr_int
% 0.33/0.62      = ( relcom8911704206367525917at_int
% 0.33/0.62        @ ( basic_5328504652464829177at_nat
% 0.33/0.62          @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/0.62          @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 0.33/0.62        @ cr_int ) ) ).
% 0.33/0.62  
% 0.33/0.62  % pcr_int_def
% 0.33/0.62  thf(fact_6057_int_Opcr__cr__eq,axiom,
% 0.33/0.62      pcr_int = cr_int ).
% 0.33/0.62  
% 0.33/0.62  % int.pcr_cr_eq
% 0.33/0.62  thf(fact_6058_cr__int__def,axiom,
% 0.33/0.62      ( cr_int
% 0.33/0.62      = ( ^ [X: product_prod_nat_nat] :
% 0.33/0.62            ( ^ [Y3: int,Z: int] : ( Y3 = Z )
% 0.33/0.62            @ ( abs_Integ @ X ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % cr_int_def
% 0.33/0.62  thf(fact_6059_Quotient__int,axiom,
% 0.33/0.62      quotie1194848508323700631at_int @ intrel @ abs_Integ @ rep_Integ @ cr_int ).
% 0.33/0.62  
% 0.33/0.62  % Quotient_int
% 0.33/0.62  thf(fact_6060_lcm__code__integer,axiom,
% 0.33/0.62      ( gcd_lcm_Code_integer
% 0.33/0.62      = ( ^ [A2: code_integer,B2: code_integer] : ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B2 ) ) @ ( gcd_gcd_Code_integer @ A2 @ B2 ) ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_code_integer
% 0.33/0.62  thf(fact_6061_lcm__0__iff__nat,axiom,
% 0.33/0.62      ! [M: nat,N: nat] :
% 0.33/0.62        ( ( ( gcd_lcm_nat @ M @ N )
% 0.33/0.62          = zero_zero_nat )
% 0.33/0.62        = ( ( M = zero_zero_nat )
% 0.33/0.62          | ( N = zero_zero_nat ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_0_iff_nat
% 0.33/0.62  thf(fact_6062_lcm__0__iff__int,axiom,
% 0.33/0.62      ! [M: int,N: int] :
% 0.33/0.62        ( ( ( gcd_lcm_int @ M @ N )
% 0.33/0.62          = zero_zero_int )
% 0.33/0.62        = ( ( M = zero_zero_int )
% 0.33/0.62          | ( N = zero_zero_int ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_0_iff_int
% 0.33/0.62  thf(fact_6063_lcm__proj2__if__dvd__nat,axiom,
% 0.33/0.62      ! [X2: nat,Y: nat] :
% 0.33/0.62        ( ( dvd_dvd_nat @ X2 @ Y )
% 0.33/0.62       => ( ( gcd_lcm_nat @ X2 @ Y )
% 0.33/0.62          = Y ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_proj2_if_dvd_nat
% 0.33/0.62  thf(fact_6064_lcm__proj1__if__dvd__nat,axiom,
% 0.33/0.62      ! [X2: nat,Y: nat] :
% 0.33/0.62        ( ( dvd_dvd_nat @ X2 @ Y )
% 0.33/0.62       => ( ( gcd_lcm_nat @ Y @ X2 )
% 0.33/0.62          = Y ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_proj1_if_dvd_nat
% 0.33/0.62  thf(fact_6065_lcm__proj2__iff__nat,axiom,
% 0.33/0.62      ! [M: nat,N: nat] :
% 0.33/0.62        ( ( ( gcd_lcm_nat @ M @ N )
% 0.33/0.62          = N )
% 0.33/0.62        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_proj2_iff_nat
% 0.33/0.62  thf(fact_6066_lcm__proj1__iff__nat,axiom,
% 0.33/0.62      ! [M: nat,N: nat] :
% 0.33/0.62        ( ( ( gcd_lcm_nat @ M @ N )
% 0.33/0.62          = M )
% 0.33/0.62        = ( dvd_dvd_nat @ N @ M ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_proj1_iff_nat
% 0.33/0.62  thf(fact_6067_lcm__int__int__eq,axiom,
% 0.33/0.62      ! [M: nat,N: nat] :
% 0.33/0.62        ( ( gcd_lcm_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.33/0.62        = ( semiri1314217659103216013at_int @ ( gcd_lcm_nat @ M @ N ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_int_int_eq
% 0.33/0.62  thf(fact_6068_abs__lcm__int,axiom,
% 0.33/0.62      ! [I: int,J: int] :
% 0.33/0.62        ( ( abs_abs_int @ ( gcd_lcm_int @ I @ J ) )
% 0.33/0.62        = ( gcd_lcm_int @ I @ J ) ) ).
% 0.33/0.62  
% 0.33/0.62  % abs_lcm_int
% 0.33/0.62  thf(fact_6069_lcm__abs1__int,axiom,
% 0.33/0.62      ! [X2: int,Y: int] :
% 0.33/0.62        ( ( gcd_lcm_int @ ( abs_abs_int @ X2 ) @ Y )
% 0.33/0.62        = ( gcd_lcm_int @ X2 @ Y ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_abs1_int
% 0.33/0.62  thf(fact_6070_lcm__abs2__int,axiom,
% 0.33/0.62      ! [X2: int,Y: int] :
% 0.33/0.62        ( ( gcd_lcm_int @ X2 @ ( abs_abs_int @ Y ) )
% 0.33/0.62        = ( gcd_lcm_int @ X2 @ Y ) ) ).
% 0.33/0.62  
% 0.33/0.62  % lcm_abs2_int
% 0.33/0.62  
% 0.33/0.62  % Helper facts (36)
% 0.33/0.62  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.33/0.62      ! [X2: int,Y: int] :
% 0.33/0.62        ( ( if_int @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.33/0.62      ! [X2: int,Y: int] :
% 0.33/0.62        ( ( if_int @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.33/0.62      ! [X2: nat,Y: nat] :
% 0.33/0.62        ( ( if_nat @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.33/0.62      ! [X2: nat,Y: nat] :
% 0.33/0.62        ( ( if_nat @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.33/0.62      ! [X2: num,Y: num] :
% 0.33/0.62        ( ( if_num @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.33/0.62      ! [X2: num,Y: num] :
% 0.33/0.62        ( ( if_num @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.33/0.62      ! [X2: rat,Y: rat] :
% 0.33/0.62        ( ( if_rat @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.33/0.62      ! [X2: rat,Y: rat] :
% 0.33/0.62        ( ( if_rat @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_fChoice_1_1_fChoice_001t__Int__Oint_T,axiom,
% 0.33/0.62      ! [P: int > $o] :
% 0.33/0.62        ( ( P @ ( fChoice_int @ P ) )
% 0.33/0.62        = ( ? [X5: int] : ( P @ X5 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_fChoice_1_1_fChoice_001t__Nat__Onat_T,axiom,
% 0.33/0.62      ! [P: nat > $o] :
% 0.33/0.62        ( ( P @ ( fChoice_nat @ P ) )
% 0.33/0.62        = ( ? [X5: nat] : ( P @ X5 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.33/0.62      ! [X2: code_integer,Y: code_integer] :
% 0.33/0.62        ( ( if_Code_integer @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.33/0.62      ! [X2: code_integer,Y: code_integer] :
% 0.33/0.62        ( ( if_Code_integer @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 0.33/0.62      ! [X2: code_natural,Y: code_natural] :
% 0.33/0.62        ( ( if_Code_natural @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 0.33/0.62      ! [X2: code_natural,Y: code_natural] :
% 0.33/0.62        ( ( if_Code_natural @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.33/0.62      ! [X2: set_int,Y: set_int] :
% 0.33/0.62        ( ( if_set_int @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.33/0.62      ! [X2: set_int,Y: set_int] :
% 0.33/0.62        ( ( if_set_int @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.33/0.62      ! [X2: list_int,Y: list_int] :
% 0.33/0.62        ( ( if_list_int @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.33/0.62      ! [X2: list_int,Y: list_int] :
% 0.33/0.62        ( ( if_list_int @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_fChoice_1_1_fChoice_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 0.33/0.62      ! [P: set_nat > $o] :
% 0.33/0.62        ( ( P @ ( fChoice_set_nat @ P ) )
% 0.33/0.62        = ( ? [X5: set_nat] : ( P @ X5 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.33/0.62      ! [X2: option_num,Y: option_num] :
% 0.33/0.62        ( ( if_option_num @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.33/0.62      ! [X2: option_num,Y: option_num] :
% 0.33/0.62        ( ( if_option_num @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_Itf__a_J_T,axiom,
% 0.33/0.62      ! [X2: heap_Time_Heap_a,Y: heap_Time_Heap_a] :
% 0.33/0.62        ( ( if_Heap_Time_Heap_a @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_Itf__a_J_T,axiom,
% 0.33/0.62      ! [X2: heap_Time_Heap_a,Y: heap_Time_Heap_a] :
% 0.33/0.62        ( ( if_Heap_Time_Heap_a @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.33/0.62      ! [X2: product_prod_int_int,Y: product_prod_int_int] :
% 0.33/0.62        ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.33/0.62      ! [X2: product_prod_int_int,Y: product_prod_int_int] :
% 0.33/0.62        ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.33/0.62      ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.33/0.62        ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.33/0.62      ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.33/0.62        ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_T,axiom,
% 0.33/0.62      ! [X2: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 0.33/0.62        ( ( if_Hea8138950348631371857t_unit @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_T,axiom,
% 0.33/0.62      ! [X2: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 0.33/0.62        ( ( if_Hea8138950348631371857t_unit @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_fChoice_1_1_fChoice_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.33/0.62      ! [P: product_prod_nat_nat > $o] :
% 0.33/0.62        ( ( P @ ( fChoic6978938873391328853at_nat @ P ) )
% 0.33/0.62        = ( ? [X5: product_prod_nat_nat] : ( P @ X5 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.33/0.62      ! [X2: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 0.33/0.62        ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.33/0.62      ! [X2: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 0.33/0.62        ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_fChoice_1_1_fChoice_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 0.33/0.62      ! [P: set_Pr958786334691620121nt_int > $o] :
% 0.33/0.62        ( ( P @ ( fChoic2749331249758569069nt_int @ P ) )
% 0.33/0.62        = ( ? [X5: set_Pr958786334691620121nt_int] : ( P @ X5 ) ) ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.33/0.62      ! [P: $o] :
% 0.33/0.62        ( ( P = $true )
% 0.33/0.62        | ( P = $false ) ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.33/0.62      ! [X2: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.33/0.62        ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y )
% 0.33/0.62        = Y ) ).
% 0.33/0.62  
% 0.33/0.62  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.33/0.62      ! [X2: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.33/0.62        ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y )
% 0.33/0.62        = X2 ) ).
% 0.33/0.62  
% 0.33/0.62  % Conjectures (1)
% 0.33/0.62  thf(conj_0,conjecture,
% 0.33/0.62      ( ord_less_eq_nat
% 0.33/0.62      @ ( time_time_a
% 0.33/0.62        @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ p )
% 0.33/0.62          @ ^ [Uu: product_unit] : m )
% 0.33/0.62        @ h )
% 0.33/0.62      @ t ) ).
% 0.33/0.62  
% 0.33/0.62  %------------------------------------------------------------------------------
% 0.33/0.62  ------------------------
% 6.67/2.78  ---- Embedded in THF ---
% 6.67/2.78  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 6.67/2.78  %%% Generated on Thu Feb 26 05:29:40 EST 2026
% 6.67/2.78  %%% using '$$dhol' embedding, version 1.3.0.
% 6.67/2.78  %%% Logic specification used:
% 6.67/2.78  %%% thf(spec, logic, $$dhol).
% 6.67/2.78  
% 6.67/2.78  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2DTF31173.p
% See solution above
% 6.88/2.80  ------------------------
% 8.57/4.51  ---- Cleaned THF ---
% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 8.57/4.51      produc6756470014200349799atural: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 8.57/4.51      option8956607266484857688it_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.57/4.51      set_Pr8693737435421807431at_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 8.57/4.51      produc8664842809031399944it_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 8.57/4.51      produc5835291356934675326atural: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.57/4.51      produc859450856879609959at_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 8.57/4.51      produc6653097349344004940it_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 8.57/4.51      set_se6260736226359567993nt_int: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 8.57/4.51      produc7822875418678951345atural: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      produc8923325533196201883nteger: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.57/4.51      filter1242075044329608583at_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.57/4.51      set_Pr1261947904930325089at_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.57/4.51      set_Pr958786334691620121nt_int: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Heap____Time____Monad__OHeap_It__Heap__Oarray_It__Nat__Onat_J_J,type,
% 8.57/4.51      heap_T3836121109492952855ay_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Heap____Time____Monad__OHeap_It__Heap__Oarray_It__Int__Oint_J_J,type,
% 8.57/4.51      heap_T1346037964561226099ay_int: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 8.57/4.51      produc6271795597528267376eger_o: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J,type,
% 8.57/4.51      heap_T5738788834812785303t_unit: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Heap____Time____Monad__OHeap_It__Heap__Oarray_I_Eo_J_J,type,
% 8.57/4.51      heap_T5660665574680485309rray_o: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 8.57/4.51      heap_e7401611519738050253t_unit: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 8.57/4.51      product_prod_num_num: $tType ).
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% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
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% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 8.57/4.51  thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 8.57/4.51  thf(ty_n_t__Filter__Ofilter_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 8.57/4.51  thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 8.57/4.51      set_list_nat: $tType ).
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% 8.57/4.51  thf(ty_n_t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      list_Code_integer: $tType ).
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% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.57/4.51      set_set_nat: $tType ).
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% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      set_Code_integer: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Heap__Oarray_It__Product____Type__Ounit_J,type,
% 8.57/4.51      array_Product_unit: $tType ).
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% 8.57/4.51  thf(ty_n_t__Heap__Oref_It__Product____Type__Ounit_J,type,
% 8.57/4.51      ref_Product_unit: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 8.57/4.51      set_Product_unit: $tType ).
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% 8.57/4.51  thf(ty_n_t__Heap____Time____Monad__OHeap_Itf__a_J,type,
% 8.57/4.51      heap_Time_Heap_a: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Multiset__Omultiset_It__Nat__Onat_J,type,
% 8.57/4.51      multiset_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
% 8.57/4.51      option_num: $tType ).
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% 8.57/4.51  thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 8.57/4.51      list_char: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
% 8.57/4.51      filter_nat: $tType ).
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% 8.57/4.51  thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 8.57/4.51      set_char: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__List__Olist_It__Rat__Orat_J,type,
% 8.57/4.51      list_rat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__List__Olist_It__Num__Onum_J,type,
% 8.57/4.51      list_num: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 8.57/4.51      list_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
% 8.57/4.51      list_int: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
% 8.57/4.51      set_rat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 8.57/4.51      set_nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 8.57/4.51      set_int: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Code____Numeral__Onatural,type,
% 8.57/4.51      code_natural: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Code____Numeral__Ointeger,type,
% 8.57/4.51      code_integer: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Product____Type__Ounit,type,
% 8.57/4.51      product_unit: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__List__Olist_I_Eo_J,type,
% 8.57/4.51      list_o: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__String__Ochar,type,
% 8.57/4.51      char: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Rat__Orat,type,
% 8.57/4.51      rat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Num__Onum,type,
% 8.57/4.51      num: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Nat__Onat,type,
% 8.57/4.51      nat: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_t__Int__Oint,type,
% 8.57/4.51      int: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(ty_n_tf__a,type,
% 8.57/4.51      a: $tType ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 8.57/4.51      archim2889992004027027881ng_rat: rat > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 8.57/4.51      archim3151403230148437115or_rat: rat > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
% 8.57/4.51      archimedean_frac_rat: rat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Array__Time_Omake_001_Eo,type,
% 8.57/4.51      array_make_o: nat > ( nat > $o ) > heap_T5660665574680485309rray_o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Array__Time_Omake_001t__Int__Oint,type,
% 8.57/4.51      array_make_int: nat > ( nat > int ) > heap_T1346037964561226099ay_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Array__Time_Omake_001t__Nat__Onat,type,
% 8.57/4.51      array_make_nat: nat > ( nat > nat ) > heap_T3836121109492952855ay_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Array__Time_Onth_001t__Product____Type__Ounit,type,
% 8.57/4.51      array_7872002506669749220t_unit: array_Product_unit > nat > heap_T5738788834812785303t_unit ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Array__Time_Oof__list_001_Eo,type,
% 8.57/4.51      array_of_list_o: list_o > heap_T5660665574680485309rray_o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Array__Time_Oof__list_001t__Int__Oint,type,
% 8.57/4.51      array_of_list_int: list_int > heap_T1346037964561226099ay_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Array__Time_Oof__list_001t__Nat__Onat,type,
% 8.57/4.51      array_of_list_nat: list_nat > heap_T3836121109492952855ay_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 8.57/4.51      bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 8.57/4.51      bNF_re6321650412969554871eger_o: ( int > code_integer > $o ) > ( ( int > $o ) > ( code_integer > $o ) > $o ) > ( int > int > $o ) > ( code_integer > code_integer > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      bNF_re398004352372739002nteger: ( int > code_integer > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( int > int > int ) > ( code_integer > code_integer > code_integer ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 8.57/4.51      bNF_re4711666741709854504_nat_o: ( int > code_integer > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( code_integer > nat > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 8.57/4.51      bNF_re6574881592172037608er_o_o: ( int > code_integer > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( code_integer > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
% 8.57/4.51      bNF_re3804157879324367682nt_int: ( int > code_integer > $o ) > ( int > int > $o ) > ( int > int ) > ( code_integer > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      bNF_re2807294637932363402at_nat: ( int > code_integer > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( code_integer > nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
% 8.57/4.51      bNF_re6718328864250387230um_num: ( int > code_integer > $o ) > ( num > num > $o ) > ( int > num ) > ( code_integer > num ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 8.57/4.51      bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.57/4.51      bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.57/4.51      bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 8.57/4.51      bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 8.57/4.51      bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 8.57/4.51      bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 8.57/4.51      bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 8.57/4.51      bNF_re7626690874201225453um_num: ( int > int > $o ) > ( num > num > $o ) > ( int > num ) > ( int > num ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.57/4.51      bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 8.57/4.51      bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      bNF_re4935368626670024657nteger: ( nat > nat > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( nat > int > int ) > ( nat > code_integer > code_integer ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.57/4.51      bNF_re4785983289428654063nt_int: ( nat > nat > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( nat > int > int ) > ( nat > int > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 8.57/4.51      bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.57/4.51      bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 8.57/4.51      bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 8.57/4.51      bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 8.57/4.51      bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 8.57/4.51      bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 8.57/4.51      bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.57/4.51      bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 8.57/4.51      bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.57/4.51      bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 8.57/4.51      bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
% 8.57/4.51      bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 8.57/4.51      bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 8.57/4.51      bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.57/4.51      bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 8.57/4.51      bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 8.57/4.51      bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 8.57/4.51      bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.57/4.51      bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 8.57/4.51      bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 8.57/4.51      bNF_re7934895593101944656at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > $o ).
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% 8.57/4.51      bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Basic__BNFs_Opred__prod_001t__Int__Oint_001t__Int__Oint,type,
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% 8.57/4.51  thf(sy_c_Basic__BNFs_Opred__prod_001t__Nat__Onat_001t__Nat__Onat,type,
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% 8.57/4.51  thf(sy_c_Binomial_Obinomial,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
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% 8.57/4.51  thf(sy_c_Bit__Operations_Oand__int__rel,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
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% 8.57/4.51  thf(sy_c_Bit__Operations_Oconcat__bit,type,
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% 8.57/4.51  thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
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% 8.57/4.51      comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 8.57/4.51      comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 8.57/4.51      comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Int__Oint,type,
% 8.57/4.51      comp_nat_num_int: ( nat > num ) > ( int > nat ) > int > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Oid_001_062_It__Nat__Onat_M_Eo_J,type,
% 8.57/4.51      id_nat_o: ( nat > $o ) > nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Oid_001_Eo,type,
% 8.57/4.51      id_o: $o > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Oid_001t__Int__Oint,type,
% 8.57/4.51      id_int: int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 8.57/4.51      id_nat: nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Oid_001t__Num__Onum,type,
% 8.57/4.51      id_num: num > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 8.57/4.51      inj_on_nat_char: ( nat > char ) > set_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 8.57/4.51      map_fu2496120808607739376eger_o: ( code_integer > int ) > ( ( int > $o ) > code_integer > $o ) > ( int > int > $o ) > code_integer > code_integer > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      map_fu8272188784021352819nteger: ( code_integer > int ) > ( ( int > int ) > code_integer > code_integer ) > ( int > int > int ) > code_integer > code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 8.57/4.51      map_fu186220595405829473_nat_o: ( code_integer > int ) > ( ( nat > $o ) > nat > $o ) > ( int > nat > $o ) > code_integer > nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo_001_Eo,type,
% 8.57/4.51      map_fu6957801986076833569nt_o_o: ( code_integer > int ) > ( $o > $o ) > ( int > $o ) > code_integer > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      map_fu2599414010547811884nteger: ( code_integer > int ) > ( int > code_integer ) > ( int > int ) > code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      map_fu1051355602067684763atural: ( code_integer > int ) > ( nat > code_natural ) > ( int > nat ) > code_integer > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      map_fu6539832666145259331at_nat: ( code_integer > int ) > ( nat > nat ) > ( int > nat ) > code_integer > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
% 8.57/4.51      map_fu1227494855608507351um_num: ( code_integer > int ) > ( num > num ) > ( int > num ) > code_integer > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Code____Numeral__Onatural_M_Eo_J,type,
% 8.57/4.51      map_fu6256889081107267320ural_o: ( code_natural > nat ) > ( ( nat > $o ) > code_natural > $o ) > ( nat > nat > $o ) > code_natural > code_natural > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 8.57/4.51      map_fu6244533035418998608_nat_o: ( code_natural > nat ) > ( ( nat > $o ) > nat > $o ) > ( nat > nat > $o ) > code_natural > nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 8.57/4.51      map_fu6549440983881763648atural: ( code_natural > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > code_natural > code_natural > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_Eo_001_Eo,type,
% 8.57/4.51      map_fu4892316939951275536at_o_o: ( code_natural > nat ) > ( $o > $o ) > ( nat > $o ) > code_natural > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      map_fu2787874002554666395nteger: ( code_natural > nat ) > ( int > code_integer ) > ( nat > int ) > code_natural > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      map_fu1239815594074539274atural: ( code_natural > nat ) > ( nat > code_natural ) > ( nat > nat ) > code_natural > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      map_fu226235371393106610at_nat: ( code_natural > nat ) > ( nat > nat ) > ( nat > nat ) > code_natural > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 8.57/4.51      map_fu7831380289885515383nt_rat: ( int > int ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 8.57/4.51      map_fu3424225382358772769nt_rat: ( int > int ) > ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 8.57/4.51      map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.57/4.51      map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 8.57/4.51      map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 8.57/4.51      map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      map_fu8224359078269604234nteger: ( nat > nat ) > ( ( int > int ) > code_integer > code_integer ) > ( nat > int > int ) > nat > code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 8.57/4.51      map_fu6981160461238011112atural: ( nat > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > nat > code_natural > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      map_fu6290471996055670595nteger: ( nat > nat ) > ( int > code_integer ) > ( nat > int ) > nat > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      map_fu4742413587575543474atural: ( nat > nat ) > ( nat > code_natural ) > ( nat > nat ) > nat > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      map_fu6891787308814931657nteger: ( num > num ) > ( ( num > int ) > num > code_integer ) > ( num > num > int ) > num > num > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      map_fu8638147718074629079nteger: ( num > num ) > ( int > code_integer ) > ( num > int ) > num > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 8.57/4.51      map_fu4333342158222067775at_rat: ( rat > product_prod_int_int ) > ( ( product_prod_int_int > product_prod_int_int ) > rat > rat ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > rat > rat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 8.57/4.51      map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 8.57/4.51      map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun__Def_Ois__measure_001t__Int__Oint,type,
% 8.57/4.51      fun_is_measure_int: ( int > nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun__Def_Opair__leq,type,
% 8.57/4.51      fun_pair_leq: set_Pr8693737435421807431at_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Fun__Def_Opair__less,type,
% 8.57/4.51      fun_pair_less: set_Pr8693737435421807431at_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 8.57/4.51      gcd_Gcd_int: set_int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 8.57/4.51      gcd_Gcd_nat: set_nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_Obezw,type,
% 8.57/4.51      bezw: nat > nat > product_prod_int_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_Obezw__rel,type,
% 8.57/4.51      bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 8.57/4.51      gcd_gcd_int: int > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 8.57/4.51      gcd_gcd_nat: nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_Ogcd__class_Olcm_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      gcd_lcm_Code_integer: code_integer > code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_Ogcd__class_Olcm_001t__Int__Oint,type,
% 8.57/4.51      gcd_lcm_int: int > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
% 8.57/4.51      gcd_lcm_nat: nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_GCD_Ogcd__nat__rel,type,
% 8.57/4.51      gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      abs_abs_Code_integer: code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 8.57/4.51      abs_abs_int: int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 8.57/4.51      abs_abs_rat: rat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      minus_7197305767214868737atural: code_natural > code_natural > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 8.57/4.51      minus_minus_int: int > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 8.57/4.51      minus_minus_nat: nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 8.57/4.51      minus_minus_rat: rat > rat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.57/4.51      minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      one_one_Code_integer: code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      one_one_Code_natural: code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
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% 8.57/4.51  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 8.57/4.51      inf_in3604695632404883862_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 8.57/4.51      inf_inf_int: int > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 8.57/4.51      inf_inf_nat: nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 8.57/4.51      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 8.57/4.51      sup_sup_int: int > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 8.57/4.51      sup_sup_nat: nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.57/4.51      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 8.57/4.51      lattic8263393255366662781ax_int: set_int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 8.57/4.51      lattic8265883725875713057ax_nat: set_nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Lifting_OQuotient_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 8.57/4.51      quotie1194848508323700631at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int > $o ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 8.57/4.51      append_int: list_int > list_int > list_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 8.57/4.51      append_nat: list_nat > list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 8.57/4.51      butlast_nat: list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 8.57/4.51      drop_nat: nat > list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
% 8.57/4.51      filter_nat2: ( nat > $o ) > list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Ofold_001t__Int__Oint_001t__Int__Oint,type,
% 8.57/4.51      fold_int_int: ( int > int > int ) > list_int > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Ofoldr_001_Eo_001t__Nat__Onat,type,
% 8.57/4.51      foldr_o_nat: ( $o > nat > nat ) > list_o > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Ofoldr_001t__Int__Oint_001t__Nat__Onat,type,
% 8.57/4.51      foldr_int_nat: ( int > nat > nat ) > list_int > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Ofoldr_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Ogen__length_001_Eo,type,
% 8.57/4.51      gen_length_o: nat > list_o > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Ogen__length_001t__Int__Oint,type,
% 8.57/4.51      gen_length_int: nat > list_int > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Ogen__length_001t__Nat__Onat,type,
% 8.57/4.51      gen_length_nat: nat > list_nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 8.57/4.51      last_nat: list_nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 8.57/4.51      linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 8.57/4.51      linord2614967742042102400et_nat: set_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_OCons_001_Eo,type,
% 8.57/4.51      cons_o: $o > list_o > list_o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 8.57/4.51      cons_int: int > list_int > list_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 8.57/4.51      cons_nat: nat > list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_OCons_001t__Num__Onum,type,
% 8.57/4.51      cons_num: num > list_num > list_num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_OCons_001t__Rat__Orat,type,
% 8.57/4.51      cons_rat: rat > list_rat > list_rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_OCons_001t__String__Ochar,type,
% 8.57/4.51      cons_char: char > list_char > list_char ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_ONil_001_Eo,type,
% 8.57/4.51      nil_o: list_o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 8.57/4.51      nil_int: list_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 8.57/4.51      nil_nat: list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_ONil_001t__Num__Onum,type,
% 8.57/4.51      nil_num: list_num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_ONil_001t__Rat__Orat,type,
% 8.57/4.51      nil_rat: list_rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_ONil_001t__String__Ochar,type,
% 8.57/4.51      nil_char: list_char ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 8.57/4.51      set_int2: list_int > set_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 8.57/4.51      set_nat2: list_nat > set_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Onth_001_Eo,type,
% 8.57/4.51      nth_o: list_o > nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      nth_Code_integer: list_Code_integer > nat > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Onth_001t__Int__Oint,type,
% 8.57/4.51      nth_int: list_int > nat > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 8.57/4.51      nth_nat: list_nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Onth_001t__Num__Onum,type,
% 8.57/4.51      nth_num: list_num > nat > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Onth_001t__Rat__Orat,type,
% 8.57/4.51      nth_rat: list_rat > nat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Onth_001t__String__Ochar,type,
% 8.57/4.51      nth_char: list_char > nat > char ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Orotate1_001_Eo,type,
% 8.57/4.51      rotate1_o: list_o > list_o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 8.57/4.51      rotate1_int: list_int > list_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 8.57/4.51      rotate1_nat: list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Orotate_001_Eo,type,
% 8.57/4.51      rotate_o: nat > list_o > list_o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Orotate_001t__Int__Oint,type,
% 8.57/4.51      rotate_int: nat > list_int > list_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Orotate_001t__Nat__Onat,type,
% 8.57/4.51      rotate_nat: nat > list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Osorted__wrt_001_Eo,type,
% 8.57/4.51      sorted_wrt_o: ( $o > $o > $o ) > list_o > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Osorted__wrt_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      sorted710888440204495920nteger: ( code_integer > code_integer > $o ) > list_Code_integer > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 8.57/4.51      sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 8.57/4.51      sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Osorted__wrt_001t__Num__Onum,type,
% 8.57/4.51      sorted_wrt_num: ( num > num > $o ) > list_num > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Osorted__wrt_001t__Rat__Orat,type,
% 8.57/4.51      sorted_wrt_rat: ( rat > rat > $o ) > list_rat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 8.57/4.51      take_nat: nat > list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Oupt,type,
% 8.57/4.51      upt: nat > nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Oupto,type,
% 8.57/4.51      upto: int > int > list_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Oupto__aux,type,
% 8.57/4.51      upto_aux: int > int > list_int > list_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_List_Oupto__rel,type,
% 8.57/4.51      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Misc_Oslice_001_Eo,type,
% 8.57/4.51      slice_o: nat > nat > list_o > list_o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Misc_Oslice_001t__Int__Oint,type,
% 8.57/4.51      slice_int: nat > nat > list_int > list_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Misc_Oslice_001t__Nat__Onat,type,
% 8.57/4.51      slice_nat: nat > nat > list_nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Misc_Oslice_001t__String__Ochar,type,
% 8.57/4.51      slice_char: nat > nat > list_char > list_char ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Multiset_Omset_001t__Nat__Onat,type,
% 8.57/4.51      mset_nat: list_nat > multiset_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Multiset_Omset__set_001t__Nat__Onat,type,
% 8.57/4.51      mset_set_nat: set_nat > multiset_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_OSuc,type,
% 8.57/4.51      suc: nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.57/4.51      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 8.57/4.51      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 8.57/4.51      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 8.57/4.51      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Onat_Opred,type,
% 8.57/4.51      pred: nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 8.57/4.51      semiring_1_Nats_int: set_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      semiri4939895301339042750nteger: nat > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      semiri3763490453095760265atural: nat > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 8.57/4.51      semiri1314217659103216013at_int: nat > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 8.57/4.51      semiri1316708129612266289at_nat: nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 8.57/4.51      semiri681578069525770553at_rat: nat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      semiri2879080225315754349atural: ( code_natural > code_natural ) > nat > code_natural > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 8.57/4.51      semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 8.57/4.51      semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 8.57/4.51      semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 8.57/4.51      size_size_list_o: list_o > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 8.57/4.51      size_s3445333598471063425nteger: list_Code_integer > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 8.57/4.51      size_size_list_int: list_int > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 8.57/4.51      size_size_list_nat: list_nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 8.57/4.51      size_size_list_num: list_num > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Rat__Orat_J,type,
% 8.57/4.51      size_size_list_rat: list_rat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__String__Ochar_J,type,
% 8.57/4.51      size_size_list_char: list_char > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 8.57/4.51      size_size_num: num > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 8.57/4.51      size_size_char: char > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Olist__decode,type,
% 8.57/4.51      nat_list_decode: nat > list_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 8.57/4.51      nat_list_decode_rel: nat > nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Olist__encode,type,
% 8.57/4.51      nat_list_encode: list_nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 8.57/4.51      nat_list_encode_rel: list_nat > list_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 8.57/4.51      nat_prod_decode: nat > product_prod_nat_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 8.57/4.51      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 8.57/4.51      nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 8.57/4.51      nat_prod_encode: product_prod_nat_nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Oset__decode,type,
% 8.57/4.51      nat_set_decode: nat > set_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Oset__encode,type,
% 8.57/4.51      nat_set_encode: set_nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Nat__Bijection_Otriangle,type,
% 8.57/4.51      nat_triangle: nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_OBitM,type,
% 8.57/4.51      bitM: num > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oinc,type,
% 8.57/4.51      inc: num > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 8.57/4.51      neg_numeral_dbl_int: int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 8.57/4.51      neg_numeral_dbl_rat: rat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 8.57/4.51      neg_nu3811975205180677377ec_int: int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 8.57/4.51      neg_nu3179335615603231917ec_rat: rat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 8.57/4.51      neg_nu5851722552734809277nc_int: int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 8.57/4.51      neg_nu5219082963157363817nc_rat: rat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      neg_nu5755505904847501662nteger: num > num > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 8.57/4.51      neg_numeral_sub_int: num > num > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onum_OBit0,type,
% 8.57/4.51      bit0: num > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onum_OBit1,type,
% 8.57/4.51      bit1: num > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onum_OOne,type,
% 8.57/4.51      one: num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 8.57/4.51      case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onum_Osize__num,type,
% 8.57/4.51      size_num: num > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onum__of__nat,type,
% 8.57/4.51      num_of_nat: nat > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      numera6620942414471956472nteger: num > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      numera5444537566228673987atural: num > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 8.57/4.51      numeral_numeral_int: num > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 8.57/4.51      numeral_numeral_nat: num > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 8.57/4.51      numeral_numeral_rat: num > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Opow,type,
% 8.57/4.51      pow: num > num > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Opred__numeral,type,
% 8.57/4.51      pred_numeral: num > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Num_Osqr,type,
% 8.57/4.51      sqr: num > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 8.57/4.51      none_num: option_num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 8.57/4.51      none_P9117596204409417319it_nat: option8956607266484857688it_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 8.57/4.51      some_num: num > option_num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 8.57/4.51      some_P1914260805536162275it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 8.57/4.51      case_option_int_num: int > ( num > int ) > option_num > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 8.57/4.51      case_option_num_num: num > ( num > num ) > option_num > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 8.57/4.51      case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 8.57/4.51      map_option_num_num: ( num > num ) > option_num > option_num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 8.57/4.51      bot_bot_nat: nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
% 8.57/4.51      bot_bot_set_int: set_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.57/4.51      bot_bot_set_nat: set_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_OLeast_001t__Nat__Onat,type,
% 8.57/4.51      ord_Least_nat: ( nat > $o ) > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless_001_Eo,type,
% 8.57/4.51      ord_less_o: $o > $o > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      ord_le5570908160329646204atural: code_natural > code_natural > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 8.57/4.51      ord_less_int: int > int > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 8.57/4.51      ord_less_nat: nat > nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
% 8.57/4.51      ord_less_num: num > num > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
% 8.57/4.51      ord_less_rat: rat > rat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.57/4.51      ord_less_set_nat: set_nat > set_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Int__Oint_J,type,
% 8.57/4.51      ord_less_eq_o_int: ( $o > int ) > ( $o > int ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Nat__Onat_J,type,
% 8.57/4.51      ord_less_eq_o_nat: ( $o > nat ) > ( $o > nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Num__Onum_J,type,
% 8.57/4.51      ord_less_eq_o_num: ( $o > num ) > ( $o > num ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Rat__Orat_J,type,
% 8.57/4.51      ord_less_eq_o_rat: ( $o > rat ) > ( $o > rat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 8.57/4.51      ord_le7022414076629706543et_nat: ( $o > set_nat ) > ( $o > set_nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
% 8.57/4.51      ord_less_eq_o: $o > $o > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      ord_le1926595141338095240atural: code_natural > code_natural > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 8.57/4.51      ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 8.57/4.51      ord_less_eq_int: int > int > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 8.57/4.51      ord_less_eq_nat: nat > nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 8.57/4.51      ord_less_eq_num: num > num > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 8.57/4.51      ord_less_eq_rat: rat > rat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.57/4.51      ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      ord_max_Code_integer: code_integer > code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      ord_max_Code_natural: code_natural > code_natural > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 8.57/4.51      ord_max_int: int > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 8.57/4.51      ord_max_nat: nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Omin_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      ord_min_Code_integer: code_integer > code_integer > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Omin_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      ord_min_Code_natural: code_natural > code_natural > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Omin_001t__Int__Oint,type,
% 8.57/4.51      ord_min_int: int > int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
% 8.57/4.51      ord_min_nat: nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Int__Oint,type,
% 8.57/4.51      order_Greatest_int: ( int > $o ) > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 8.57/4.51      order_Greatest_nat: ( nat > $o ) > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Num__Onum,type,
% 8.57/4.51      order_Greatest_num: ( num > $o ) > num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Rat__Orat,type,
% 8.57/4.51      order_Greatest_rat: ( rat > $o ) > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.57/4.51      order_5724808138429204845et_nat: ( set_nat > $o ) > set_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      order_mono_nat_nat: ( nat > nat ) > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Oordering__top_001t__Nat__Onat,type,
% 8.57/4.51      ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Int__Oint_J,type,
% 8.57/4.51      top_top_set_int: set_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.57/4.51      top_top_set_nat: set_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 8.57/4.51      top_to1996260823553986621t_unit: set_Product_unit ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
% 8.57/4.51      top_top_set_char: set_char ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      power_7079662738309270450atural: code_natural > nat > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 8.57/4.51      power_power_int: int > nat > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 8.57/4.51      power_power_nat: nat > nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 8.57/4.51      power_power_rat: rat > nat > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 8.57/4.51      produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural,type,
% 8.57/4.51      produc3574140220909816553atural: code_natural > code_natural > produc7822875418678951345atural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 8.57/4.51      produc6639722614265839536atural: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OPair_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
% 8.57/4.51      produc584006145561248582it_nat: heap_e7401611519738050253t_unit > nat > produc6653097349344004940it_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 8.57/4.51      product_Pair_int_int: int > int > product_prod_int_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 8.57/4.51      product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_OUnity,type,
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% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__String__Ochar,type,
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% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
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% 8.57/4.51  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,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
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% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
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% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 8.57/4.51      produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
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% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
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% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 8.57/4.51      product_snd_int_int: product_prod_int_int > int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.57/4.51      product_snd_nat_nat: product_prod_nat_nat > nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Product__Type_Oscomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Random_Oinc__shift,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Random_Oiterate_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Random_Olog,type,
% 8.57/4.51      log: code_natural > code_natural > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Random_Olog__rel,type,
% 8.57/4.51      log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Random_Ominus__shift,type,
% 8.57/4.51      minus_shift: code_natural > code_natural > code_natural > code_natural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Random_Onext,type,
% 8.57/4.51      next: produc7822875418678951345atural > produc5835291356934675326atural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Random_Orange,type,
% 8.57/4.51      range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Random_Osplit__seed,type,
% 8.57/4.51      split_seed: produc7822875418678951345atural > produc6756470014200349799atural ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_OAbs__Rat,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_OFract,type,
% 8.57/4.51      fract: int > int > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_OFrct,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_ORep__Rat,type,
% 8.57/4.51      rep_Rat: rat > product_prod_int_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_Ocr__rat,type,
% 8.57/4.51      cr_rat: product_prod_int_int > rat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_Onormalize,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_Oof__int,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_Opcr__rat,type,
% 8.57/4.51      pcr_rat: product_prod_int_int > rat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_Opositive,type,
% 8.57/4.51      positive: rat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_Oquotient__of,type,
% 8.57/4.51      quotient_of: rat > product_prod_int_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_Orat_OAbs__rat,type,
% 8.57/4.51      abs_rat: set_Pr958786334691620121nt_int > rat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_Orat_ORep__rat,type,
% 8.57/4.51      rep_rat: rat > set_Pr958786334691620121nt_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rat_Oratrel,type,
% 8.57/4.51      ratrel: product_prod_int_int > product_prod_int_int > $o ).
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% 8.57/4.51  thf(sy_c_Ref__Time_Ochange_001t__Product____Type__Ounit,type,
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% 8.57/4.51  thf(sy_c_Ref__Time_Olookup_001t__Product____Type__Ounit,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Refine__Imp__Hol_Oassert_H,type,
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% 8.57/4.51  
% 8.57/4.51  thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
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% 8.57/4.51      fChoice_set_nat: ( set_nat > $o ) > set_nat ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_fChoice_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.57/4.51      fChoic2749331249758569069nt_int: ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 8.57/4.51      member_Code_integer: code_integer > set_Code_integer > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_member_001t__Int__Oint,type,
% 8.57/4.51      member_int: int > set_int > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 8.57/4.51      member_list_nat: list_nat > set_list_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_member_001t__Nat__Onat,type,
% 8.57/4.51      member_nat: nat > set_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.57/4.51      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.57/4.51      member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_member_001t__Rat__Orat,type,
% 8.57/4.51      member_rat: rat > set_rat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.57/4.51      member_set_nat: set_nat > set_set_nat > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.57/4.51      member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_v_P,type,
% 8.57/4.51      p: $o ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_v_h,type,
% 8.57/4.51      h: heap_e7401611519738050253t_unit ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_v_m,type,
% 8.57/4.51      m: heap_Time_Heap_a ).
% 8.57/4.51  
% 8.57/4.51  thf(sy_v_t,type,
% 8.57/4.51      t: nat ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_0__092_060open_062_092_060And_062h_O_AP_A_092_060Longrightarrow_062_Atime_Am_Ah_A_092_060le_062_At_092_060close_062,axiom,
% 8.57/4.51      ! [H: heap_e7401611519738050253t_unit] :
% 8.57/4.51        ( p
% 8.57/4.51       => ( ord_less_eq_nat @ ( time_time_a @ m @ H ) @ t ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_1_assms,axiom,
% 8.57/4.51      ( p
% 8.57/4.51     => ( time_TBOUND_a @ m @ t ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_2_Heap__Time__Monad_Obind__bind,axiom,
% 8.57/4.51      ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_Time_Heap_a,K: a > heap_T5738788834812785303t_unit] :
% 8.57/4.51        ( ( heap_T8685611227969916822t_unit @ ( heap_T757603679106148408unit_a @ F @ G ) @ K )
% 8.57/4.51        = ( heap_T2633723481742716231t_unit @ F
% 8.57/4.51          @ ^ [X: product_unit] : ( heap_T8685611227969916822t_unit @ ( G @ X ) @ K ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_3_Heap__Time__Monad_Obind__bind,axiom,
% 8.57/4.51      ! [F: heap_Time_Heap_a,G: a > heap_T5738788834812785303t_unit,K: product_unit > heap_Time_Heap_a] :
% 8.57/4.51        ( ( heap_T757603679106148408unit_a @ ( heap_T8685611227969916822t_unit @ F @ G ) @ K )
% 8.57/4.51        = ( heap_Time_bind_a_a @ F
% 8.57/4.51          @ ^ [X: a] : ( heap_T757603679106148408unit_a @ ( G @ X ) @ K ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_4_Heap__Time__Monad_Obind__bind,axiom,
% 8.57/4.51      ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_T5738788834812785303t_unit,K: product_unit > heap_T5738788834812785303t_unit] :
% 8.57/4.51        ( ( heap_T2633723481742716231t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ K )
% 8.57/4.51        = ( heap_T2633723481742716231t_unit @ F
% 8.57/4.51          @ ^ [X: product_unit] : ( heap_T2633723481742716231t_unit @ ( G @ X ) @ K ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_5_Heap__Time__Monad_Obind__bind,axiom,
% 8.57/4.51      ! [F: heap_Time_Heap_a,G: a > heap_Time_Heap_a,K: a > heap_Time_Heap_a] :
% 8.57/4.51        ( ( heap_Time_bind_a_a @ ( heap_Time_bind_a_a @ F @ G ) @ K )
% 8.57/4.51        = ( heap_Time_bind_a_a @ F
% 8.57/4.51          @ ^ [X: a] : ( heap_Time_bind_a_a @ ( G @ X ) @ K ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_6_Heap__Time__Monad_Obind__bind,axiom,
% 8.57/4.51      ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_Time_Heap_a,K: a > heap_Time_Heap_a] :
% 8.57/4.51        ( ( heap_Time_bind_a_a @ ( heap_T757603679106148408unit_a @ F @ G ) @ K )
% 8.57/4.51        = ( heap_T757603679106148408unit_a @ F
% 8.57/4.51          @ ^ [X: product_unit] : ( heap_Time_bind_a_a @ ( G @ X ) @ K ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_7_Heap__Time__Monad_Obind__bind,axiom,
% 8.57/4.51      ! [F: heap_T5738788834812785303t_unit,G: product_unit > heap_T5738788834812785303t_unit,K: product_unit > heap_Time_Heap_a] :
% 8.57/4.51        ( ( heap_T757603679106148408unit_a @ ( heap_T2633723481742716231t_unit @ F @ G ) @ K )
% 8.57/4.51        = ( heap_T757603679106148408unit_a @ F
% 8.57/4.51          @ ^ [X: product_unit] : ( heap_T757603679106148408unit_a @ ( G @ X ) @ K ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_8_order__refl,axiom,
% 8.57/4.51      ! [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ X2 ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_9_order__refl,axiom,
% 8.57/4.51      ! [X2: rat] : ( ord_less_eq_rat @ X2 @ X2 ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_10_order__refl,axiom,
% 8.57/4.51      ! [X2: num] : ( ord_less_eq_num @ X2 @ X2 ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_11_order__refl,axiom,
% 8.57/4.51      ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_12_order__refl,axiom,
% 8.57/4.51      ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_13_dual__order_Orefl,axiom,
% 8.57/4.51      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_14_dual__order_Orefl,axiom,
% 8.57/4.51      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_15_dual__order_Orefl,axiom,
% 8.57/4.51      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_16_dual__order_Orefl,axiom,
% 8.57/4.51      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_17_dual__order_Orefl,axiom,
% 8.57/4.51      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_18_distrib__if__bind,axiom,
% 8.57/4.51      ! [B: $o,C: heap_T5738788834812785303t_unit,D: heap_T5738788834812785303t_unit,F: product_unit > heap_T5738788834812785303t_unit] :
% 8.57/4.51        ( ( B
% 8.57/4.51         => ( ( heap_T2633723481742716231t_unit @ ( if_Hea8138950348631371857t_unit @ B @ C @ D ) @ F )
% 8.57/4.51            = ( heap_T2633723481742716231t_unit @ C @ F ) ) )
% 8.57/4.51        & ( ~ B
% 8.57/4.51         => ( ( heap_T2633723481742716231t_unit @ ( if_Hea8138950348631371857t_unit @ B @ C @ D ) @ F )
% 8.57/4.51            = ( heap_T2633723481742716231t_unit @ D @ F ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_19_distrib__if__bind,axiom,
% 8.57/4.51      ! [B: $o,C: heap_Time_Heap_a,D: heap_Time_Heap_a,F: a > heap_Time_Heap_a] :
% 8.57/4.51        ( ( B
% 8.57/4.51         => ( ( heap_Time_bind_a_a @ ( if_Heap_Time_Heap_a @ B @ C @ D ) @ F )
% 8.57/4.51            = ( heap_Time_bind_a_a @ C @ F ) ) )
% 8.57/4.51        & ( ~ B
% 8.57/4.51         => ( ( heap_Time_bind_a_a @ ( if_Heap_Time_Heap_a @ B @ C @ D ) @ F )
% 8.57/4.51            = ( heap_Time_bind_a_a @ D @ F ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_20_distrib__if__bind,axiom,
% 8.57/4.51      ! [B: $o,C: heap_T5738788834812785303t_unit,D: heap_T5738788834812785303t_unit,F: product_unit > heap_Time_Heap_a] :
% 8.57/4.51        ( ( B
% 8.57/4.51         => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ B @ C @ D ) @ F )
% 8.57/4.51            = ( heap_T757603679106148408unit_a @ C @ F ) ) )
% 8.57/4.51        & ( ~ B
% 8.57/4.51         => ( ( heap_T757603679106148408unit_a @ ( if_Hea8138950348631371857t_unit @ B @ C @ D ) @ F )
% 8.57/4.51            = ( heap_T757603679106148408unit_a @ D @ F ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_21_TBOUNDD,axiom,
% 8.57/4.51      ! [M: heap_T5738788834812785303t_unit,T: nat,H: heap_e7401611519738050253t_unit] :
% 8.57/4.51        ( ( time_T7469515765551943773t_unit @ M @ T )
% 8.57/4.51       => ( ord_less_eq_nat @ ( time_t4224138285095624986t_unit @ M @ H ) @ T ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_22_TBOUNDD,axiom,
% 8.57/4.51      ! [M: heap_Time_Heap_a,T: nat,H: heap_e7401611519738050253t_unit] :
% 8.57/4.51        ( ( time_TBOUND_a @ M @ T )
% 8.57/4.51       => ( ord_less_eq_nat @ ( time_time_a @ M @ H ) @ T ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_23_TBOUNDI,axiom,
% 8.57/4.51      ! [M: heap_T5738788834812785303t_unit,T: nat] :
% 8.57/4.51        ( ! [H2: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_t4224138285095624986t_unit @ M @ H2 ) @ T )
% 8.57/4.51       => ( time_T7469515765551943773t_unit @ M @ T ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_24_TBOUNDI,axiom,
% 8.57/4.51      ! [M: heap_Time_Heap_a,T: nat] :
% 8.57/4.51        ( ! [H2: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_a @ M @ H2 ) @ T )
% 8.57/4.51       => ( time_TBOUND_a @ M @ T ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_25_TBOUND__def,axiom,
% 8.57/4.51      ( time_T7469515765551943773t_unit
% 8.57/4.51      = ( ^ [M2: heap_T5738788834812785303t_unit,T2: nat] :
% 8.57/4.51          ! [H3: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_t4224138285095624986t_unit @ M2 @ H3 ) @ T2 ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_26_TBOUND__def,axiom,
% 8.57/4.51      ( time_TBOUND_a
% 8.57/4.51      = ( ^ [M2: heap_Time_Heap_a,T2: nat] :
% 8.57/4.51          ! [H3: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_a @ M2 @ H3 ) @ T2 ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_27_le__refl,axiom,
% 8.57/4.51      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_28_le__trans,axiom,
% 8.57/4.51      ! [I: nat,J: nat,K: nat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.51       => ( ( ord_less_eq_nat @ J @ K )
% 8.57/4.51         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_29_eq__imp__le,axiom,
% 8.57/4.51      ! [M: nat,N: nat] :
% 8.57/4.51        ( ( M = N )
% 8.57/4.51       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_30_le__antisym,axiom,
% 8.57/4.51      ! [M: nat,N: nat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.51       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.51         => ( M = N ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_31_nat__le__linear,axiom,
% 8.57/4.51      ! [M: nat,N: nat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.51        | ( ord_less_eq_nat @ N @ M ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_32_TBOUND__mono,axiom,
% 8.57/4.51      ! [C: heap_Time_Heap_a,T: nat,T3: nat] :
% 8.57/4.51        ( ( time_TBOUND_a @ C @ T )
% 8.57/4.51       => ( ( ord_less_eq_nat @ T @ T3 )
% 8.57/4.51         => ( time_TBOUND_a @ C @ T3 ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_33_TBOUND__mono,axiom,
% 8.57/4.51      ! [C: heap_T5738788834812785303t_unit,T: nat,T3: nat] :
% 8.57/4.51        ( ( time_T7469515765551943773t_unit @ C @ T )
% 8.57/4.51       => ( ( ord_less_eq_nat @ T @ T3 )
% 8.57/4.51         => ( time_T7469515765551943773t_unit @ C @ T3 ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_34_TBOUND__eqI,axiom,
% 8.57/4.51      ! [M: heap_Time_Heap_a,T: nat] :
% 8.57/4.51        ( ! [H2: heap_e7401611519738050253t_unit] :
% 8.57/4.51            ( ( time_time_a @ M @ H2 )
% 8.57/4.51            = T )
% 8.57/4.51       => ( time_TBOUND_a @ M @ T ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_35_TBOUND__eqI,axiom,
% 8.57/4.51      ! [M: heap_T5738788834812785303t_unit,T: nat] :
% 8.57/4.51        ( ! [H2: heap_e7401611519738050253t_unit] :
% 8.57/4.51            ( ( time_t4224138285095624986t_unit @ M @ H2 )
% 8.57/4.51            = T )
% 8.57/4.51       => ( time_T7469515765551943773t_unit @ M @ T ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_36_order__antisym__conv,axiom,
% 8.57/4.51      ! [Y: set_nat,X2: set_nat] :
% 8.57/4.51        ( ( ord_less_eq_set_nat @ Y @ X2 )
% 8.57/4.51       => ( ( ord_less_eq_set_nat @ X2 @ Y )
% 8.57/4.51          = ( X2 = Y ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_37_order__antisym__conv,axiom,
% 8.57/4.51      ! [Y: rat,X2: rat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ Y @ X2 )
% 8.57/4.51       => ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.51          = ( X2 = Y ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_38_order__antisym__conv,axiom,
% 8.57/4.51      ! [Y: num,X2: num] :
% 8.57/4.51        ( ( ord_less_eq_num @ Y @ X2 )
% 8.57/4.51       => ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.51          = ( X2 = Y ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_39_order__antisym__conv,axiom,
% 8.57/4.51      ! [Y: nat,X2: nat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ Y @ X2 )
% 8.57/4.51       => ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.51          = ( X2 = Y ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_40_order__antisym__conv,axiom,
% 8.57/4.51      ! [Y: int,X2: int] :
% 8.57/4.51        ( ( ord_less_eq_int @ Y @ X2 )
% 8.57/4.51       => ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.51          = ( X2 = Y ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_41_linorder__le__cases,axiom,
% 8.57/4.51      ! [X2: rat,Y: rat] :
% 8.57/4.51        ( ~ ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.51       => ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_42_linorder__le__cases,axiom,
% 8.57/4.51      ! [X2: num,Y: num] :
% 8.57/4.51        ( ~ ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.51       => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_43_linorder__le__cases,axiom,
% 8.57/4.51      ! [X2: nat,Y: nat] :
% 8.57/4.51        ( ~ ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.51       => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_44_linorder__le__cases,axiom,
% 8.57/4.51      ! [X2: int,Y: int] :
% 8.57/4.51        ( ~ ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.51       => ( ord_less_eq_int @ Y @ X2 ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_45_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_46_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_47_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_48_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_49_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: num,B: num,F: num > rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_50_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: num,B: num,F: num > num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_51_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: num,B: num,F: num > nat,C: nat] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_52_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: num,B: num,F: num > int,C: int] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_53_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.51                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_54_ord__le__eq__subst,axiom,
% 8.57/4.51      ! [A: nat,B: nat,F: nat > num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.51       => ( ( ( F @ B )
% 8.57/4.51            = C )
% 8.57/4.51         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.51                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_55_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_56_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: num,F: rat > num,B: rat,C: rat] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_57_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_58_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: int,F: rat > int,B: rat,C: rat] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_59_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_60_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: num,F: num > num,B: num,C: num] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_61_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: nat,F: num > nat,B: num,C: num] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_62_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: int,F: num > int,B: num,C: num] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_63_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.51         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.51                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_64_ord__eq__le__subst,axiom,
% 8.57/4.51      ! [A: num,F: nat > num,B: nat,C: nat] :
% 8.57/4.51        ( ( A
% 8.57/4.51          = ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.51         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.51                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_65_linorder__linear,axiom,
% 8.57/4.51      ! [X2: rat,Y: rat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.51        | ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_66_linorder__linear,axiom,
% 8.57/4.51      ! [X2: num,Y: num] :
% 8.57/4.51        ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.51        | ( ord_less_eq_num @ Y @ X2 ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_67_linorder__linear,axiom,
% 8.57/4.51      ! [X2: nat,Y: nat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.51        | ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_68_linorder__linear,axiom,
% 8.57/4.51      ! [X2: int,Y: int] :
% 8.57/4.51        ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.51        | ( ord_less_eq_int @ Y @ X2 ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_69_order__eq__refl,axiom,
% 8.57/4.51      ! [X2: set_nat,Y: set_nat] :
% 8.57/4.51        ( ( X2 = Y )
% 8.57/4.51       => ( ord_less_eq_set_nat @ X2 @ Y ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_70_order__eq__refl,axiom,
% 8.57/4.51      ! [X2: rat,Y: rat] :
% 8.57/4.51        ( ( X2 = Y )
% 8.57/4.51       => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_71_order__eq__refl,axiom,
% 8.57/4.51      ! [X2: num,Y: num] :
% 8.57/4.51        ( ( X2 = Y )
% 8.57/4.51       => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_72_order__eq__refl,axiom,
% 8.57/4.51      ! [X2: nat,Y: nat] :
% 8.57/4.51        ( ( X2 = Y )
% 8.57/4.51       => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_73_order__eq__refl,axiom,
% 8.57/4.51      ! [X2: int,Y: int] :
% 8.57/4.51        ( ( X2 = Y )
% 8.57/4.51       => ( ord_less_eq_int @ X2 @ Y ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_74_order__subst2,axiom,
% 8.57/4.51      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_75_order__subst2,axiom,
% 8.57/4.51      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_76_order__subst2,axiom,
% 8.57/4.51      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_77_order__subst2,axiom,
% 8.57/4.51      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_78_order__subst2,axiom,
% 8.57/4.51      ! [A: num,B: num,F: num > rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_79_order__subst2,axiom,
% 8.57/4.51      ! [A: num,B: num,F: num > num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_80_order__subst2,axiom,
% 8.57/4.51      ! [A: num,B: num,F: num > nat,C: nat] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_81_order__subst2,axiom,
% 8.57/4.51      ! [A: num,B: num,F: num > int,C: int] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_82_order__subst2,axiom,
% 8.57/4.51      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.51                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_83_order__subst2,axiom,
% 8.57/4.51      ! [A: nat,B: nat,F: nat > num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 8.57/4.51         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.51                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_84_order__subst1,axiom,
% 8.57/4.51      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_85_order__subst1,axiom,
% 8.57/4.51      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_86_order__subst1,axiom,
% 8.57/4.51      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.51         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.51                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_87_order__subst1,axiom,
% 8.57/4.51      ! [A: rat,F: int > rat,B: int,C: int] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_int @ B @ C )
% 8.57/4.51         => ( ! [X3: int,Y2: int] :
% 8.57/4.51                ( ( ord_less_eq_int @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_88_order__subst1,axiom,
% 8.57/4.51      ! [A: num,F: rat > num,B: rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_89_order__subst1,axiom,
% 8.57/4.51      ! [A: num,F: num > num,B: num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_90_order__subst1,axiom,
% 8.57/4.51      ! [A: num,F: nat > num,B: nat,C: nat] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.51         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.51                ( ( ord_less_eq_nat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_91_order__subst1,axiom,
% 8.57/4.51      ! [A: num,F: int > num,B: int,C: int] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_int @ B @ C )
% 8.57/4.51         => ( ! [X3: int,Y2: int] :
% 8.57/4.51                ( ( ord_less_eq_int @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_92_order__subst1,axiom,
% 8.57/4.51      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.51         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.51                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_93_order__subst1,axiom,
% 8.57/4.51      ! [A: nat,F: num > nat,B: num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 8.57/4.51       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.51         => ( ! [X3: num,Y2: num] :
% 8.57/4.51                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.51               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.51           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_94_Orderings_Oorder__eq__iff,axiom,
% 8.57/4.51      ( ( ^ [Y3: set_nat,Z: set_nat] : ( Y3 = Z ) )
% 8.57/4.51      = ( ^ [A2: set_nat,B2: set_nat] :
% 8.57/4.51            ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 8.57/4.51            & ( ord_less_eq_set_nat @ B2 @ A2 ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_95_Orderings_Oorder__eq__iff,axiom,
% 8.57/4.51      ( ( ^ [Y3: rat,Z: rat] : ( Y3 = Z ) )
% 8.57/4.51      = ( ^ [A2: rat,B2: rat] :
% 8.57/4.51            ( ( ord_less_eq_rat @ A2 @ B2 )
% 8.57/4.51            & ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_96_Orderings_Oorder__eq__iff,axiom,
% 8.57/4.51      ( ( ^ [Y3: num,Z: num] : ( Y3 = Z ) )
% 8.57/4.51      = ( ^ [A2: num,B2: num] :
% 8.57/4.51            ( ( ord_less_eq_num @ A2 @ B2 )
% 8.57/4.51            & ( ord_less_eq_num @ B2 @ A2 ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_97_Orderings_Oorder__eq__iff,axiom,
% 8.57/4.51      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.57/4.51      = ( ^ [A2: nat,B2: nat] :
% 8.57/4.51            ( ( ord_less_eq_nat @ A2 @ B2 )
% 8.57/4.51            & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_98_Orderings_Oorder__eq__iff,axiom,
% 8.57/4.51      ( ( ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.57/4.51      = ( ^ [A2: int,B2: int] :
% 8.57/4.51            ( ( ord_less_eq_int @ A2 @ B2 )
% 8.57/4.51            & ( ord_less_eq_int @ B2 @ A2 ) ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_99_antisym,axiom,
% 8.57/4.51      ! [A: set_nat,B: set_nat] :
% 8.57/4.51        ( ( ord_less_eq_set_nat @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_set_nat @ B @ A )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_100_antisym,axiom,
% 8.57/4.51      ! [A: rat,B: rat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_101_antisym,axiom,
% 8.57/4.51      ! [A: num,B: num] :
% 8.57/4.51        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_num @ B @ A )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_102_antisym,axiom,
% 8.57/4.51      ! [A: nat,B: nat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_nat @ B @ A )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_103_antisym,axiom,
% 8.57/4.51      ! [A: int,B: int] :
% 8.57/4.51        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.51       => ( ( ord_less_eq_int @ B @ A )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_104_dual__order_Otrans,axiom,
% 8.57/4.51      ! [B: set_nat,A: set_nat,C: set_nat] :
% 8.57/4.51        ( ( ord_less_eq_set_nat @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_set_nat @ C @ B )
% 8.57/4.51         => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_105_dual__order_Otrans,axiom,
% 8.57/4.51      ! [B: rat,A: rat,C: rat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_rat @ C @ B )
% 8.57/4.51         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_106_dual__order_Otrans,axiom,
% 8.57/4.51      ! [B: num,A: num,C: num] :
% 8.57/4.51        ( ( ord_less_eq_num @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_num @ C @ B )
% 8.57/4.51         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_107_dual__order_Otrans,axiom,
% 8.57/4.51      ! [B: nat,A: nat,C: nat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_nat @ C @ B )
% 8.57/4.51         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_108_dual__order_Otrans,axiom,
% 8.57/4.51      ! [B: int,A: int,C: int] :
% 8.57/4.51        ( ( ord_less_eq_int @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_int @ C @ B )
% 8.57/4.51         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_109_dual__order_Oantisym,axiom,
% 8.57/4.51      ! [B: set_nat,A: set_nat] :
% 8.57/4.51        ( ( ord_less_eq_set_nat @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_set_nat @ A @ B )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_110_dual__order_Oantisym,axiom,
% 8.57/4.51      ! [B: rat,A: rat] :
% 8.57/4.51        ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_111_dual__order_Oantisym,axiom,
% 8.57/4.51      ! [B: num,A: num] :
% 8.57/4.51        ( ( ord_less_eq_num @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_num @ A @ B )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_112_dual__order_Oantisym,axiom,
% 8.57/4.51      ! [B: nat,A: nat] :
% 8.57/4.51        ( ( ord_less_eq_nat @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_113_dual__order_Oantisym,axiom,
% 8.57/4.51      ! [B: int,A: int] :
% 8.57/4.51        ( ( ord_less_eq_int @ B @ A )
% 8.57/4.51       => ( ( ord_less_eq_int @ A @ B )
% 8.57/4.51         => ( A = B ) ) ) ).
% 8.57/4.51  
% 8.57/4.51  thf(fact_114_dual__order_Oeq__iff,axiom,
% 8.57/4.51      ( ( ^ [Y3: set_nat,Z: set_nat] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [A2: set_nat,B2: set_nat] :
% 8.57/4.52            ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 8.57/4.52            & ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_115_dual__order_Oeq__iff,axiom,
% 8.57/4.52      ( ( ^ [Y3: rat,Z: rat] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [A2: rat,B2: rat] :
% 8.57/4.52            ( ( ord_less_eq_rat @ B2 @ A2 )
% 8.57/4.52            & ( ord_less_eq_rat @ A2 @ B2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_116_dual__order_Oeq__iff,axiom,
% 8.57/4.52      ( ( ^ [Y3: num,Z: num] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [A2: num,B2: num] :
% 8.57/4.52            ( ( ord_less_eq_num @ B2 @ A2 )
% 8.57/4.52            & ( ord_less_eq_num @ A2 @ B2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_117_dual__order_Oeq__iff,axiom,
% 8.57/4.52      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [A2: nat,B2: nat] :
% 8.57/4.52            ( ( ord_less_eq_nat @ B2 @ A2 )
% 8.57/4.52            & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_118_dual__order_Oeq__iff,axiom,
% 8.57/4.52      ( ( ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [A2: int,B2: int] :
% 8.57/4.52            ( ( ord_less_eq_int @ B2 @ A2 )
% 8.57/4.52            & ( ord_less_eq_int @ A2 @ B2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_119_linorder__wlog,axiom,
% 8.57/4.52      ! [P: rat > rat > $o,A: rat,B: rat] :
% 8.57/4.52        ( ! [A3: rat,B3: rat] :
% 8.57/4.52            ( ( ord_less_eq_rat @ A3 @ B3 )
% 8.57/4.52           => ( P @ A3 @ B3 ) )
% 8.57/4.52       => ( ! [A3: rat,B3: rat] :
% 8.57/4.52              ( ( P @ B3 @ A3 )
% 8.57/4.52             => ( P @ A3 @ B3 ) )
% 8.57/4.52         => ( P @ A @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_120_linorder__wlog,axiom,
% 8.57/4.52      ! [P: num > num > $o,A: num,B: num] :
% 8.57/4.52        ( ! [A3: num,B3: num] :
% 8.57/4.52            ( ( ord_less_eq_num @ A3 @ B3 )
% 8.57/4.52           => ( P @ A3 @ B3 ) )
% 8.57/4.52       => ( ! [A3: num,B3: num] :
% 8.57/4.52              ( ( P @ B3 @ A3 )
% 8.57/4.52             => ( P @ A3 @ B3 ) )
% 8.57/4.52         => ( P @ A @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_121_linorder__wlog,axiom,
% 8.57/4.52      ! [P: nat > nat > $o,A: nat,B: nat] :
% 8.57/4.52        ( ! [A3: nat,B3: nat] :
% 8.57/4.52            ( ( ord_less_eq_nat @ A3 @ B3 )
% 8.57/4.52           => ( P @ A3 @ B3 ) )
% 8.57/4.52       => ( ! [A3: nat,B3: nat] :
% 8.57/4.52              ( ( P @ B3 @ A3 )
% 8.57/4.52             => ( P @ A3 @ B3 ) )
% 8.57/4.52         => ( P @ A @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_122_linorder__wlog,axiom,
% 8.57/4.52      ! [P: int > int > $o,A: int,B: int] :
% 8.57/4.52        ( ! [A3: int,B3: int] :
% 8.57/4.52            ( ( ord_less_eq_int @ A3 @ B3 )
% 8.57/4.52           => ( P @ A3 @ B3 ) )
% 8.57/4.52       => ( ! [A3: int,B3: int] :
% 8.57/4.52              ( ( P @ B3 @ A3 )
% 8.57/4.52             => ( P @ A3 @ B3 ) )
% 8.57/4.52         => ( P @ A @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_123_order__trans,axiom,
% 8.57/4.52      ! [X2: set_nat,Y: set_nat,Z2: set_nat] :
% 8.57/4.52        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_set_nat @ Y @ Z2 )
% 8.57/4.52         => ( ord_less_eq_set_nat @ X2 @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_124_order__trans,axiom,
% 8.57/4.52      ! [X2: rat,Y: rat,Z2: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_rat @ Y @ Z2 )
% 8.57/4.52         => ( ord_less_eq_rat @ X2 @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_125_order__trans,axiom,
% 8.57/4.52      ! [X2: num,Y: num,Z2: num] :
% 8.57/4.52        ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_num @ Y @ Z2 )
% 8.57/4.52         => ( ord_less_eq_num @ X2 @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_126_order__trans,axiom,
% 8.57/4.52      ! [X2: nat,Y: nat,Z2: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_nat @ Y @ Z2 )
% 8.57/4.52         => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_127_order__trans,axiom,
% 8.57/4.52      ! [X2: int,Y: int,Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_int @ Y @ Z2 )
% 8.57/4.52         => ( ord_less_eq_int @ X2 @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_128_order_Otrans,axiom,
% 8.57/4.52      ! [A: set_nat,B: set_nat,C: set_nat] :
% 8.57/4.52        ( ( ord_less_eq_set_nat @ A @ B )
% 8.57/4.52       => ( ( ord_less_eq_set_nat @ B @ C )
% 8.57/4.52         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_129_order_Otrans,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.52       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.52         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_130_order_Otrans,axiom,
% 8.57/4.52      ! [A: num,B: num,C: num] :
% 8.57/4.52        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.52       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.52         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_131_order_Otrans,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.52       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.52         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_132_order_Otrans,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.52       => ( ( ord_less_eq_int @ B @ C )
% 8.57/4.52         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_133_order__antisym,axiom,
% 8.57/4.52      ! [X2: set_nat,Y: set_nat] :
% 8.57/4.52        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_set_nat @ Y @ X2 )
% 8.57/4.52         => ( X2 = Y ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_134_order__antisym,axiom,
% 8.57/4.52      ! [X2: rat,Y: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_rat @ Y @ X2 )
% 8.57/4.52         => ( X2 = Y ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_135_order__antisym,axiom,
% 8.57/4.52      ! [X2: num,Y: num] :
% 8.57/4.52        ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_num @ Y @ X2 )
% 8.57/4.52         => ( X2 = Y ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_136_order__antisym,axiom,
% 8.57/4.52      ! [X2: nat,Y: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_nat @ Y @ X2 )
% 8.57/4.52         => ( X2 = Y ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_137_order__antisym,axiom,
% 8.57/4.52      ! [X2: int,Y: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.52       => ( ( ord_less_eq_int @ Y @ X2 )
% 8.57/4.52         => ( X2 = Y ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_138_ord__le__eq__trans,axiom,
% 8.57/4.52      ! [A: set_nat,B: set_nat,C: set_nat] :
% 8.57/4.52        ( ( ord_less_eq_set_nat @ A @ B )
% 8.57/4.52       => ( ( B = C )
% 8.57/4.52         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_139_ord__le__eq__trans,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.52       => ( ( B = C )
% 8.57/4.52         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_140_ord__le__eq__trans,axiom,
% 8.57/4.52      ! [A: num,B: num,C: num] :
% 8.57/4.52        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.52       => ( ( B = C )
% 8.57/4.52         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_141_ord__le__eq__trans,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.52       => ( ( B = C )
% 8.57/4.52         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_142_ord__le__eq__trans,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.52       => ( ( B = C )
% 8.57/4.52         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_143_ord__eq__le__trans,axiom,
% 8.57/4.52      ! [A: set_nat,B: set_nat,C: set_nat] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_set_nat @ B @ C )
% 8.57/4.52         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_144_ord__eq__le__trans,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.52         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_145_ord__eq__le__trans,axiom,
% 8.57/4.52      ! [A: num,B: num,C: num] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.52         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_146_ord__eq__le__trans,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.52         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_147_ord__eq__le__trans,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_int @ B @ C )
% 8.57/4.52         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_148_order__class_Oorder__eq__iff,axiom,
% 8.57/4.52      ( ( ^ [Y3: set_nat,Z: set_nat] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [X: set_nat,Y4: set_nat] :
% 8.57/4.52            ( ( ord_less_eq_set_nat @ X @ Y4 )
% 8.57/4.52            & ( ord_less_eq_set_nat @ Y4 @ X ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_149_order__class_Oorder__eq__iff,axiom,
% 8.57/4.52      ( ( ^ [Y3: rat,Z: rat] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [X: rat,Y4: rat] :
% 8.57/4.52            ( ( ord_less_eq_rat @ X @ Y4 )
% 8.57/4.52            & ( ord_less_eq_rat @ Y4 @ X ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_150_order__class_Oorder__eq__iff,axiom,
% 8.57/4.52      ( ( ^ [Y3: num,Z: num] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [X: num,Y4: num] :
% 8.57/4.52            ( ( ord_less_eq_num @ X @ Y4 )
% 8.57/4.52            & ( ord_less_eq_num @ Y4 @ X ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_151_order__class_Oorder__eq__iff,axiom,
% 8.57/4.52      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [X: nat,Y4: nat] :
% 8.57/4.52            ( ( ord_less_eq_nat @ X @ Y4 )
% 8.57/4.52            & ( ord_less_eq_nat @ Y4 @ X ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_152_order__class_Oorder__eq__iff,axiom,
% 8.57/4.52      ( ( ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [X: int,Y4: int] :
% 8.57/4.52            ( ( ord_less_eq_int @ X @ Y4 )
% 8.57/4.52            & ( ord_less_eq_int @ Y4 @ X ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_153_le__cases3,axiom,
% 8.57/4.52      ! [X2: rat,Y: rat,Z2: rat] :
% 8.57/4.52        ( ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.52         => ~ ( ord_less_eq_rat @ Y @ Z2 ) )
% 8.57/4.52       => ( ( ( ord_less_eq_rat @ Y @ X2 )
% 8.57/4.52           => ~ ( ord_less_eq_rat @ X2 @ Z2 ) )
% 8.57/4.52         => ( ( ( ord_less_eq_rat @ X2 @ Z2 )
% 8.57/4.52             => ~ ( ord_less_eq_rat @ Z2 @ Y ) )
% 8.57/4.52           => ( ( ( ord_less_eq_rat @ Z2 @ Y )
% 8.57/4.52               => ~ ( ord_less_eq_rat @ Y @ X2 ) )
% 8.57/4.52             => ( ( ( ord_less_eq_rat @ Y @ Z2 )
% 8.57/4.52                 => ~ ( ord_less_eq_rat @ Z2 @ X2 ) )
% 8.57/4.52               => ~ ( ( ord_less_eq_rat @ Z2 @ X2 )
% 8.57/4.52                   => ~ ( ord_less_eq_rat @ X2 @ Y ) ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_154_le__cases3,axiom,
% 8.57/4.52      ! [X2: num,Y: num,Z2: num] :
% 8.57/4.52        ( ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.52         => ~ ( ord_less_eq_num @ Y @ Z2 ) )
% 8.57/4.52       => ( ( ( ord_less_eq_num @ Y @ X2 )
% 8.57/4.52           => ~ ( ord_less_eq_num @ X2 @ Z2 ) )
% 8.57/4.52         => ( ( ( ord_less_eq_num @ X2 @ Z2 )
% 8.57/4.52             => ~ ( ord_less_eq_num @ Z2 @ Y ) )
% 8.57/4.52           => ( ( ( ord_less_eq_num @ Z2 @ Y )
% 8.57/4.52               => ~ ( ord_less_eq_num @ Y @ X2 ) )
% 8.57/4.52             => ( ( ( ord_less_eq_num @ Y @ Z2 )
% 8.57/4.52                 => ~ ( ord_less_eq_num @ Z2 @ X2 ) )
% 8.57/4.52               => ~ ( ( ord_less_eq_num @ Z2 @ X2 )
% 8.57/4.52                   => ~ ( ord_less_eq_num @ X2 @ Y ) ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_155_le__cases3,axiom,
% 8.57/4.52      ! [X2: nat,Y: nat,Z2: nat] :
% 8.57/4.52        ( ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.52         => ~ ( ord_less_eq_nat @ Y @ Z2 ) )
% 8.57/4.52       => ( ( ( ord_less_eq_nat @ Y @ X2 )
% 8.57/4.52           => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 8.57/4.52         => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 8.57/4.52             => ~ ( ord_less_eq_nat @ Z2 @ Y ) )
% 8.57/4.52           => ( ( ( ord_less_eq_nat @ Z2 @ Y )
% 8.57/4.52               => ~ ( ord_less_eq_nat @ Y @ X2 ) )
% 8.57/4.52             => ( ( ( ord_less_eq_nat @ Y @ Z2 )
% 8.57/4.52                 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 8.57/4.52               => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 8.57/4.52                   => ~ ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_156_le__cases3,axiom,
% 8.57/4.52      ! [X2: int,Y: int,Z2: int] :
% 8.57/4.52        ( ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.52         => ~ ( ord_less_eq_int @ Y @ Z2 ) )
% 8.57/4.52       => ( ( ( ord_less_eq_int @ Y @ X2 )
% 8.57/4.52           => ~ ( ord_less_eq_int @ X2 @ Z2 ) )
% 8.57/4.52         => ( ( ( ord_less_eq_int @ X2 @ Z2 )
% 8.57/4.52             => ~ ( ord_less_eq_int @ Z2 @ Y ) )
% 8.57/4.52           => ( ( ( ord_less_eq_int @ Z2 @ Y )
% 8.57/4.52               => ~ ( ord_less_eq_int @ Y @ X2 ) )
% 8.57/4.52             => ( ( ( ord_less_eq_int @ Y @ Z2 )
% 8.57/4.52                 => ~ ( ord_less_eq_int @ Z2 @ X2 ) )
% 8.57/4.52               => ~ ( ( ord_less_eq_int @ Z2 @ X2 )
% 8.57/4.52                   => ~ ( ord_less_eq_int @ X2 @ Y ) ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_157_nle__le,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 8.57/4.52        = ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.52          & ( B != A ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_158_nle__le,axiom,
% 8.57/4.52      ! [A: num,B: num] :
% 8.57/4.52        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 8.57/4.52        = ( ( ord_less_eq_num @ B @ A )
% 8.57/4.52          & ( B != A ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_159_nle__le,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 8.57/4.52        = ( ( ord_less_eq_nat @ B @ A )
% 8.57/4.52          & ( B != A ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_160_nle__le,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 8.57/4.52        = ( ( ord_less_eq_int @ B @ A )
% 8.57/4.52          & ( B != A ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_161_Nat_Oex__has__greatest__nat,axiom,
% 8.57/4.52      ! [P: nat > $o,K: nat,B: nat] :
% 8.57/4.52        ( ( P @ K )
% 8.57/4.52       => ( ! [Y2: nat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_nat @ Y2 @ B ) )
% 8.57/4.52         => ? [X3: nat] :
% 8.57/4.52              ( ( P @ X3 )
% 8.57/4.52              & ! [Y5: nat] :
% 8.57/4.52                  ( ( P @ Y5 )
% 8.57/4.52                 => ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_162_raise__bind,axiom,
% 8.57/4.52      ! [E: list_char,F: a > heap_Time_Heap_a] :
% 8.57/4.52        ( ( heap_Time_bind_a_a @ ( heap_Time_raise_a @ E ) @ F )
% 8.57/4.52        = ( heap_Time_raise_a @ E ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_163_raise__bind,axiom,
% 8.57/4.52      ! [E: list_char,F: product_unit > heap_Time_Heap_a] :
% 8.57/4.52        ( ( heap_T757603679106148408unit_a @ ( heap_T2927564422264180874t_unit @ E ) @ F )
% 8.57/4.52        = ( heap_Time_raise_a @ E ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_164_raise__bind,axiom,
% 8.57/4.52      ! [E: list_char,F: product_unit > heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( heap_T2633723481742716231t_unit @ ( heap_T2927564422264180874t_unit @ E ) @ F )
% 8.57/4.52        = ( heap_T2927564422264180874t_unit @ E ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_165_Greatest__equality,axiom,
% 8.57/4.52      ! [P: set_nat > $o,X2: set_nat] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: set_nat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_set_nat @ Y2 @ X2 ) )
% 8.57/4.52         => ( ( order_5724808138429204845et_nat @ P )
% 8.57/4.52            = X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_166_Greatest__equality,axiom,
% 8.57/4.52      ! [P: rat > $o,X2: rat] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: rat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_rat @ Y2 @ X2 ) )
% 8.57/4.52         => ( ( order_Greatest_rat @ P )
% 8.57/4.52            = X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_167_Greatest__equality,axiom,
% 8.57/4.52      ! [P: num > $o,X2: num] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: num] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_num @ Y2 @ X2 ) )
% 8.57/4.52         => ( ( order_Greatest_num @ P )
% 8.57/4.52            = X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_168_Greatest__equality,axiom,
% 8.57/4.52      ! [P: int > $o,X2: int] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: int] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_int @ Y2 @ X2 ) )
% 8.57/4.52         => ( ( order_Greatest_int @ P )
% 8.57/4.52            = X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_169_Greatest__equality,axiom,
% 8.57/4.52      ! [P: nat > $o,X2: nat] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: nat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_nat @ Y2 @ X2 ) )
% 8.57/4.52         => ( ( order_Greatest_nat @ P )
% 8.57/4.52            = X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_170_mem__Collect__eq,axiom,
% 8.57/4.52      ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 8.57/4.52        ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 8.57/4.52        = ( P @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_171_mem__Collect__eq,axiom,
% 8.57/4.52      ! [A: list_nat,P: list_nat > $o] :
% 8.57/4.52        ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 8.57/4.52        = ( P @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_172_mem__Collect__eq,axiom,
% 8.57/4.52      ! [A: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 8.57/4.52        ( ( member2340774599025711042nt_int @ A @ ( collec5210948495886036740nt_int @ P ) )
% 8.57/4.52        = ( P @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_173_mem__Collect__eq,axiom,
% 8.57/4.52      ! [A: set_nat,P: set_nat > $o] :
% 8.57/4.52        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 8.57/4.52        = ( P @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_174_mem__Collect__eq,axiom,
% 8.57/4.52      ! [A: nat,P: nat > $o] :
% 8.57/4.52        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 8.57/4.52        = ( P @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_175_mem__Collect__eq,axiom,
% 8.57/4.52      ! [A: int,P: int > $o] :
% 8.57/4.52        ( ( member_int @ A @ ( collect_int @ P ) )
% 8.57/4.52        = ( P @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_176_Collect__mem__eq,axiom,
% 8.57/4.52      ! [A4: set_Pr1261947904930325089at_nat] :
% 8.57/4.52        ( ( collec3392354462482085612at_nat
% 8.57/4.52          @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A4 ) )
% 8.57/4.52        = A4 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_177_Collect__mem__eq,axiom,
% 8.57/4.52      ! [A4: set_list_nat] :
% 8.57/4.52        ( ( collect_list_nat
% 8.57/4.52          @ ^ [X: list_nat] : ( member_list_nat @ X @ A4 ) )
% 8.57/4.52        = A4 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_178_Collect__mem__eq,axiom,
% 8.57/4.52      ! [A4: set_se6260736226359567993nt_int] :
% 8.57/4.52        ( ( collec5210948495886036740nt_int
% 8.57/4.52          @ ^ [X: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X @ A4 ) )
% 8.57/4.52        = A4 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_179_Collect__mem__eq,axiom,
% 8.57/4.52      ! [A4: set_set_nat] :
% 8.57/4.52        ( ( collect_set_nat
% 8.57/4.52          @ ^ [X: set_nat] : ( member_set_nat @ X @ A4 ) )
% 8.57/4.52        = A4 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_180_Collect__mem__eq,axiom,
% 8.57/4.52      ! [A4: set_nat] :
% 8.57/4.52        ( ( collect_nat
% 8.57/4.52          @ ^ [X: nat] : ( member_nat @ X @ A4 ) )
% 8.57/4.52        = A4 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_181_Collect__mem__eq,axiom,
% 8.57/4.52      ! [A4: set_int] :
% 8.57/4.52        ( ( collect_int
% 8.57/4.52          @ ^ [X: int] : ( member_int @ X @ A4 ) )
% 8.57/4.52        = A4 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_182_Collect__cong,axiom,
% 8.57/4.52      ! [P: list_nat > $o,Q: list_nat > $o] :
% 8.57/4.52        ( ! [X3: list_nat] :
% 8.57/4.52            ( ( P @ X3 )
% 8.57/4.52            = ( Q @ X3 ) )
% 8.57/4.52       => ( ( collect_list_nat @ P )
% 8.57/4.52          = ( collect_list_nat @ Q ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_183_Collect__cong,axiom,
% 8.57/4.52      ! [P: set_Pr958786334691620121nt_int > $o,Q: set_Pr958786334691620121nt_int > $o] :
% 8.57/4.52        ( ! [X3: set_Pr958786334691620121nt_int] :
% 8.57/4.52            ( ( P @ X3 )
% 8.57/4.52            = ( Q @ X3 ) )
% 8.57/4.52       => ( ( collec5210948495886036740nt_int @ P )
% 8.57/4.52          = ( collec5210948495886036740nt_int @ Q ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_184_Collect__cong,axiom,
% 8.57/4.52      ! [P: set_nat > $o,Q: set_nat > $o] :
% 8.57/4.52        ( ! [X3: set_nat] :
% 8.57/4.52            ( ( P @ X3 )
% 8.57/4.52            = ( Q @ X3 ) )
% 8.57/4.52       => ( ( collect_set_nat @ P )
% 8.57/4.52          = ( collect_set_nat @ Q ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_185_Collect__cong,axiom,
% 8.57/4.52      ! [P: nat > $o,Q: nat > $o] :
% 8.57/4.52        ( ! [X3: nat] :
% 8.57/4.52            ( ( P @ X3 )
% 8.57/4.52            = ( Q @ X3 ) )
% 8.57/4.52       => ( ( collect_nat @ P )
% 8.57/4.52          = ( collect_nat @ Q ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_186_Collect__cong,axiom,
% 8.57/4.52      ! [P: int > $o,Q: int > $o] :
% 8.57/4.52        ( ! [X3: int] :
% 8.57/4.52            ( ( P @ X3 )
% 8.57/4.52            = ( Q @ X3 ) )
% 8.57/4.52       => ( ( collect_int @ P )
% 8.57/4.52          = ( collect_int @ Q ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_187_GreatestI2__order,axiom,
% 8.57/4.52      ! [P: set_nat > $o,X2: set_nat,Q: set_nat > $o] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: set_nat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_set_nat @ Y2 @ X2 ) )
% 8.57/4.52         => ( ! [X3: set_nat] :
% 8.57/4.52                ( ( P @ X3 )
% 8.57/4.52               => ( ! [Y5: set_nat] :
% 8.57/4.52                      ( ( P @ Y5 )
% 8.57/4.52                     => ( ord_less_eq_set_nat @ Y5 @ X3 ) )
% 8.57/4.52                 => ( Q @ X3 ) ) )
% 8.57/4.52           => ( Q @ ( order_5724808138429204845et_nat @ P ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_188_GreatestI2__order,axiom,
% 8.57/4.52      ! [P: rat > $o,X2: rat,Q: rat > $o] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: rat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_rat @ Y2 @ X2 ) )
% 8.57/4.52         => ( ! [X3: rat] :
% 8.57/4.52                ( ( P @ X3 )
% 8.57/4.52               => ( ! [Y5: rat] :
% 8.57/4.52                      ( ( P @ Y5 )
% 8.57/4.52                     => ( ord_less_eq_rat @ Y5 @ X3 ) )
% 8.57/4.52                 => ( Q @ X3 ) ) )
% 8.57/4.52           => ( Q @ ( order_Greatest_rat @ P ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_189_GreatestI2__order,axiom,
% 8.57/4.52      ! [P: num > $o,X2: num,Q: num > $o] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: num] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_num @ Y2 @ X2 ) )
% 8.57/4.52         => ( ! [X3: num] :
% 8.57/4.52                ( ( P @ X3 )
% 8.57/4.52               => ( ! [Y5: num] :
% 8.57/4.52                      ( ( P @ Y5 )
% 8.57/4.52                     => ( ord_less_eq_num @ Y5 @ X3 ) )
% 8.57/4.52                 => ( Q @ X3 ) ) )
% 8.57/4.52           => ( Q @ ( order_Greatest_num @ P ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_190_GreatestI2__order,axiom,
% 8.57/4.52      ! [P: int > $o,X2: int,Q: int > $o] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: int] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_int @ Y2 @ X2 ) )
% 8.57/4.52         => ( ! [X3: int] :
% 8.57/4.52                ( ( P @ X3 )
% 8.57/4.52               => ( ! [Y5: int] :
% 8.57/4.52                      ( ( P @ Y5 )
% 8.57/4.52                     => ( ord_less_eq_int @ Y5 @ X3 ) )
% 8.57/4.52                 => ( Q @ X3 ) ) )
% 8.57/4.52           => ( Q @ ( order_Greatest_int @ P ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_191_GreatestI2__order,axiom,
% 8.57/4.52      ! [P: nat > $o,X2: nat,Q: nat > $o] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [Y2: nat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_nat @ Y2 @ X2 ) )
% 8.57/4.52         => ( ! [X3: nat] :
% 8.57/4.52                ( ( P @ X3 )
% 8.57/4.52               => ( ! [Y5: nat] :
% 8.57/4.52                      ( ( P @ Y5 )
% 8.57/4.52                     => ( ord_less_eq_nat @ Y5 @ X3 ) )
% 8.57/4.52                 => ( Q @ X3 ) ) )
% 8.57/4.52           => ( Q @ ( order_Greatest_nat @ P ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_192_TBOUND__assert_H__bind,axiom,
% 8.57/4.52      ! [P: $o,P2: $o,M: heap_Time_Heap_a,T: nat] :
% 8.57/4.52        ( ( time_EQ_o @ P @ P2 )
% 8.57/4.52       => ( ( P
% 8.57/4.52           => ( time_TBOUND_a @ M @ T ) )
% 8.57/4.52         => ( time_TBOUND_a
% 8.57/4.52            @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ P )
% 8.57/4.52              @ ^ [Uu: product_unit] : M )
% 8.57/4.52            @ ( if_nat @ P2 @ T @ zero_zero_nat ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_193_TBOUND__assert_H__bind,axiom,
% 8.57/4.52      ! [P: $o,P2: $o,M: heap_T5738788834812785303t_unit,T: nat] :
% 8.57/4.52        ( ( time_EQ_o @ P @ P2 )
% 8.57/4.52       => ( ( P
% 8.57/4.52           => ( time_T7469515765551943773t_unit @ M @ T ) )
% 8.57/4.52         => ( time_T7469515765551943773t_unit
% 8.57/4.52            @ ( heap_T2633723481742716231t_unit @ ( refine_Imp_assert @ P )
% 8.57/4.52              @ ^ [Uu: product_unit] : M )
% 8.57/4.52            @ ( if_nat @ P2 @ T @ zero_zero_nat ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_194_bounded__Max__nat,axiom,
% 8.57/4.52      ! [P: nat > $o,X2: nat,M3: nat] :
% 8.57/4.52        ( ( P @ X2 )
% 8.57/4.52       => ( ! [X3: nat] :
% 8.57/4.52              ( ( P @ X3 )
% 8.57/4.52             => ( ord_less_eq_nat @ X3 @ M3 ) )
% 8.57/4.52         => ~ ! [M4: nat] :
% 8.57/4.52                ( ( P @ M4 )
% 8.57/4.52               => ~ ! [X4: nat] :
% 8.57/4.52                      ( ( P @ X4 )
% 8.57/4.52                     => ( ord_less_eq_nat @ X4 @ M4 ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_195_le__rel__bool__arg__iff,axiom,
% 8.57/4.52      ( ord_le7022414076629706543et_nat
% 8.57/4.52      = ( ^ [X5: $o > set_nat,Y6: $o > set_nat] :
% 8.57/4.52            ( ( ord_less_eq_set_nat @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 8.57/4.52            & ( ord_less_eq_set_nat @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_196_le__rel__bool__arg__iff,axiom,
% 8.57/4.52      ( ord_less_eq_o_rat
% 8.57/4.52      = ( ^ [X5: $o > rat,Y6: $o > rat] :
% 8.57/4.52            ( ( ord_less_eq_rat @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 8.57/4.52            & ( ord_less_eq_rat @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_197_le__rel__bool__arg__iff,axiom,
% 8.57/4.52      ( ord_less_eq_o_num
% 8.57/4.52      = ( ^ [X5: $o > num,Y6: $o > num] :
% 8.57/4.52            ( ( ord_less_eq_num @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 8.57/4.52            & ( ord_less_eq_num @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_198_le__rel__bool__arg__iff,axiom,
% 8.57/4.52      ( ord_less_eq_o_nat
% 8.57/4.52      = ( ^ [X5: $o > nat,Y6: $o > nat] :
% 8.57/4.52            ( ( ord_less_eq_nat @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 8.57/4.52            & ( ord_less_eq_nat @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_199_le__rel__bool__arg__iff,axiom,
% 8.57/4.52      ( ord_less_eq_o_int
% 8.57/4.52      = ( ^ [X5: $o > int,Y6: $o > int] :
% 8.57/4.52            ( ( ord_less_eq_int @ ( X5 @ $false ) @ ( Y6 @ $false ) )
% 8.57/4.52            & ( ord_less_eq_int @ ( X5 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_200_verit__la__disequality,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52        | ~ ( ord_less_eq_rat @ A @ B )
% 8.57/4.52        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_201_verit__la__disequality,axiom,
% 8.57/4.52      ! [A: num,B: num] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52        | ~ ( ord_less_eq_num @ A @ B )
% 8.57/4.52        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_202_verit__la__disequality,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52        | ~ ( ord_less_eq_nat @ A @ B )
% 8.57/4.52        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_203_verit__la__disequality,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52        | ~ ( ord_less_eq_int @ A @ B )
% 8.57/4.52        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_204_ord__eq__le__eq__trans,axiom,
% 8.57/4.52      ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_set_nat @ B @ C )
% 8.57/4.52         => ( ( C = D )
% 8.57/4.52           => ( ord_less_eq_set_nat @ A @ D ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_205_ord__eq__le__eq__trans,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.52         => ( ( C = D )
% 8.57/4.52           => ( ord_less_eq_rat @ A @ D ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_206_ord__eq__le__eq__trans,axiom,
% 8.57/4.52      ! [A: num,B: num,C: num,D: num] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.52         => ( ( C = D )
% 8.57/4.52           => ( ord_less_eq_num @ A @ D ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_207_ord__eq__le__eq__trans,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.52         => ( ( C = D )
% 8.57/4.52           => ( ord_less_eq_nat @ A @ D ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_208_ord__eq__le__eq__trans,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.52        ( ( A = B )
% 8.57/4.52       => ( ( ord_less_eq_int @ B @ C )
% 8.57/4.52         => ( ( C = D )
% 8.57/4.52           => ( ord_less_eq_int @ A @ D ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_209_verit__comp__simplify1_I2_J,axiom,
% 8.57/4.52      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_210_verit__comp__simplify1_I2_J,axiom,
% 8.57/4.52      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_211_verit__comp__simplify1_I2_J,axiom,
% 8.57/4.52      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_212_verit__comp__simplify1_I2_J,axiom,
% 8.57/4.52      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_213_verit__comp__simplify1_I2_J,axiom,
% 8.57/4.52      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_214_refines__assert_H__bind,axiom,
% 8.57/4.52      ! [P3: heap_Time_Heap_a,Q2: heap_Time_Heap_a,Phi: $o] :
% 8.57/4.52        ( ( refine_Imp_refines_a @ P3 @ Q2 )
% 8.57/4.52       => ( refine_Imp_refines_a @ P3
% 8.57/4.52          @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ Phi )
% 8.57/4.52            @ ^ [Uu: product_unit] : Q2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_215_refines__assert_H__bind,axiom,
% 8.57/4.52      ! [P3: heap_T5738788834812785303t_unit,Q2: heap_T5738788834812785303t_unit,Phi: $o] :
% 8.57/4.52        ( ( refine451278484176762712t_unit @ P3 @ Q2 )
% 8.57/4.52       => ( refine451278484176762712t_unit @ P3
% 8.57/4.52          @ ( heap_T2633723481742716231t_unit @ ( refine_Imp_assert @ Phi )
% 8.57/4.52            @ ^ [Uu: product_unit] : Q2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_216_ureturn__bind,axiom,
% 8.57/4.52      ! [X2: a,F: a > heap_Time_Heap_a] :
% 8.57/4.52        ( ( heap_Time_bind_a_a @ ( heap_Time_ureturn_a @ X2 ) @ F )
% 8.57/4.52        = ( F @ X2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_217_ureturn__bind,axiom,
% 8.57/4.52      ! [X2: product_unit,F: product_unit > heap_Time_Heap_a] :
% 8.57/4.52        ( ( heap_T757603679106148408unit_a @ ( heap_T4284346855313245393t_unit @ X2 ) @ F )
% 8.57/4.52        = ( F @ X2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_218_ureturn__bind,axiom,
% 8.57/4.52      ! [X2: product_unit,F: product_unit > heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( heap_T2633723481742716231t_unit @ ( heap_T4284346855313245393t_unit @ X2 ) @ F )
% 8.57/4.52        = ( F @ X2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_219_bot__nat__0_Oextremum,axiom,
% 8.57/4.52      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_220_le0,axiom,
% 8.57/4.52      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_221_refines__refl,axiom,
% 8.57/4.52      ! [P3: heap_T5738788834812785303t_unit] : ( refine451278484176762712t_unit @ P3 @ P3 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_222_refines__If,axiom,
% 8.57/4.52      ! [B: $o,T: heap_T5738788834812785303t_unit,T3: heap_T5738788834812785303t_unit,E: heap_T5738788834812785303t_unit,E2: heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( B
% 8.57/4.52         => ( refine451278484176762712t_unit @ T @ T3 ) )
% 8.57/4.52       => ( ( ~ B
% 8.57/4.52           => ( refine451278484176762712t_unit @ E @ E2 ) )
% 8.57/4.52         => ( refine451278484176762712t_unit @ ( if_Hea8138950348631371857t_unit @ B @ T @ E ) @ ( if_Hea8138950348631371857t_unit @ B @ T3 @ E2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_223_time__raise,axiom,
% 8.57/4.52      ! [Msg: list_char,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_time_a @ ( heap_Time_raise_a @ Msg ) @ H )
% 8.57/4.52        = zero_zero_nat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_224_time__raise,axiom,
% 8.57/4.52      ! [Msg: list_char,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_t4224138285095624986t_unit @ ( heap_T2927564422264180874t_unit @ Msg ) @ H )
% 8.57/4.52        = zero_zero_nat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_225_refines__bind,axiom,
% 8.57/4.52      ! [M: heap_Time_Heap_a,M5: heap_Time_Heap_a,F: a > heap_Time_Heap_a,F2: a > heap_Time_Heap_a] :
% 8.57/4.52        ( ( refine_Imp_refines_a @ M @ M5 )
% 8.57/4.52       => ( ! [X3: a] : ( refine_Imp_refines_a @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 8.57/4.52         => ( refine_Imp_refines_a @ ( heap_Time_bind_a_a @ M @ F ) @ ( heap_Time_bind_a_a @ M5 @ F2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_226_refines__bind,axiom,
% 8.57/4.52      ! [M: heap_T5738788834812785303t_unit,M5: heap_T5738788834812785303t_unit,F: product_unit > heap_Time_Heap_a,F2: product_unit > heap_Time_Heap_a] :
% 8.57/4.52        ( ( refine451278484176762712t_unit @ M @ M5 )
% 8.57/4.52       => ( ! [X3: product_unit] : ( refine_Imp_refines_a @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 8.57/4.52         => ( refine_Imp_refines_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ ( heap_T757603679106148408unit_a @ M5 @ F2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_227_refines__bind,axiom,
% 8.57/4.52      ! [M: heap_T5738788834812785303t_unit,M5: heap_T5738788834812785303t_unit,F: product_unit > heap_T5738788834812785303t_unit,F2: product_unit > heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( refine451278484176762712t_unit @ M @ M5 )
% 8.57/4.52       => ( ! [X3: product_unit] : ( refine451278484176762712t_unit @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 8.57/4.52         => ( refine451278484176762712t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ ( heap_T2633723481742716231t_unit @ M5 @ F2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_228_less__eq__nat_Osimps_I1_J,axiom,
% 8.57/4.52      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_229_bot__nat__0_Oextremum__unique,axiom,
% 8.57/4.52      ! [A: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.57/4.52        = ( A = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_230_bot__nat__0_Oextremum__uniqueI,axiom,
% 8.57/4.52      ! [A: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.57/4.52       => ( A = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_231_le__0__eq,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 8.57/4.52        = ( N = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_232_time__assert_H,axiom,
% 8.57/4.52      ! [P: $o,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_t4224138285095624986t_unit @ ( refine_Imp_assert @ P ) @ H )
% 8.57/4.52        = zero_zero_nat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_233_TBOUND__refines,axiom,
% 8.57/4.52      ! [C: heap_Time_Heap_a,T: nat,D: heap_Time_Heap_a] :
% 8.57/4.52        ( ( time_TBOUND_a @ C @ T )
% 8.57/4.52       => ( ( refine_Imp_refines_a @ C @ D )
% 8.57/4.52         => ( time_TBOUND_a @ D @ T ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_234_TBOUND__refines,axiom,
% 8.57/4.52      ! [C: heap_T5738788834812785303t_unit,T: nat,D: heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( time_T7469515765551943773t_unit @ C @ T )
% 8.57/4.52       => ( ( refine451278484176762712t_unit @ C @ D )
% 8.57/4.52         => ( time_T7469515765551943773t_unit @ D @ T ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_235_GreatestI__nat,axiom,
% 8.57/4.52      ! [P: nat > $o,K: nat,B: nat] :
% 8.57/4.52        ( ( P @ K )
% 8.57/4.52       => ( ! [Y2: nat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_nat @ Y2 @ B ) )
% 8.57/4.52         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_236_Greatest__le__nat,axiom,
% 8.57/4.52      ! [P: nat > $o,K: nat,B: nat] :
% 8.57/4.52        ( ( P @ K )
% 8.57/4.52       => ( ! [Y2: nat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_nat @ Y2 @ B ) )
% 8.57/4.52         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_237_GreatestI__ex__nat,axiom,
% 8.57/4.52      ! [P: nat > $o,B: nat] :
% 8.57/4.52        ( ? [X_1: nat] : ( P @ X_1 )
% 8.57/4.52       => ( ! [Y2: nat] :
% 8.57/4.52              ( ( P @ Y2 )
% 8.57/4.52             => ( ord_less_eq_nat @ Y2 @ B ) )
% 8.57/4.52         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_238_bind__ureturn,axiom,
% 8.57/4.52      ! [F: heap_Time_Heap_a] :
% 8.57/4.52        ( ( heap_Time_bind_a_a @ F @ heap_Time_ureturn_a )
% 8.57/4.52        = F ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_239_bind__ureturn,axiom,
% 8.57/4.52      ! [F: heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( heap_T2633723481742716231t_unit @ F @ heap_T4284346855313245393t_unit )
% 8.57/4.52        = F ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_240_le__zero__eq,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 8.57/4.52        = ( N = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_241_le__numeral__extra_I3_J,axiom,
% 8.57/4.52      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_242_le__numeral__extra_I3_J,axiom,
% 8.57/4.52      ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ zero_z2226904508553997617atural ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_243_le__numeral__extra_I3_J,axiom,
% 8.57/4.52      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_244_le__numeral__extra_I3_J,axiom,
% 8.57/4.52      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_245_le__numeral__extra_I3_J,axiom,
% 8.57/4.52      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_246_zero__le,axiom,
% 8.57/4.52      ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_247_time__refines,axiom,
% 8.57/4.52      ! [C: heap_Time_Heap_a,C2: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( refine_Imp_refines_a @ C @ C2 )
% 8.57/4.52       => ( ~ ( time_fails_a @ C2 @ H )
% 8.57/4.52         => ( ord_less_eq_nat @ ( time_time_a @ C @ H ) @ ( time_time_a @ C2 @ H ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_248_time__refines,axiom,
% 8.57/4.52      ! [C: heap_T5738788834812785303t_unit,C2: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( refine451278484176762712t_unit @ C @ C2 )
% 8.57/4.52       => ( ~ ( time_f8834461667527620124t_unit @ C2 @ H )
% 8.57/4.52         => ( ord_less_eq_nat @ ( time_t4224138285095624986t_unit @ C @ H ) @ ( time_t4224138285095624986t_unit @ C2 @ H ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_249_of__nat__le__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_250_of__nat__le__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ M ) @ zero_z2226904508553997617atural )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_251_of__nat__le__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_252_of__nat__le__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_253_of__nat__le__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_254_zero__natural_Orsp,axiom,
% 8.57/4.52      zero_zero_nat = zero_zero_nat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_255_zero__reorient,axiom,
% 8.57/4.52      ! [X2: nat] :
% 8.57/4.52        ( ( zero_zero_nat = X2 )
% 8.57/4.52        = ( X2 = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_256_zero__reorient,axiom,
% 8.57/4.52      ! [X2: int] :
% 8.57/4.52        ( ( zero_zero_int = X2 )
% 8.57/4.52        = ( X2 = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_257_zero__reorient,axiom,
% 8.57/4.52      ! [X2: code_integer] :
% 8.57/4.52        ( ( zero_z3403309356797280102nteger = X2 )
% 8.57/4.52        = ( X2 = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_258_zero__reorient,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52        ( ( zero_zero_rat = X2 )
% 8.57/4.52        = ( X2 = zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_259_zero__reorient,axiom,
% 8.57/4.52      ! [X2: code_natural] :
% 8.57/4.52        ( ( zero_z2226904508553997617atural = X2 )
% 8.57/4.52        = ( X2 = zero_z2226904508553997617atural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_260_of__nat__eq__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ( semiri1314217659103216013at_int @ M )
% 8.57/4.52          = ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( M = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_261_of__nat__eq__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ( semiri1316708129612266289at_nat @ M )
% 8.57/4.52          = ( semiri1316708129612266289at_nat @ N ) )
% 8.57/4.52        = ( M = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_262_of__nat__eq__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ( semiri4939895301339042750nteger @ M )
% 8.57/4.52          = ( semiri4939895301339042750nteger @ N ) )
% 8.57/4.52        = ( M = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_263_of__nat__eq__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ( semiri681578069525770553at_rat @ M )
% 8.57/4.52          = ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.52        = ( M = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_264_of__nat__eq__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ( semiri3763490453095760265atural @ M )
% 8.57/4.52          = ( semiri3763490453095760265atural @ N ) )
% 8.57/4.52        = ( M = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_265_of__nat__eq__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ( semiri1314217659103216013at_int @ M )
% 8.57/4.52          = zero_zero_int )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_266_of__nat__eq__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ( semiri1316708129612266289at_nat @ M )
% 8.57/4.52          = zero_zero_nat )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_267_of__nat__eq__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ( semiri4939895301339042750nteger @ M )
% 8.57/4.52          = zero_z3403309356797280102nteger )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_268_of__nat__eq__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ( semiri681578069525770553at_rat @ M )
% 8.57/4.52          = zero_zero_rat )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_269_of__nat__eq__0__iff,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( ( semiri3763490453095760265atural @ M )
% 8.57/4.52          = zero_z2226904508553997617atural )
% 8.57/4.52        = ( M = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_270_of__nat__0__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( zero_zero_int
% 8.57/4.52          = ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( zero_zero_nat = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_271_of__nat__0__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( zero_zero_nat
% 8.57/4.52          = ( semiri1316708129612266289at_nat @ N ) )
% 8.57/4.52        = ( zero_zero_nat = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_272_of__nat__0__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( zero_z3403309356797280102nteger
% 8.57/4.52          = ( semiri4939895301339042750nteger @ N ) )
% 8.57/4.52        = ( zero_zero_nat = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_273_of__nat__0__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( zero_zero_rat
% 8.57/4.52          = ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.52        = ( zero_zero_nat = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_274_of__nat__0__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( zero_z2226904508553997617atural
% 8.57/4.52          = ( semiri3763490453095760265atural @ N ) )
% 8.57/4.52        = ( zero_zero_nat = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_275_of__nat__0,axiom,
% 8.57/4.52      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 8.57/4.52      = zero_zero_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_276_of__nat__0,axiom,
% 8.57/4.52      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 8.57/4.52      = zero_zero_nat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_277_of__nat__0,axiom,
% 8.57/4.52      ( ( semiri4939895301339042750nteger @ zero_zero_nat )
% 8.57/4.52      = zero_z3403309356797280102nteger ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_278_of__nat__0,axiom,
% 8.57/4.52      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 8.57/4.52      = zero_zero_rat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_279_of__nat__0,axiom,
% 8.57/4.52      ( ( semiri3763490453095760265atural @ zero_zero_nat )
% 8.57/4.52      = zero_z2226904508553997617atural ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_280_of__nat__le__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 8.57/4.52        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_281_of__nat__le__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) )
% 8.57/4.52        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_282_of__nat__le__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.52        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_283_of__nat__le__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.57/4.52        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_284_of__nat__le__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_285_int__ops_I1_J,axiom,
% 8.57/4.52      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 8.57/4.52      = zero_zero_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_286_nat__int__comparison_I3_J,axiom,
% 8.57/4.52      ( ord_less_eq_nat
% 8.57/4.52      = ( ^ [A2: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_287_nat__leq__as__int,axiom,
% 8.57/4.52      ( ord_less_eq_nat
% 8.57/4.52      = ( ^ [A2: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_288_of__nat__0__le__iff,axiom,
% 8.57/4.52      ! [N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_289_of__nat__0__le__iff,axiom,
% 8.57/4.52      ! [N: nat] : ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( semiri3763490453095760265atural @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_290_of__nat__0__le__iff,axiom,
% 8.57/4.52      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_291_of__nat__0__le__iff,axiom,
% 8.57/4.52      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_292_of__nat__0__le__iff,axiom,
% 8.57/4.52      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_293_of__nat__mono,axiom,
% 8.57/4.52      ! [I: nat,J: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52       => ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ I ) @ ( semiri4939895301339042750nteger @ J ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_294_of__nat__mono,axiom,
% 8.57/4.52      ! [I: nat,J: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52       => ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ I ) @ ( semiri3763490453095760265atural @ J ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_295_of__nat__mono,axiom,
% 8.57/4.52      ! [I: nat,J: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_296_of__nat__mono,axiom,
% 8.57/4.52      ! [I: nat,J: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_297_of__nat__mono,axiom,
% 8.57/4.52      ! [I: nat,J: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_298_fails__refines,axiom,
% 8.57/4.52      ! [C: heap_T5738788834812785303t_unit,C2: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( refine451278484176762712t_unit @ C @ C2 )
% 8.57/4.52       => ( ( time_f8834461667527620124t_unit @ C @ H )
% 8.57/4.52         => ( time_f8834461667527620124t_unit @ C2 @ H ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_299_fails__assert_H,axiom,
% 8.57/4.52      ! [P: $o,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_f8834461667527620124t_unit @ ( refine_Imp_assert @ P ) @ H )
% 8.57/4.52        = ~ P ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_300_real__arch__simple,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52      ? [N2: nat] : ( ord_less_eq_rat @ X2 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_301_time__wait,axiom,
% 8.57/4.52      ! [N: nat,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_t4224138285095624986t_unit @ ( heap_Time_wait @ N ) @ H )
% 8.57/4.52        = N ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_302_zle__int,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_303_dbl__simps_I2_J,axiom,
% 8.57/4.52      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 8.57/4.52      = zero_zero_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_304_dbl__simps_I2_J,axiom,
% 8.57/4.52      ( ( neg_nu8804712462038260780nteger @ zero_z3403309356797280102nteger )
% 8.57/4.52      = zero_z3403309356797280102nteger ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_305_dbl__simps_I2_J,axiom,
% 8.57/4.52      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 8.57/4.52      = zero_zero_rat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_306_fails__bind,axiom,
% 8.57/4.52      ! [M: heap_Time_Heap_a,F: a > heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_fails_a @ ( heap_Time_bind_a_a @ M @ F ) @ H )
% 8.57/4.52        = ( ~ ( time_fails_a @ M @ H )
% 8.57/4.52         => ( time_fails_a @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_307_fails__bind,axiom,
% 8.57/4.52      ! [M: heap_T5738788834812785303t_unit,F: product_unit > heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_fails_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ H )
% 8.57/4.52        = ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 8.57/4.52         => ( time_fails_a @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_308_fails__bind,axiom,
% 8.57/4.52      ! [M: heap_T5738788834812785303t_unit,F: product_unit > heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_f8834461667527620124t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ H )
% 8.57/4.52        = ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 8.57/4.52         => ( time_f8834461667527620124t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_309_TBOUND__bind,axiom,
% 8.57/4.52      ! [M: heap_Time_Heap_a,T_1: nat,F: a > heap_Time_Heap_a,T_2: nat] :
% 8.57/4.52        ( ( time_TBOUND_a @ M @ T_1 )
% 8.57/4.52       => ( ! [X3: a,H2: heap_e7401611519738050253t_unit] :
% 8.57/4.52              ( ( X3
% 8.57/4.52                = ( time_the_res_a @ M @ H2 ) )
% 8.57/4.52             => ( ~ ( time_fails_a @ M @ H2 )
% 8.57/4.52               => ( time_TBOUND_a @ ( F @ X3 ) @ T_2 ) ) )
% 8.57/4.52         => ( time_TBOUND_a @ ( heap_Time_bind_a_a @ M @ F ) @ ( plus_plus_nat @ T_1 @ T_2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_310_TBOUND__bind,axiom,
% 8.57/4.52      ! [M: heap_Time_Heap_a,T_1: nat,F: a > heap_T5738788834812785303t_unit,T_2: nat] :
% 8.57/4.52        ( ( time_TBOUND_a @ M @ T_1 )
% 8.57/4.52       => ( ! [X3: a,H2: heap_e7401611519738050253t_unit] :
% 8.57/4.52              ( ( X3
% 8.57/4.52                = ( time_the_res_a @ M @ H2 ) )
% 8.57/4.52             => ( ~ ( time_fails_a @ M @ H2 )
% 8.57/4.52               => ( time_T7469515765551943773t_unit @ ( F @ X3 ) @ T_2 ) ) )
% 8.57/4.52         => ( time_T7469515765551943773t_unit @ ( heap_T8685611227969916822t_unit @ M @ F ) @ ( plus_plus_nat @ T_1 @ T_2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_311_TBOUND__bind,axiom,
% 8.57/4.52      ! [M: heap_T5738788834812785303t_unit,T_1: nat,F: product_unit > heap_Time_Heap_a,T_2: nat] :
% 8.57/4.52        ( ( time_T7469515765551943773t_unit @ M @ T_1 )
% 8.57/4.52       => ( ! [X3: product_unit,H2: heap_e7401611519738050253t_unit] :
% 8.57/4.52              ( ( X3
% 8.57/4.52                = ( time_t2745601220510131320t_unit @ M @ H2 ) )
% 8.57/4.52             => ( ~ ( time_f8834461667527620124t_unit @ M @ H2 )
% 8.57/4.52               => ( time_TBOUND_a @ ( F @ X3 ) @ T_2 ) ) )
% 8.57/4.52         => ( time_TBOUND_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ ( plus_plus_nat @ T_1 @ T_2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_312_TBOUND__bind,axiom,
% 8.57/4.52      ! [M: heap_T5738788834812785303t_unit,T_1: nat,F: product_unit > heap_T5738788834812785303t_unit,T_2: nat] :
% 8.57/4.52        ( ( time_T7469515765551943773t_unit @ M @ T_1 )
% 8.57/4.52       => ( ! [X3: product_unit,H2: heap_e7401611519738050253t_unit] :
% 8.57/4.52              ( ( X3
% 8.57/4.52                = ( time_t2745601220510131320t_unit @ M @ H2 ) )
% 8.57/4.52             => ( ~ ( time_f8834461667527620124t_unit @ M @ H2 )
% 8.57/4.52               => ( time_T7469515765551943773t_unit @ ( F @ X3 ) @ T_2 ) ) )
% 8.57/4.52         => ( time_T7469515765551943773t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ ( plus_plus_nat @ T_1 @ T_2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_313_add__left__cancel,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.52        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ A @ C ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_314_add__left__cancel,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( ( plus_plus_rat @ A @ B )
% 8.57/4.52          = ( plus_plus_rat @ A @ C ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_315_add__left__cancel,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat] :
% 8.57/4.52        ( ( ( plus_plus_nat @ A @ B )
% 8.57/4.52          = ( plus_plus_nat @ A @ C ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_316_add__left__cancel,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( ( plus_plus_int @ A @ B )
% 8.57/4.52          = ( plus_plus_int @ A @ C ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_317_add__right__cancel,axiom,
% 8.57/4.52      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.52        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ C @ A ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_318_add__right__cancel,axiom,
% 8.57/4.52      ! [B: rat,A: rat,C: rat] :
% 8.57/4.52        ( ( ( plus_plus_rat @ B @ A )
% 8.57/4.52          = ( plus_plus_rat @ C @ A ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_319_add__right__cancel,axiom,
% 8.57/4.52      ! [B: nat,A: nat,C: nat] :
% 8.57/4.52        ( ( ( plus_plus_nat @ B @ A )
% 8.57/4.52          = ( plus_plus_nat @ C @ A ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_320_add__right__cancel,axiom,
% 8.57/4.52      ! [B: int,A: int,C: int] :
% 8.57/4.52        ( ( ( plus_plus_int @ B @ A )
% 8.57/4.52          = ( plus_plus_int @ C @ A ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_321_add__le__cancel__left,axiom,
% 8.57/4.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 8.57/4.52        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_322_add__le__cancel__left,axiom,
% 8.57/4.52      ! [C: rat,A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.57/4.52        = ( ord_less_eq_rat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_323_add__le__cancel__left,axiom,
% 8.57/4.52      ! [C: nat,A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.57/4.52        = ( ord_less_eq_nat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_324_add__le__cancel__left,axiom,
% 8.57/4.52      ! [C: int,A: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.57/4.52        = ( ord_less_eq_int @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_325_add__le__cancel__right,axiom,
% 8.57/4.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.52        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_326_add__le__cancel__right,axiom,
% 8.57/4.52      ! [A: rat,C: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.52        = ( ord_less_eq_rat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_327_add__le__cancel__right,axiom,
% 8.57/4.52      ! [A: nat,C: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.57/4.52        = ( ord_less_eq_nat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_328_add__le__cancel__right,axiom,
% 8.57/4.52      ! [A: int,C: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.57/4.52        = ( ord_less_eq_int @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_329_double__eq__0__iff,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( ( plus_plus_int @ A @ A )
% 8.57/4.52          = zero_zero_int )
% 8.57/4.52        = ( A = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_330_double__eq__0__iff,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 8.57/4.52          = zero_z3403309356797280102nteger )
% 8.57/4.52        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_331_double__eq__0__iff,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( ( plus_plus_rat @ A @ A )
% 8.57/4.52          = zero_zero_rat )
% 8.57/4.52        = ( A = zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_332_add__0,axiom,
% 8.57/4.52      ! [A: nat] :
% 8.57/4.52        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_333_add__0,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( plus_plus_int @ zero_zero_int @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_334_add__0,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_335_add__0,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_336_add__0,axiom,
% 8.57/4.52      ! [A: code_natural] :
% 8.57/4.52        ( ( plus_p4538020629002901425atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_337_zero__eq__add__iff__both__eq__0,axiom,
% 8.57/4.52      ! [X2: nat,Y: nat] :
% 8.57/4.52        ( ( zero_zero_nat
% 8.57/4.52          = ( plus_plus_nat @ X2 @ Y ) )
% 8.57/4.52        = ( ( X2 = zero_zero_nat )
% 8.57/4.52          & ( Y = zero_zero_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_338_add__eq__0__iff__both__eq__0,axiom,
% 8.57/4.52      ! [X2: nat,Y: nat] :
% 8.57/4.52        ( ( ( plus_plus_nat @ X2 @ Y )
% 8.57/4.52          = zero_zero_nat )
% 8.57/4.52        = ( ( X2 = zero_zero_nat )
% 8.57/4.52          & ( Y = zero_zero_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_339_add__cancel__right__right,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_plus_nat @ A @ B ) )
% 8.57/4.52        = ( B = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_340_add__cancel__right__right,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_plus_int @ A @ B ) )
% 8.57/4.52        = ( B = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_341_add__cancel__right__right,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.57/4.52        = ( B = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_342_add__cancel__right__right,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_plus_rat @ A @ B ) )
% 8.57/4.52        = ( B = zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_343_add__cancel__right__right,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_p4538020629002901425atural @ A @ B ) )
% 8.57/4.52        = ( B = zero_z2226904508553997617atural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_344_add__cancel__right__left,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_plus_nat @ B @ A ) )
% 8.57/4.52        = ( B = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_345_add__cancel__right__left,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_plus_int @ B @ A ) )
% 8.57/4.52        = ( B = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_346_add__cancel__right__left,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ B @ A ) )
% 8.57/4.52        = ( B = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_347_add__cancel__right__left,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_plus_rat @ B @ A ) )
% 8.57/4.52        = ( B = zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_348_add__cancel__right__left,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( A
% 8.57/4.52          = ( plus_p4538020629002901425atural @ B @ A ) )
% 8.57/4.52        = ( B = zero_z2226904508553997617atural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_349_add__cancel__left__right,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ( plus_plus_nat @ A @ B )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_350_add__cancel__left__right,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ( plus_plus_int @ A @ B )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_351_add__cancel__left__right,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_352_add__cancel__left__right,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ( plus_plus_rat @ A @ B )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_353_add__cancel__left__right,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ( plus_p4538020629002901425atural @ A @ B )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_z2226904508553997617atural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_354_add__cancel__left__left,axiom,
% 8.57/4.52      ! [B: nat,A: nat] :
% 8.57/4.52        ( ( ( plus_plus_nat @ B @ A )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_355_add__cancel__left__left,axiom,
% 8.57/4.52      ! [B: int,A: int] :
% 8.57/4.52        ( ( ( plus_plus_int @ B @ A )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_356_add__cancel__left__left,axiom,
% 8.57/4.52      ! [B: code_integer,A: code_integer] :
% 8.57/4.52        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_357_add__cancel__left__left,axiom,
% 8.57/4.52      ! [B: rat,A: rat] :
% 8.57/4.52        ( ( ( plus_plus_rat @ B @ A )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_358_add__cancel__left__left,axiom,
% 8.57/4.52      ! [B: code_natural,A: code_natural] :
% 8.57/4.52        ( ( ( plus_p4538020629002901425atural @ B @ A )
% 8.57/4.52          = A )
% 8.57/4.52        = ( B = zero_z2226904508553997617atural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_359_double__zero__sym,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( zero_zero_int
% 8.57/4.52          = ( plus_plus_int @ A @ A ) )
% 8.57/4.52        = ( A = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_360_double__zero__sym,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( zero_z3403309356797280102nteger
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ A @ A ) )
% 8.57/4.52        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_361_double__zero__sym,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( zero_zero_rat
% 8.57/4.52          = ( plus_plus_rat @ A @ A ) )
% 8.57/4.52        = ( A = zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_362_add_Oright__neutral,axiom,
% 8.57/4.52      ! [A: nat] :
% 8.57/4.52        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_363_add_Oright__neutral,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( plus_plus_int @ A @ zero_zero_int )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_364_add_Oright__neutral,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_365_add_Oright__neutral,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_366_add_Oright__neutral,axiom,
% 8.57/4.52      ! [A: code_natural] :
% 8.57/4.52        ( ( plus_p4538020629002901425atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_367_add__is__0,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ( plus_plus_nat @ M @ N )
% 8.57/4.52          = zero_zero_nat )
% 8.57/4.52        = ( ( M = zero_zero_nat )
% 8.57/4.52          & ( N = zero_zero_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_368_Nat_Oadd__0__right,axiom,
% 8.57/4.52      ! [M: nat] :
% 8.57/4.52        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 8.57/4.52        = M ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_369_nat__add__left__cancel__le,axiom,
% 8.57/4.52      ! [K: nat,M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 8.57/4.52        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_370_add__le__same__cancel1,axiom,
% 8.57/4.52      ! [B: code_integer,A: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 8.57/4.52        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_371_add__le__same__cancel1,axiom,
% 8.57/4.52      ! [B: code_natural,A: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 8.57/4.52        = ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_372_add__le__same__cancel1,axiom,
% 8.57/4.52      ! [B: rat,A: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 8.57/4.52        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_373_add__le__same__cancel1,axiom,
% 8.57/4.52      ! [B: nat,A: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.57/4.52        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_374_add__le__same__cancel1,axiom,
% 8.57/4.52      ! [B: int,A: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.57/4.52        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_375_add__le__same__cancel2,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 8.57/4.52        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_376_add__le__same__cancel2,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 8.57/4.52        = ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_377_add__le__same__cancel2,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.57/4.52        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_378_add__le__same__cancel2,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.57/4.52        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_379_add__le__same__cancel2,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.57/4.52        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_380_le__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.57/4.52        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_381_le__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 8.57/4.52        = ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_382_le__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.57/4.52        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_383_le__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.57/4.52        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_384_le__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.57/4.52        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_385_le__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 8.57/4.52        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_386_le__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ A @ ( plus_p4538020629002901425atural @ B @ A ) )
% 8.57/4.52        = ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_387_le__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 8.57/4.52        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_388_le__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 8.57/4.52        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_389_le__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 8.57/4.52        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_390_double__add__le__zero__iff__single__add__le__zero,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 8.57/4.52        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_391_double__add__le__zero__iff__single__add__le__zero,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 8.57/4.52        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_392_double__add__le__zero__iff__single__add__le__zero,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 8.57/4.52        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_393_zero__le__double__add__iff__zero__le__single__add,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 8.57/4.52        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_394_zero__le__double__add__iff__zero__le__single__add,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 8.57/4.52        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_395_zero__le__double__add__iff__zero__le__single__add,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 8.57/4.52        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_396_of__nat__add,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.52        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_397_of__nat__add,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.52        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_398_of__nat__add,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.52        = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_399_of__nat__add,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.52        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_400_of__nat__add,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( semiri3763490453095760265atural @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.52        = ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_401_less__eq__int__code_I1_J,axiom,
% 8.57/4.52      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_402_nonneg__int__cases,axiom,
% 8.57/4.52      ! [K: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.52       => ~ ! [N2: nat] :
% 8.57/4.52              ( K
% 8.57/4.52             != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_403_zero__le__imp__eq__int,axiom,
% 8.57/4.52      ! [K: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.52       => ? [N2: nat] :
% 8.57/4.52            ( K
% 8.57/4.52            = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_404_int__if,axiom,
% 8.57/4.52      ! [P: $o,A: nat,B: nat] :
% 8.57/4.52        ( ( P
% 8.57/4.52         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 8.57/4.52            = ( semiri1314217659103216013at_int @ A ) ) )
% 8.57/4.52        & ( ~ P
% 8.57/4.52         => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 8.57/4.52            = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_405_zero__integer_Orsp,axiom,
% 8.57/4.52      zero_zero_int = zero_zero_int ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_406_nat__int__comparison_I1_J,axiom,
% 8.57/4.52      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.57/4.52      = ( ^ [A2: nat,B2: nat] :
% 8.57/4.52            ( ( semiri1314217659103216013at_int @ A2 )
% 8.57/4.52            = ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_407_is__num__normalize_I1_J,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.52        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.52        = ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_408_is__num__normalize_I1_J,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.57/4.52        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_409_is__num__normalize_I1_J,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.57/4.52        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_410_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.57/4.52      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 8.57/4.52        ( ( ( I = J )
% 8.57/4.52          & ( K = L ) )
% 8.57/4.52       => ( ( plus_p5714425477246183910nteger @ I @ K )
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_411_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.57/4.52      ! [I: rat,J: rat,K: rat,L: rat] :
% 8.57/4.52        ( ( ( I = J )
% 8.57/4.52          & ( K = L ) )
% 8.57/4.52       => ( ( plus_plus_rat @ I @ K )
% 8.57/4.52          = ( plus_plus_rat @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_412_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.57/4.52      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.52        ( ( ( I = J )
% 8.57/4.52          & ( K = L ) )
% 8.57/4.52       => ( ( plus_plus_nat @ I @ K )
% 8.57/4.52          = ( plus_plus_nat @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_413_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.57/4.52      ! [I: int,J: int,K: int,L: int] :
% 8.57/4.52        ( ( ( I = J )
% 8.57/4.52          & ( K = L ) )
% 8.57/4.52       => ( ( plus_plus_int @ I @ K )
% 8.57/4.52          = ( plus_plus_int @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_414_group__cancel_Oadd1,axiom,
% 8.57/4.52      ! [A4: code_integer,K: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( A4
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 8.57/4.52       => ( ( plus_p5714425477246183910nteger @ A4 @ B )
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ K @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_415_group__cancel_Oadd1,axiom,
% 8.57/4.52      ! [A4: rat,K: rat,A: rat,B: rat] :
% 8.57/4.52        ( ( A4
% 8.57/4.52          = ( plus_plus_rat @ K @ A ) )
% 8.57/4.52       => ( ( plus_plus_rat @ A4 @ B )
% 8.57/4.52          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_416_group__cancel_Oadd1,axiom,
% 8.57/4.52      ! [A4: nat,K: nat,A: nat,B: nat] :
% 8.57/4.52        ( ( A4
% 8.57/4.52          = ( plus_plus_nat @ K @ A ) )
% 8.57/4.52       => ( ( plus_plus_nat @ A4 @ B )
% 8.57/4.52          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_417_group__cancel_Oadd1,axiom,
% 8.57/4.52      ! [A4: int,K: int,A: int,B: int] :
% 8.57/4.52        ( ( A4
% 8.57/4.52          = ( plus_plus_int @ K @ A ) )
% 8.57/4.52       => ( ( plus_plus_int @ A4 @ B )
% 8.57/4.52          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_418_group__cancel_Oadd2,axiom,
% 8.57/4.52      ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 8.57/4.52        ( ( B4
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 8.57/4.52       => ( ( plus_p5714425477246183910nteger @ A @ B4 )
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ K @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_419_group__cancel_Oadd2,axiom,
% 8.57/4.52      ! [B4: rat,K: rat,B: rat,A: rat] :
% 8.57/4.52        ( ( B4
% 8.57/4.52          = ( plus_plus_rat @ K @ B ) )
% 8.57/4.52       => ( ( plus_plus_rat @ A @ B4 )
% 8.57/4.52          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_420_group__cancel_Oadd2,axiom,
% 8.57/4.52      ! [B4: nat,K: nat,B: nat,A: nat] :
% 8.57/4.52        ( ( B4
% 8.57/4.52          = ( plus_plus_nat @ K @ B ) )
% 8.57/4.52       => ( ( plus_plus_nat @ A @ B4 )
% 8.57/4.52          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_421_group__cancel_Oadd2,axiom,
% 8.57/4.52      ! [B4: int,K: int,B: int,A: int] :
% 8.57/4.52        ( ( B4
% 8.57/4.52          = ( plus_plus_int @ K @ B ) )
% 8.57/4.52       => ( ( plus_plus_int @ A @ B4 )
% 8.57/4.52          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_422_dbl__def,axiom,
% 8.57/4.52      ( neg_nu8804712462038260780nteger
% 8.57/4.52      = ( ^ [X: code_integer] : ( plus_p5714425477246183910nteger @ X @ X ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_423_dbl__def,axiom,
% 8.57/4.52      ( neg_numeral_dbl_rat
% 8.57/4.52      = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_424_dbl__def,axiom,
% 8.57/4.52      ( neg_numeral_dbl_int
% 8.57/4.52      = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_425_add_Oassoc,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.52        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.52        = ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_426_add_Oassoc,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.57/4.52        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_427_add_Oassoc,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat] :
% 8.57/4.52        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.57/4.52        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_428_add_Oassoc,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.57/4.52        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_429_add_Oleft__cancel,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.52        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ A @ C ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_430_add_Oleft__cancel,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( ( plus_plus_rat @ A @ B )
% 8.57/4.52          = ( plus_plus_rat @ A @ C ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_431_add_Oleft__cancel,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( ( plus_plus_int @ A @ B )
% 8.57/4.52          = ( plus_plus_int @ A @ C ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_432_add_Oright__cancel,axiom,
% 8.57/4.52      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.52        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ C @ A ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_433_add_Oright__cancel,axiom,
% 8.57/4.52      ! [B: rat,A: rat,C: rat] :
% 8.57/4.52        ( ( ( plus_plus_rat @ B @ A )
% 8.57/4.52          = ( plus_plus_rat @ C @ A ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_434_add_Oright__cancel,axiom,
% 8.57/4.52      ! [B: int,A: int,C: int] :
% 8.57/4.52        ( ( ( plus_plus_int @ B @ A )
% 8.57/4.52          = ( plus_plus_int @ C @ A ) )
% 8.57/4.52        = ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_435_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 8.57/4.52      ( plus_p5714425477246183910nteger
% 8.57/4.52      = ( ^ [A2: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ B2 @ A2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_436_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 8.57/4.52      ( plus_plus_rat
% 8.57/4.52      = ( ^ [A2: rat,B2: rat] : ( plus_plus_rat @ B2 @ A2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_437_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 8.57/4.52      ( plus_plus_nat
% 8.57/4.52      = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_438_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 8.57/4.52      ( plus_plus_int
% 8.57/4.52      = ( ^ [A2: int,B2: int] : ( plus_plus_int @ B2 @ A2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_439_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 8.57/4.52      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.52        ( ( plus_p5714425477246183910nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) )
% 8.57/4.52        = ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_440_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 8.57/4.52      ! [B: rat,A: rat,C: rat] :
% 8.57/4.52        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 8.57/4.52        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_441_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 8.57/4.52      ! [B: nat,A: nat,C: nat] :
% 8.57/4.52        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 8.57/4.52        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_442_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 8.57/4.52      ! [B: int,A: int,C: int] :
% 8.57/4.52        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 8.57/4.52        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_443_add__left__imp__eq,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.52        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ A @ C ) )
% 8.57/4.52       => ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_444_add__left__imp__eq,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( ( plus_plus_rat @ A @ B )
% 8.57/4.52          = ( plus_plus_rat @ A @ C ) )
% 8.57/4.52       => ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_445_add__left__imp__eq,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat] :
% 8.57/4.52        ( ( ( plus_plus_nat @ A @ B )
% 8.57/4.52          = ( plus_plus_nat @ A @ C ) )
% 8.57/4.52       => ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_446_add__left__imp__eq,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( ( plus_plus_int @ A @ B )
% 8.57/4.52          = ( plus_plus_int @ A @ C ) )
% 8.57/4.52       => ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_447_add__right__imp__eq,axiom,
% 8.57/4.52      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.52        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ C @ A ) )
% 8.57/4.52       => ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_448_add__right__imp__eq,axiom,
% 8.57/4.52      ! [B: rat,A: rat,C: rat] :
% 8.57/4.52        ( ( ( plus_plus_rat @ B @ A )
% 8.57/4.52          = ( plus_plus_rat @ C @ A ) )
% 8.57/4.52       => ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_449_add__right__imp__eq,axiom,
% 8.57/4.52      ! [B: nat,A: nat,C: nat] :
% 8.57/4.52        ( ( ( plus_plus_nat @ B @ A )
% 8.57/4.52          = ( plus_plus_nat @ C @ A ) )
% 8.57/4.52       => ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_450_add__right__imp__eq,axiom,
% 8.57/4.52      ! [B: int,A: int,C: int] :
% 8.57/4.52        ( ( ( plus_plus_int @ B @ A )
% 8.57/4.52          = ( plus_plus_int @ C @ A ) )
% 8.57/4.52       => ( B = C ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_451_int__int__eq,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ( semiri1314217659103216013at_int @ M )
% 8.57/4.52          = ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( M = N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_452_verit__la__generic,axiom,
% 8.57/4.52      ! [A: int,X2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ X2 )
% 8.57/4.52        | ( A = X2 )
% 8.57/4.52        | ( ord_less_eq_int @ X2 @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_453_fails__wait,axiom,
% 8.57/4.52      ! [X2: nat,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ~ ( time_f8834461667527620124t_unit @ ( heap_Time_wait @ X2 ) @ H ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_454_size__neq__size__imp__neq,axiom,
% 8.57/4.52      ! [X2: list_nat,Y: list_nat] :
% 8.57/4.52        ( ( ( size_size_list_nat @ X2 )
% 8.57/4.52         != ( size_size_list_nat @ Y ) )
% 8.57/4.52       => ( X2 != Y ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_455_size__neq__size__imp__neq,axiom,
% 8.57/4.52      ! [X2: list_int,Y: list_int] :
% 8.57/4.52        ( ( ( size_size_list_int @ X2 )
% 8.57/4.52         != ( size_size_list_int @ Y ) )
% 8.57/4.52       => ( X2 != Y ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_456_size__neq__size__imp__neq,axiom,
% 8.57/4.52      ! [X2: num,Y: num] :
% 8.57/4.52        ( ( ( size_size_num @ X2 )
% 8.57/4.52         != ( size_size_num @ Y ) )
% 8.57/4.52       => ( X2 != Y ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_457_size__neq__size__imp__neq,axiom,
% 8.57/4.52      ! [X2: list_o,Y: list_o] :
% 8.57/4.52        ( ( ( size_size_list_o @ X2 )
% 8.57/4.52         != ( size_size_list_o @ Y ) )
% 8.57/4.52       => ( X2 != Y ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_458_size__neq__size__imp__neq,axiom,
% 8.57/4.52      ! [X2: char,Y: char] :
% 8.57/4.52        ( ( ( size_size_char @ X2 )
% 8.57/4.52         != ( size_size_char @ Y ) )
% 8.57/4.52       => ( X2 != Y ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_459_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.57/4.52      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 8.57/4.52        ( ( ( ord_le3102999989581377725nteger @ I @ J )
% 8.57/4.52          & ( K = L ) )
% 8.57/4.52       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_460_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.57/4.52      ! [I: rat,J: rat,K: rat,L: rat] :
% 8.57/4.52        ( ( ( ord_less_eq_rat @ I @ J )
% 8.57/4.52          & ( K = L ) )
% 8.57/4.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_461_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.57/4.52      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.52        ( ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52          & ( K = L ) )
% 8.57/4.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_462_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.57/4.52      ! [I: int,J: int,K: int,L: int] :
% 8.57/4.52        ( ( ( ord_less_eq_int @ I @ J )
% 8.57/4.52          & ( K = L ) )
% 8.57/4.52       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_463_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.57/4.52      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 8.57/4.52        ( ( ( I = J )
% 8.57/4.52          & ( ord_le3102999989581377725nteger @ K @ L ) )
% 8.57/4.52       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_464_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.57/4.52      ! [I: rat,J: rat,K: rat,L: rat] :
% 8.57/4.52        ( ( ( I = J )
% 8.57/4.52          & ( ord_less_eq_rat @ K @ L ) )
% 8.57/4.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_465_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.57/4.52      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.52        ( ( ( I = J )
% 8.57/4.52          & ( ord_less_eq_nat @ K @ L ) )
% 8.57/4.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_466_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.57/4.52      ! [I: int,J: int,K: int,L: int] :
% 8.57/4.52        ( ( ( I = J )
% 8.57/4.52          & ( ord_less_eq_int @ K @ L ) )
% 8.57/4.52       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_467_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.57/4.52      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 8.57/4.52        ( ( ( ord_le3102999989581377725nteger @ I @ J )
% 8.57/4.52          & ( ord_le3102999989581377725nteger @ K @ L ) )
% 8.57/4.52       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_468_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.57/4.52      ! [I: rat,J: rat,K: rat,L: rat] :
% 8.57/4.52        ( ( ( ord_less_eq_rat @ I @ J )
% 8.57/4.52          & ( ord_less_eq_rat @ K @ L ) )
% 8.57/4.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_469_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.57/4.52      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.52        ( ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52          & ( ord_less_eq_nat @ K @ L ) )
% 8.57/4.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_470_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.57/4.52      ! [I: int,J: int,K: int,L: int] :
% 8.57/4.52        ( ( ( ord_less_eq_int @ I @ J )
% 8.57/4.52          & ( ord_less_eq_int @ K @ L ) )
% 8.57/4.52       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_471_add__mono,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.52       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 8.57/4.52         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_472_add__mono,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.52       => ( ( ord_less_eq_rat @ C @ D )
% 8.57/4.52         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_473_add__mono,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.52       => ( ( ord_less_eq_nat @ C @ D )
% 8.57/4.52         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_474_add__mono,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.52       => ( ( ord_less_eq_int @ C @ D )
% 8.57/4.52         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_475_add__left__mono,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.52       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_476_add__left__mono,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_477_add__left__mono,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_478_add__left__mono,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.52       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_479_less__eqE,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.52       => ~ ! [C3: nat] :
% 8.57/4.52              ( B
% 8.57/4.52             != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_480_add__right__mono,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.52       => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_481_add__right__mono,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.52       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_482_add__right__mono,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_483_add__right__mono,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.52       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_484_le__iff__add,axiom,
% 8.57/4.52      ( ord_less_eq_nat
% 8.57/4.52      = ( ^ [A2: nat,B2: nat] :
% 8.57/4.52          ? [C4: nat] :
% 8.57/4.52            ( B2
% 8.57/4.52            = ( plus_plus_nat @ A2 @ C4 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_485_add__le__imp__le__left,axiom,
% 8.57/4.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 8.57/4.52       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_486_add__le__imp__le__left,axiom,
% 8.57/4.52      ! [C: rat,A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.57/4.52       => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_487_add__le__imp__le__left,axiom,
% 8.57/4.52      ! [C: nat,A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.57/4.52       => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_488_add__le__imp__le__left,axiom,
% 8.57/4.52      ! [C: int,A: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.57/4.52       => ( ord_less_eq_int @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_489_add__le__imp__le__right,axiom,
% 8.57/4.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.52       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_490_add__le__imp__le__right,axiom,
% 8.57/4.52      ! [A: rat,C: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.52       => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_491_add__le__imp__le__right,axiom,
% 8.57/4.52      ! [A: nat,C: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.57/4.52       => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_492_add__le__imp__le__right,axiom,
% 8.57/4.52      ! [A: int,C: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.57/4.52       => ( ord_less_eq_int @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_493_verit__sum__simplify,axiom,
% 8.57/4.52      ! [A: nat] :
% 8.57/4.52        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_494_verit__sum__simplify,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( plus_plus_int @ A @ zero_zero_int )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_495_verit__sum__simplify,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_496_verit__sum__simplify,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_497_verit__sum__simplify,axiom,
% 8.57/4.52      ! [A: code_natural] :
% 8.57/4.52        ( ( plus_p4538020629002901425atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_498_add_Ogroup__left__neutral,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( plus_plus_int @ zero_zero_int @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_499_add_Ogroup__left__neutral,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_500_add_Ogroup__left__neutral,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_501_add_Ocomm__neutral,axiom,
% 8.57/4.52      ! [A: nat] :
% 8.57/4.52        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_502_add_Ocomm__neutral,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( plus_plus_int @ A @ zero_zero_int )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_503_add_Ocomm__neutral,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_504_add_Ocomm__neutral,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_505_add_Ocomm__neutral,axiom,
% 8.57/4.52      ! [A: code_natural] :
% 8.57/4.52        ( ( plus_p4538020629002901425atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_506_comm__monoid__add__class_Oadd__0,axiom,
% 8.57/4.52      ! [A: nat] :
% 8.57/4.52        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_507_comm__monoid__add__class_Oadd__0,axiom,
% 8.57/4.52      ! [A: int] :
% 8.57/4.52        ( ( plus_plus_int @ zero_zero_int @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_508_comm__monoid__add__class_Oadd__0,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_509_comm__monoid__add__class_Oadd__0,axiom,
% 8.57/4.52      ! [A: rat] :
% 8.57/4.52        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_510_comm__monoid__add__class_Oadd__0,axiom,
% 8.57/4.52      ! [A: code_natural] :
% 8.57/4.52        ( ( plus_p4538020629002901425atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.52        = A ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_511_plus__nat_Oadd__0,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( plus_plus_nat @ zero_zero_nat @ N )
% 8.57/4.52        = N ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_512_add__eq__self__zero,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ( plus_plus_nat @ M @ N )
% 8.57/4.52          = M )
% 8.57/4.52       => ( N = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_513_add__leE,axiom,
% 8.57/4.52      ! [M: nat,K: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 8.57/4.52       => ~ ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.52           => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_514_le__add1,axiom,
% 8.57/4.52      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_515_le__add2,axiom,
% 8.57/4.52      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_516_add__leD1,axiom,
% 8.57/4.52      ! [M: nat,K: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 8.57/4.52       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_517_add__leD2,axiom,
% 8.57/4.52      ! [M: nat,K: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 8.57/4.52       => ( ord_less_eq_nat @ K @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_518_le__Suc__ex,axiom,
% 8.57/4.52      ! [K: nat,L: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ K @ L )
% 8.57/4.52       => ? [N2: nat] :
% 8.57/4.52            ( L
% 8.57/4.52            = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_519_add__le__mono,axiom,
% 8.57/4.52      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52       => ( ( ord_less_eq_nat @ K @ L )
% 8.57/4.52         => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_520_add__le__mono1,axiom,
% 8.57/4.52      ! [I: nat,J: nat,K: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_521_trans__le__add1,axiom,
% 8.57/4.52      ! [I: nat,J: nat,M: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_522_trans__le__add2,axiom,
% 8.57/4.52      ! [I: nat,J: nat,M: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.52       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_523_nat__le__iff__add,axiom,
% 8.57/4.52      ( ord_less_eq_nat
% 8.57/4.52      = ( ^ [M2: nat,N3: nat] :
% 8.57/4.52          ? [K2: nat] :
% 8.57/4.52            ( N3
% 8.57/4.52            = ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_524_add__decreasing,axiom,
% 8.57/4.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.52       => ( ( ord_le3102999989581377725nteger @ C @ B )
% 8.57/4.52         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_525_add__decreasing,axiom,
% 8.57/4.52      ! [A: code_natural,C: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.52       => ( ( ord_le1926595141338095240atural @ C @ B )
% 8.57/4.52         => ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_526_add__decreasing,axiom,
% 8.57/4.52      ! [A: rat,C: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.52       => ( ( ord_less_eq_rat @ C @ B )
% 8.57/4.52         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_527_add__decreasing,axiom,
% 8.57/4.52      ! [A: nat,C: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.57/4.52       => ( ( ord_less_eq_nat @ C @ B )
% 8.57/4.52         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_528_add__decreasing,axiom,
% 8.57/4.52      ! [A: int,C: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.52       => ( ( ord_less_eq_int @ C @ B )
% 8.57/4.52         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_529_add__increasing,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.52       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 8.57/4.52         => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_530_add__increasing,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.52       => ( ( ord_le1926595141338095240atural @ B @ C )
% 8.57/4.52         => ( ord_le1926595141338095240atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_531_add__increasing,axiom,
% 8.57/4.52      ! [A: rat,B: rat,C: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.52       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.52         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_532_add__increasing,axiom,
% 8.57/4.52      ! [A: nat,B: nat,C: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.52       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.52         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_533_add__increasing,axiom,
% 8.57/4.52      ! [A: int,B: int,C: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.52       => ( ( ord_less_eq_int @ B @ C )
% 8.57/4.52         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_534_add__decreasing2,axiom,
% 8.57/4.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.52       => ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.52         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_535_add__decreasing2,axiom,
% 8.57/4.52      ! [C: code_natural,A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ C @ zero_z2226904508553997617atural )
% 8.57/4.52       => ( ( ord_le1926595141338095240atural @ A @ B )
% 8.57/4.52         => ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_536_add__decreasing2,axiom,
% 8.57/4.52      ! [C: rat,A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.52       => ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.52         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_537_add__decreasing2,axiom,
% 8.57/4.52      ! [C: nat,A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 8.57/4.52       => ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.52         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_538_add__decreasing2,axiom,
% 8.57/4.52      ! [C: int,A: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.57/4.52       => ( ( ord_less_eq_int @ A @ B )
% 8.57/4.52         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_539_add__increasing2,axiom,
% 8.57/4.52      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.52       => ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.57/4.52         => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_540_add__increasing2,axiom,
% 8.57/4.52      ! [C: code_natural,B: code_natural,A: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.52       => ( ( ord_le1926595141338095240atural @ B @ A )
% 8.57/4.52         => ( ord_le1926595141338095240atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_541_add__increasing2,axiom,
% 8.57/4.52      ! [C: rat,B: rat,A: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.52       => ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.52         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_542_add__increasing2,axiom,
% 8.57/4.52      ! [C: nat,B: nat,A: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.52       => ( ( ord_less_eq_nat @ B @ A )
% 8.57/4.52         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_543_add__increasing2,axiom,
% 8.57/4.52      ! [C: int,B: int,A: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.52       => ( ( ord_less_eq_int @ B @ A )
% 8.57/4.52         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_544_add__nonneg__nonneg,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.52       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.52         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_545_add__nonneg__nonneg,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.52       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.52         => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_546_add__nonneg__nonneg,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.52         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_547_add__nonneg__nonneg,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.52         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_548_add__nonneg__nonneg,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.52       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.52         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_549_add__nonpos__nonpos,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.52       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.52         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_550_add__nonpos__nonpos,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.52       => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 8.57/4.52         => ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_551_add__nonpos__nonpos,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.52       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.57/4.52         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_552_add__nonpos__nonpos,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.57/4.52       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.57/4.52         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_553_add__nonpos__nonpos,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.52       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.57/4.52         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_554_add__nonneg__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 8.57/4.52       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 8.57/4.52         => ( ( ( plus_p5714425477246183910nteger @ X2 @ Y )
% 8.57/4.52              = zero_z3403309356797280102nteger )
% 8.57/4.52            = ( ( X2 = zero_z3403309356797280102nteger )
% 8.57/4.52              & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_555_add__nonneg__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: code_natural,Y: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ X2 )
% 8.57/4.52       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ Y )
% 8.57/4.52         => ( ( ( plus_p4538020629002901425atural @ X2 @ Y )
% 8.57/4.52              = zero_z2226904508553997617atural )
% 8.57/4.52            = ( ( X2 = zero_z2226904508553997617atural )
% 8.57/4.52              & ( Y = zero_z2226904508553997617atural ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_556_add__nonneg__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: rat,Y: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.57/4.52         => ( ( ( plus_plus_rat @ X2 @ Y )
% 8.57/4.52              = zero_zero_rat )
% 8.57/4.52            = ( ( X2 = zero_zero_rat )
% 8.57/4.52              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_557_add__nonneg__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: nat,Y: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 8.57/4.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.57/4.52         => ( ( ( plus_plus_nat @ X2 @ Y )
% 8.57/4.52              = zero_zero_nat )
% 8.57/4.52            = ( ( X2 = zero_zero_nat )
% 8.57/4.52              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_558_add__nonneg__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: int,Y: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.52       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.52         => ( ( ( plus_plus_int @ X2 @ Y )
% 8.57/4.52              = zero_zero_int )
% 8.57/4.52            = ( ( X2 = zero_zero_int )
% 8.57/4.52              & ( Y = zero_zero_int ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_559_add__nonpos__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ X2 @ zero_z3403309356797280102nteger )
% 8.57/4.52       => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 8.57/4.52         => ( ( ( plus_p5714425477246183910nteger @ X2 @ Y )
% 8.57/4.52              = zero_z3403309356797280102nteger )
% 8.57/4.52            = ( ( X2 = zero_z3403309356797280102nteger )
% 8.57/4.52              & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_560_add__nonpos__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: code_natural,Y: code_natural] :
% 8.57/4.52        ( ( ord_le1926595141338095240atural @ X2 @ zero_z2226904508553997617atural )
% 8.57/4.52       => ( ( ord_le1926595141338095240atural @ Y @ zero_z2226904508553997617atural )
% 8.57/4.52         => ( ( ( plus_p4538020629002901425atural @ X2 @ Y )
% 8.57/4.52              = zero_z2226904508553997617atural )
% 8.57/4.52            = ( ( X2 = zero_z2226904508553997617atural )
% 8.57/4.52              & ( Y = zero_z2226904508553997617atural ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_561_add__nonpos__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: rat,Y: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 8.57/4.52       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 8.57/4.52         => ( ( ( plus_plus_rat @ X2 @ Y )
% 8.57/4.52              = zero_zero_rat )
% 8.57/4.52            = ( ( X2 = zero_zero_rat )
% 8.57/4.52              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_562_add__nonpos__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: nat,Y: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ X2 @ zero_zero_nat )
% 8.57/4.52       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 8.57/4.52         => ( ( ( plus_plus_nat @ X2 @ Y )
% 8.57/4.52              = zero_zero_nat )
% 8.57/4.52            = ( ( X2 = zero_zero_nat )
% 8.57/4.52              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_563_add__nonpos__eq__0__iff,axiom,
% 8.57/4.52      ! [X2: int,Y: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 8.57/4.52       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 8.57/4.52         => ( ( ( plus_plus_int @ X2 @ Y )
% 8.57/4.52              = zero_zero_int )
% 8.57/4.52            = ( ( X2 = zero_zero_int )
% 8.57/4.52              & ( Y = zero_zero_int ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_564_time__bind,axiom,
% 8.57/4.52      ! [M: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,F: a > heap_Time_Heap_a] :
% 8.57/4.52        ( ( ( ~ ( time_fails_a @ M @ H )
% 8.57/4.52            & ~ ( time_fails_a @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) )
% 8.57/4.52         => ( ( time_time_a @ ( heap_Time_bind_a_a @ M @ F ) @ H )
% 8.57/4.52            = ( plus_plus_nat @ ( time_time_a @ M @ H ) @ ( time_time_a @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) ) ) )
% 8.57/4.52        & ( ~ ( ~ ( time_fails_a @ M @ H )
% 8.57/4.52              & ~ ( time_fails_a @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) )
% 8.57/4.52         => ( ( time_time_a @ ( heap_Time_bind_a_a @ M @ F ) @ H )
% 8.57/4.52            = zero_zero_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_565_time__bind,axiom,
% 8.57/4.52      ! [M: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,F: a > heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( ( ~ ( time_fails_a @ M @ H )
% 8.57/4.52            & ~ ( time_f8834461667527620124t_unit @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) )
% 8.57/4.52         => ( ( time_t4224138285095624986t_unit @ ( heap_T8685611227969916822t_unit @ M @ F ) @ H )
% 8.57/4.52            = ( plus_plus_nat @ ( time_time_a @ M @ H ) @ ( time_t4224138285095624986t_unit @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) ) ) )
% 8.57/4.52        & ( ~ ( ~ ( time_fails_a @ M @ H )
% 8.57/4.52              & ~ ( time_f8834461667527620124t_unit @ ( F @ ( time_the_res_a @ M @ H ) ) @ ( time_the_heap_a @ M @ H ) ) )
% 8.57/4.52         => ( ( time_t4224138285095624986t_unit @ ( heap_T8685611227969916822t_unit @ M @ F ) @ H )
% 8.57/4.52            = zero_zero_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_566_time__bind,axiom,
% 8.57/4.52      ! [M: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,F: product_unit > heap_Time_Heap_a] :
% 8.57/4.52        ( ( ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 8.57/4.52            & ~ ( time_fails_a @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) )
% 8.57/4.52         => ( ( time_time_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ H )
% 8.57/4.52            = ( plus_plus_nat @ ( time_t4224138285095624986t_unit @ M @ H ) @ ( time_time_a @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) ) ) )
% 8.57/4.52        & ( ~ ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 8.57/4.52              & ~ ( time_fails_a @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) )
% 8.57/4.52         => ( ( time_time_a @ ( heap_T757603679106148408unit_a @ M @ F ) @ H )
% 8.57/4.52            = zero_zero_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_567_time__bind,axiom,
% 8.57/4.52      ! [M: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,F: product_unit > heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 8.57/4.52            & ~ ( time_f8834461667527620124t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) )
% 8.57/4.52         => ( ( time_t4224138285095624986t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ H )
% 8.57/4.52            = ( plus_plus_nat @ ( time_t4224138285095624986t_unit @ M @ H ) @ ( time_t4224138285095624986t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) ) ) )
% 8.57/4.52        & ( ~ ( ~ ( time_f8834461667527620124t_unit @ M @ H )
% 8.57/4.52              & ~ ( time_f8834461667527620124t_unit @ ( F @ ( time_t2745601220510131320t_unit @ M @ H ) ) @ ( time_t3350536682685678164t_unit @ M @ H ) ) )
% 8.57/4.52         => ( ( time_t4224138285095624986t_unit @ ( heap_T2633723481742716231t_unit @ M @ F ) @ H )
% 8.57/4.52            = zero_zero_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_568_imp__le__cong,axiom,
% 8.57/4.52      ! [X2: int,X6: int,P: $o,P2: $o] :
% 8.57/4.52        ( ( X2 = X6 )
% 8.57/4.52       => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 8.57/4.52           => ( P = P2 ) )
% 8.57/4.52         => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.52             => P )
% 8.57/4.52            = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 8.57/4.52             => P2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_569_conj__le__cong,axiom,
% 8.57/4.52      ! [X2: int,X6: int,P: $o,P2: $o] :
% 8.57/4.52        ( ( X2 = X6 )
% 8.57/4.52       => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 8.57/4.52           => ( P = P2 ) )
% 8.57/4.52         => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.52              & P )
% 8.57/4.52            = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 8.57/4.52              & P2 ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_570_Euclid__induct,axiom,
% 8.57/4.52      ! [P: nat > nat > $o,A: nat,B: nat] :
% 8.57/4.52        ( ! [A3: nat,B3: nat] :
% 8.57/4.52            ( ( P @ A3 @ B3 )
% 8.57/4.52            = ( P @ B3 @ A3 ) )
% 8.57/4.52       => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 8.57/4.52         => ( ! [A3: nat,B3: nat] :
% 8.57/4.52                ( ( P @ A3 @ B3 )
% 8.57/4.52               => ( P @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 8.57/4.52           => ( P @ A @ B ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_571_add__0__iff,axiom,
% 8.57/4.52      ! [B: nat,A: nat] :
% 8.57/4.52        ( ( B
% 8.57/4.52          = ( plus_plus_nat @ B @ A ) )
% 8.57/4.52        = ( A = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_572_add__0__iff,axiom,
% 8.57/4.52      ! [B: int,A: int] :
% 8.57/4.52        ( ( B
% 8.57/4.52          = ( plus_plus_int @ B @ A ) )
% 8.57/4.52        = ( A = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_573_add__0__iff,axiom,
% 8.57/4.52      ! [B: code_integer,A: code_integer] :
% 8.57/4.52        ( ( B
% 8.57/4.52          = ( plus_p5714425477246183910nteger @ B @ A ) )
% 8.57/4.52        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_574_add__0__iff,axiom,
% 8.57/4.52      ! [B: rat,A: rat] :
% 8.57/4.52        ( ( B
% 8.57/4.52          = ( plus_plus_rat @ B @ A ) )
% 8.57/4.52        = ( A = zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_575_of__nat__code,axiom,
% 8.57/4.52      ( semiri1314217659103216013at_int
% 8.57/4.52      = ( ^ [N3: nat] :
% 8.57/4.52            ( semiri8420488043553186161ux_int
% 8.57/4.52            @ ^ [I2: int] : ( plus_plus_int @ I2 @ one_one_int )
% 8.57/4.52            @ N3
% 8.57/4.52            @ zero_zero_int ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_576_of__nat__code,axiom,
% 8.57/4.52      ( semiri1316708129612266289at_nat
% 8.57/4.52      = ( ^ [N3: nat] :
% 8.57/4.52            ( semiri8422978514062236437ux_nat
% 8.57/4.52            @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ one_one_nat )
% 8.57/4.52            @ N3
% 8.57/4.52            @ zero_zero_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_577_of__nat__code,axiom,
% 8.57/4.52      ( semiri4939895301339042750nteger
% 8.57/4.52      = ( ^ [N3: nat] :
% 8.57/4.52            ( semiri4055485073559036834nteger
% 8.57/4.52            @ ^ [I2: code_integer] : ( plus_p5714425477246183910nteger @ I2 @ one_one_Code_integer )
% 8.57/4.52            @ N3
% 8.57/4.52            @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_578_of__nat__code,axiom,
% 8.57/4.52      ( semiri681578069525770553at_rat
% 8.57/4.52      = ( ^ [N3: nat] :
% 8.57/4.52            ( semiri7787848453975740701ux_rat
% 8.57/4.52            @ ^ [I2: rat] : ( plus_plus_rat @ I2 @ one_one_rat )
% 8.57/4.52            @ N3
% 8.57/4.52            @ zero_zero_rat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_579_of__nat__code,axiom,
% 8.57/4.52      ( semiri3763490453095760265atural
% 8.57/4.52      = ( ^ [N3: nat] :
% 8.57/4.52            ( semiri2879080225315754349atural
% 8.57/4.52            @ ^ [I2: code_natural] : ( plus_p4538020629002901425atural @ I2 @ one_one_Code_natural )
% 8.57/4.52            @ N3
% 8.57/4.52            @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_580_of__nat__eq__1__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ( semiri1314217659103216013at_int @ N )
% 8.57/4.52          = one_one_int )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_581_of__nat__eq__1__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ( semiri1316708129612266289at_nat @ N )
% 8.57/4.52          = one_one_nat )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_582_of__nat__eq__1__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ( semiri4939895301339042750nteger @ N )
% 8.57/4.52          = one_one_Code_integer )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_583_of__nat__eq__1__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ( semiri681578069525770553at_rat @ N )
% 8.57/4.52          = one_one_rat )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_584_of__nat__eq__1__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ( semiri3763490453095760265atural @ N )
% 8.57/4.52          = one_one_Code_natural )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_585_of__nat__1__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( one_one_int
% 8.57/4.52          = ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_586_of__nat__1__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( one_one_nat
% 8.57/4.52          = ( semiri1316708129612266289at_nat @ N ) )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_587_of__nat__1__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( one_one_Code_integer
% 8.57/4.52          = ( semiri4939895301339042750nteger @ N ) )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_588_of__nat__1__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( one_one_rat
% 8.57/4.52          = ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_589_of__nat__1__eq__iff,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( one_one_Code_natural
% 8.57/4.52          = ( semiri3763490453095760265atural @ N ) )
% 8.57/4.52        = ( N = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_590_of__nat__1,axiom,
% 8.57/4.52      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 8.57/4.52      = one_one_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_591_of__nat__1,axiom,
% 8.57/4.52      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 8.57/4.52      = one_one_nat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_592_of__nat__1,axiom,
% 8.57/4.52      ( ( semiri4939895301339042750nteger @ one_one_nat )
% 8.57/4.52      = one_one_Code_integer ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_593_of__nat__1,axiom,
% 8.57/4.52      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 8.57/4.52      = one_one_rat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_594_of__nat__1,axiom,
% 8.57/4.52      ( ( semiri3763490453095760265atural @ one_one_nat )
% 8.57/4.52      = one_one_Code_natural ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_595_one__reorient,axiom,
% 8.57/4.52      ! [X2: int] :
% 8.57/4.52        ( ( one_one_int = X2 )
% 8.57/4.52        = ( X2 = one_one_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_596_one__reorient,axiom,
% 8.57/4.52      ! [X2: nat] :
% 8.57/4.52        ( ( one_one_nat = X2 )
% 8.57/4.52        = ( X2 = one_one_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_597_one__reorient,axiom,
% 8.57/4.52      ! [X2: code_integer] :
% 8.57/4.52        ( ( one_one_Code_integer = X2 )
% 8.57/4.52        = ( X2 = one_one_Code_integer ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_598_one__reorient,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52        ( ( one_one_rat = X2 )
% 8.57/4.52        = ( X2 = one_one_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_599_one__reorient,axiom,
% 8.57/4.52      ! [X2: code_natural] :
% 8.57/4.52        ( ( one_one_Code_natural = X2 )
% 8.57/4.52        = ( X2 = one_one_Code_natural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_600_odd__nonzero,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 )
% 8.57/4.52       != zero_zero_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_601_int__ge__induct,axiom,
% 8.57/4.52      ! [K: int,I: int,P: int > $o] :
% 8.57/4.52        ( ( ord_less_eq_int @ K @ I )
% 8.57/4.52       => ( ( P @ K )
% 8.57/4.52         => ( ! [I3: int] :
% 8.57/4.52                ( ( ord_less_eq_int @ K @ I3 )
% 8.57/4.52               => ( ( P @ I3 )
% 8.57/4.52                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 8.57/4.52           => ( P @ I ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_602_int__ops_I2_J,axiom,
% 8.57/4.52      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 8.57/4.52      = one_one_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_603_plus__int__code_I2_J,axiom,
% 8.57/4.52      ! [L: int] :
% 8.57/4.52        ( ( plus_plus_int @ zero_zero_int @ L )
% 8.57/4.52        = L ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_604_plus__int__code_I1_J,axiom,
% 8.57/4.52      ! [K: int] :
% 8.57/4.52        ( ( plus_plus_int @ K @ zero_zero_int )
% 8.57/4.52        = K ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_605_le__numeral__extra_I4_J,axiom,
% 8.57/4.52      ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_606_le__numeral__extra_I4_J,axiom,
% 8.57/4.52      ord_le1926595141338095240atural @ one_one_Code_natural @ one_one_Code_natural ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_607_le__numeral__extra_I4_J,axiom,
% 8.57/4.52      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_608_le__numeral__extra_I4_J,axiom,
% 8.57/4.52      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_609_le__numeral__extra_I4_J,axiom,
% 8.57/4.52      ord_less_eq_int @ one_one_int @ one_one_int ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_610_zadd__int__left,axiom,
% 8.57/4.52      ! [M: nat,N: nat,Z2: int] :
% 8.57/4.52        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z2 ) )
% 8.57/4.52        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_611_int__ops_I5_J,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 8.57/4.52        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_612_int__plus,axiom,
% 8.57/4.52      ! [N: nat,M: nat] :
% 8.57/4.52        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 8.57/4.52        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_613_zle__iff__zadd,axiom,
% 8.57/4.52      ( ord_less_eq_int
% 8.57/4.52      = ( ^ [W: int,Z3: int] :
% 8.57/4.52          ? [N3: nat] :
% 8.57/4.52            ( Z3
% 8.57/4.52            = ( plus_plus_int @ W @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_614_nat__geq__1__eq__neqz,axiom,
% 8.57/4.52      ! [X2: nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ one_one_nat @ X2 )
% 8.57/4.52        = ( X2 != zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_615_someI2__bex,axiom,
% 8.57/4.52      ! [A4: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 8.57/4.52        ( ? [X4: product_prod_nat_nat] :
% 8.57/4.52            ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 8.57/4.52            & ( P @ X4 ) )
% 8.57/4.52       => ( ! [X3: product_prod_nat_nat] :
% 8.57/4.52              ( ( ( member8440522571783428010at_nat @ X3 @ A4 )
% 8.57/4.52                & ( P @ X3 ) )
% 8.57/4.52             => ( Q @ X3 ) )
% 8.57/4.52         => ( Q
% 8.57/4.52            @ ( fChoic6978938873391328853at_nat
% 8.57/4.52              @ ^ [X: product_prod_nat_nat] :
% 8.57/4.52                  ( ( member8440522571783428010at_nat @ X @ A4 )
% 8.57/4.52                  & ( P @ X ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_616_someI2__bex,axiom,
% 8.57/4.52      ! [A4: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o,Q: set_Pr958786334691620121nt_int > $o] :
% 8.57/4.52        ( ? [X4: set_Pr958786334691620121nt_int] :
% 8.57/4.52            ( ( member2340774599025711042nt_int @ X4 @ A4 )
% 8.57/4.52            & ( P @ X4 ) )
% 8.57/4.52       => ( ! [X3: set_Pr958786334691620121nt_int] :
% 8.57/4.52              ( ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 8.57/4.52                & ( P @ X3 ) )
% 8.57/4.52             => ( Q @ X3 ) )
% 8.57/4.52         => ( Q
% 8.57/4.52            @ ( fChoic2749331249758569069nt_int
% 8.57/4.52              @ ^ [X: set_Pr958786334691620121nt_int] :
% 8.57/4.52                  ( ( member2340774599025711042nt_int @ X @ A4 )
% 8.57/4.52                  & ( P @ X ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_617_someI2__bex,axiom,
% 8.57/4.52      ! [A4: set_set_nat,P: set_nat > $o,Q: set_nat > $o] :
% 8.57/4.52        ( ? [X4: set_nat] :
% 8.57/4.52            ( ( member_set_nat @ X4 @ A4 )
% 8.57/4.52            & ( P @ X4 ) )
% 8.57/4.52       => ( ! [X3: set_nat] :
% 8.57/4.52              ( ( ( member_set_nat @ X3 @ A4 )
% 8.57/4.52                & ( P @ X3 ) )
% 8.57/4.52             => ( Q @ X3 ) )
% 8.57/4.52         => ( Q
% 8.57/4.52            @ ( fChoice_set_nat
% 8.57/4.52              @ ^ [X: set_nat] :
% 8.57/4.52                  ( ( member_set_nat @ X @ A4 )
% 8.57/4.52                  & ( P @ X ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_618_someI2__bex,axiom,
% 8.57/4.52      ! [A4: set_nat,P: nat > $o,Q: nat > $o] :
% 8.57/4.52        ( ? [X4: nat] :
% 8.57/4.52            ( ( member_nat @ X4 @ A4 )
% 8.57/4.52            & ( P @ X4 ) )
% 8.57/4.52       => ( ! [X3: nat] :
% 8.57/4.52              ( ( ( member_nat @ X3 @ A4 )
% 8.57/4.52                & ( P @ X3 ) )
% 8.57/4.52             => ( Q @ X3 ) )
% 8.57/4.52         => ( Q
% 8.57/4.52            @ ( fChoice_nat
% 8.57/4.52              @ ^ [X: nat] :
% 8.57/4.52                  ( ( member_nat @ X @ A4 )
% 8.57/4.52                  & ( P @ X ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_619_someI2__bex,axiom,
% 8.57/4.52      ! [A4: set_int,P: int > $o,Q: int > $o] :
% 8.57/4.52        ( ? [X4: int] :
% 8.57/4.52            ( ( member_int @ X4 @ A4 )
% 8.57/4.52            & ( P @ X4 ) )
% 8.57/4.52       => ( ! [X3: int] :
% 8.57/4.52              ( ( ( member_int @ X3 @ A4 )
% 8.57/4.52                & ( P @ X3 ) )
% 8.57/4.52             => ( Q @ X3 ) )
% 8.57/4.52         => ( Q
% 8.57/4.52            @ ( fChoice_int
% 8.57/4.52              @ ^ [X: int] :
% 8.57/4.52                  ( ( member_int @ X @ A4 )
% 8.57/4.52                  & ( P @ X ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_620_not__one__le__zero,axiom,
% 8.57/4.52      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_621_not__one__le__zero,axiom,
% 8.57/4.52      ~ ( ord_le1926595141338095240atural @ one_one_Code_natural @ zero_z2226904508553997617atural ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_622_not__one__le__zero,axiom,
% 8.57/4.52      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_623_not__one__le__zero,axiom,
% 8.57/4.52      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_624_not__one__le__zero,axiom,
% 8.57/4.52      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_625_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_626_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_627_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_628_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_629_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_630_zero__less__one__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_631_zero__less__one__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_632_zero__less__one__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_633_zero__less__one__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_634_zero__less__one__class_Ozero__le__one,axiom,
% 8.57/4.52      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_635_zero__neq__one,axiom,
% 8.57/4.52      zero_zero_nat != one_one_nat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_636_zero__neq__one,axiom,
% 8.57/4.52      zero_zero_int != one_one_int ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_637_zero__neq__one,axiom,
% 8.57/4.52      zero_z3403309356797280102nteger != one_one_Code_integer ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_638_zero__neq__one,axiom,
% 8.57/4.52      zero_zero_rat != one_one_rat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_639_zero__neq__one,axiom,
% 8.57/4.52      zero_z2226904508553997617atural != one_one_Code_natural ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_640_return__bind,axiom,
% 8.57/4.52      ! [X2: product_unit,F: product_unit > heap_Time_Heap_a] :
% 8.57/4.52        ( ( heap_T757603679106148408unit_a @ ( heap_T7507251653302230130t_unit @ X2 ) @ F )
% 8.57/4.52        = ( heap_T757603679106148408unit_a @ ( heap_Time_wait @ one_one_nat )
% 8.57/4.52          @ ^ [Uu: product_unit] : ( F @ X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_641_return__bind,axiom,
% 8.57/4.52      ! [X2: product_unit,F: product_unit > heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( heap_T2633723481742716231t_unit @ ( heap_T7507251653302230130t_unit @ X2 ) @ F )
% 8.57/4.52        = ( heap_T2633723481742716231t_unit @ ( heap_Time_wait @ one_one_nat )
% 8.57/4.52          @ ^ [Uu: product_unit] : ( F @ X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_642_return__bind,axiom,
% 8.57/4.52      ! [X2: a,F: a > heap_Time_Heap_a] :
% 8.57/4.52        ( ( heap_Time_bind_a_a @ ( heap_Time_return_a @ X2 ) @ F )
% 8.57/4.52        = ( heap_T757603679106148408unit_a @ ( heap_Time_wait @ one_one_nat )
% 8.57/4.52          @ ^ [Uu: product_unit] : ( F @ X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_643_bind__return,axiom,
% 8.57/4.52      ! [F: heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( heap_T2633723481742716231t_unit @ F @ heap_T7507251653302230130t_unit )
% 8.57/4.52        = ( heap_T2633723481742716231t_unit @ ( heap_Time_wait @ one_one_nat )
% 8.57/4.52          @ ^ [Uu: product_unit] : F ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_644_bind__return,axiom,
% 8.57/4.52      ! [F: heap_Time_Heap_a] :
% 8.57/4.52        ( ( heap_Time_bind_a_a @ F @ heap_Time_return_a )
% 8.57/4.52        = ( heap_T757603679106148408unit_a @ ( heap_Time_wait @ one_one_nat )
% 8.57/4.52          @ ^ [Uu: product_unit] : F ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_645_time__array__nth,axiom,
% 8.57/4.52      ! [P3: array_Product_unit,I: nat,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( ( time_f8834461667527620124t_unit @ ( array_7872002506669749220t_unit @ P3 @ I ) @ H )
% 8.57/4.52         => ( ( time_t4224138285095624986t_unit @ ( array_7872002506669749220t_unit @ P3 @ I ) @ H )
% 8.57/4.52            = zero_zero_nat ) )
% 8.57/4.52        & ( ~ ( time_f8834461667527620124t_unit @ ( array_7872002506669749220t_unit @ P3 @ I ) @ H )
% 8.57/4.52         => ( ( time_t4224138285095624986t_unit @ ( array_7872002506669749220t_unit @ P3 @ I ) @ H )
% 8.57/4.52            = one_one_nat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_646_dbl__inc__simps_I2_J,axiom,
% 8.57/4.52      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 8.57/4.52      = one_one_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_647_dbl__inc__simps_I2_J,axiom,
% 8.57/4.52      ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 8.57/4.52      = one_one_Code_integer ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_648_dbl__inc__simps_I2_J,axiom,
% 8.57/4.52      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 8.57/4.52      = one_one_rat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_649_one__natural_Orsp,axiom,
% 8.57/4.52      one_one_nat = one_one_nat ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_650_one__integer_Orsp,axiom,
% 8.57/4.52      one_one_int = one_one_int ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_651_time__return,axiom,
% 8.57/4.52      ! [X2: a,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_time_a @ ( heap_Time_return_a @ X2 ) @ H )
% 8.57/4.52        = one_one_nat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_652_time__return,axiom,
% 8.57/4.52      ! [X2: product_unit,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ( ( time_t4224138285095624986t_unit @ ( heap_T7507251653302230130t_unit @ X2 ) @ H )
% 8.57/4.52        = one_one_nat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_653_fails__return,axiom,
% 8.57/4.52      ! [X2: product_unit,H: heap_e7401611519738050253t_unit] :
% 8.57/4.52        ~ ( time_f8834461667527620124t_unit @ ( heap_T7507251653302230130t_unit @ X2 ) @ H ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_654_dbl__inc__def,axiom,
% 8.57/4.52      ( neg_nu5831290666863070958nteger
% 8.57/4.52      = ( ^ [X: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X @ X ) @ one_one_Code_integer ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_655_dbl__inc__def,axiom,
% 8.57/4.52      ( neg_nu5219082963157363817nc_rat
% 8.57/4.52      = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_656_dbl__inc__def,axiom,
% 8.57/4.52      ( neg_nu5851722552734809277nc_int
% 8.57/4.52      = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_657_bind__lift,axiom,
% 8.57/4.52      ! [F: heap_T5738788834812785303t_unit,G: product_unit > a] :
% 8.57/4.52        ( ( heap_T757603679106148408unit_a @ F @ ( heap_T6901581777565460678unit_a @ G ) )
% 8.57/4.52        = ( heap_T757603679106148408unit_a @ F
% 8.57/4.52          @ ^ [X: product_unit] : ( heap_Time_return_a @ ( G @ X ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_658_bind__lift,axiom,
% 8.57/4.52      ! [F: heap_T5738788834812785303t_unit,G: product_unit > product_unit] :
% 8.57/4.52        ( ( heap_T2633723481742716231t_unit @ F @ ( heap_T7011250591035762645t_unit @ G ) )
% 8.57/4.52        = ( heap_T2633723481742716231t_unit @ F
% 8.57/4.52          @ ^ [X: product_unit] : ( heap_T7507251653302230130t_unit @ ( G @ X ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_659_bind__lift,axiom,
% 8.57/4.52      ! [F: heap_Time_Heap_a,G: a > a] :
% 8.57/4.52        ( ( heap_Time_bind_a_a @ F @ ( heap_Time_lift_a_a @ G ) )
% 8.57/4.52        = ( heap_Time_bind_a_a @ F
% 8.57/4.52          @ ^ [X: a] : ( heap_Time_return_a @ ( G @ X ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_660_lookup__chain,axiom,
% 8.57/4.52      ! [R: ref_Product_unit,F: heap_Time_Heap_a] :
% 8.57/4.52        ( ( heap_T757603679106148408unit_a @ ( ref_lo7930775386976318366t_unit @ R )
% 8.57/4.52          @ ^ [Uu: product_unit] : F )
% 8.57/4.52        = ( heap_T757603679106148408unit_a @ ( heap_Time_wait @ one_one_nat )
% 8.57/4.52          @ ^ [Uu: product_unit] : F ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_661_lookup__chain,axiom,
% 8.57/4.52      ! [R: ref_Product_unit,F: heap_T5738788834812785303t_unit] :
% 8.57/4.52        ( ( heap_T2633723481742716231t_unit @ ( ref_lo7930775386976318366t_unit @ R )
% 8.57/4.52          @ ^ [Uu: product_unit] : F )
% 8.57/4.52        = ( heap_T2633723481742716231t_unit @ ( heap_Time_wait @ one_one_nat )
% 8.57/4.52          @ ^ [Uu: product_unit] : F ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_662_ceiling__add__one,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 8.57/4.52        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_663_ceiling__le__one,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 8.57/4.52        = ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_664_ceiling__le__zero,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 8.57/4.52        = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_665_of__int__le__1__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ one_one_Code_integer )
% 8.57/4.52        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_666_of__int__le__1__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 8.57/4.52        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_667_of__int__le__1__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 8.57/4.52        = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_668_of__int__1__le__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.52        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_669_of__int__1__le__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.52        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_670_of__int__1__le__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.52        = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_671_of__int__eq__iff,axiom,
% 8.57/4.52      ! [W2: int,Z2: int] :
% 8.57/4.52        ( ( ( ring_18347121197199848620nteger @ W2 )
% 8.57/4.52          = ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.52        = ( W2 = Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_672_of__int__eq__iff,axiom,
% 8.57/4.52      ! [W2: int,Z2: int] :
% 8.57/4.52        ( ( ( ring_1_of_int_rat @ W2 )
% 8.57/4.52          = ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.52        = ( W2 = Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_673_of__int__eq__iff,axiom,
% 8.57/4.52      ! [W2: int,Z2: int] :
% 8.57/4.52        ( ( ( ring_1_of_int_int @ W2 )
% 8.57/4.52          = ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.52        = ( W2 = Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_674_ceiling__of__int,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( archim2889992004027027881ng_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.52        = Z2 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_675_of__int__0,axiom,
% 8.57/4.52      ( ( ring_18347121197199848620nteger @ zero_zero_int )
% 8.57/4.52      = zero_z3403309356797280102nteger ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_676_of__int__0,axiom,
% 8.57/4.52      ( ( ring_1_of_int_rat @ zero_zero_int )
% 8.57/4.52      = zero_zero_rat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_677_of__int__0,axiom,
% 8.57/4.52      ( ( ring_1_of_int_int @ zero_zero_int )
% 8.57/4.52      = zero_zero_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_678_of__int__0__eq__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( zero_z3403309356797280102nteger
% 8.57/4.52          = ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.52        = ( Z2 = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_679_of__int__0__eq__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( zero_zero_rat
% 8.57/4.52          = ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.52        = ( Z2 = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_680_of__int__0__eq__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( zero_zero_int
% 8.57/4.52          = ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.52        = ( Z2 = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_681_of__int__eq__0__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ( ring_18347121197199848620nteger @ Z2 )
% 8.57/4.52          = zero_z3403309356797280102nteger )
% 8.57/4.52        = ( Z2 = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_682_of__int__eq__0__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ( ring_1_of_int_rat @ Z2 )
% 8.57/4.52          = zero_zero_rat )
% 8.57/4.52        = ( Z2 = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_683_of__int__eq__0__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ( ring_1_of_int_int @ Z2 )
% 8.57/4.52          = zero_zero_int )
% 8.57/4.52        = ( Z2 = zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_684_of__int__le__iff,axiom,
% 8.57/4.52      ! [W2: int,Z2: int] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.52        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_685_of__int__le__iff,axiom,
% 8.57/4.52      ! [W2: int,Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.52        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_686_of__int__le__iff,axiom,
% 8.57/4.52      ! [W2: int,Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.52        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_687_of__int__eq__1__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ( ring_18347121197199848620nteger @ Z2 )
% 8.57/4.52          = one_one_Code_integer )
% 8.57/4.52        = ( Z2 = one_one_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_688_of__int__eq__1__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ( ring_1_of_int_rat @ Z2 )
% 8.57/4.52          = one_one_rat )
% 8.57/4.52        = ( Z2 = one_one_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_689_of__int__eq__1__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ( ring_1_of_int_int @ Z2 )
% 8.57/4.52          = one_one_int )
% 8.57/4.52        = ( Z2 = one_one_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_690_of__int__1,axiom,
% 8.57/4.52      ( ( ring_18347121197199848620nteger @ one_one_int )
% 8.57/4.52      = one_one_Code_integer ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_691_of__int__1,axiom,
% 8.57/4.52      ( ( ring_1_of_int_rat @ one_one_int )
% 8.57/4.52      = one_one_rat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_692_of__int__1,axiom,
% 8.57/4.52      ( ( ring_1_of_int_int @ one_one_int )
% 8.57/4.52      = one_one_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_693_of__int__add,axiom,
% 8.57/4.52      ! [W2: int,Z2: int] :
% 8.57/4.52        ( ( ring_18347121197199848620nteger @ ( plus_plus_int @ W2 @ Z2 ) )
% 8.57/4.52        = ( plus_p5714425477246183910nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_694_of__int__add,axiom,
% 8.57/4.52      ! [W2: int,Z2: int] :
% 8.57/4.52        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W2 @ Z2 ) )
% 8.57/4.52        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_695_of__int__add,axiom,
% 8.57/4.52      ! [W2: int,Z2: int] :
% 8.57/4.52        ( ( ring_1_of_int_int @ ( plus_plus_int @ W2 @ Z2 ) )
% 8.57/4.52        = ( plus_plus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_696_ceiling__zero,axiom,
% 8.57/4.52      ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 8.57/4.52      = zero_zero_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_697_of__int__of__nat__eq,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( semiri1314217659103216013at_int @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_698_of__int__of__nat__eq,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ring_18347121197199848620nteger @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( semiri4939895301339042750nteger @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_699_of__int__of__nat__eq,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( semiri681578069525770553at_rat @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_700_ceiling__one,axiom,
% 8.57/4.52      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 8.57/4.52      = one_one_int ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_701_ceiling__of__nat,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( archim2889992004027027881ng_rat @ ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.52        = ( semiri1314217659103216013at_int @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_702_ceiling__add__of__int,axiom,
% 8.57/4.52      ! [X2: rat,Z2: int] :
% 8.57/4.52        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) )
% 8.57/4.52        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_703_of__int__le__0__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ zero_z3403309356797280102nteger )
% 8.57/4.52        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_704_of__int__le__0__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 8.57/4.52        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_705_of__int__le__0__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 8.57/4.52        = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_706_of__int__0__le__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.52        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_707_of__int__0__le__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.52        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_708_of__int__0__le__iff,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.52        = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_709_le__of__int__ceiling,axiom,
% 8.57/4.52      ! [X2: rat] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_710_ceiling__le__iff,axiom,
% 8.57/4.52      ! [X2: rat,Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z2 )
% 8.57/4.52        = ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_711_ex__le__of__int,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52      ? [Z4: int] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z4 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_712_ceiling__mono,axiom,
% 8.57/4.52      ! [Y: rat,X2: rat] :
% 8.57/4.52        ( ( ord_less_eq_rat @ Y @ X2 )
% 8.57/4.52       => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_713_ceiling__add__le,axiom,
% 8.57/4.52      ! [X2: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_714_of__int__nonneg,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.52       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_715_of__int__nonneg,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.52       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_716_of__int__nonneg,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.52       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_717_change__def,axiom,
% 8.57/4.52      ( ref_ch7259622376331601608t_unit
% 8.57/4.52      = ( ^ [F3: product_unit > product_unit,R2: ref_Product_unit] :
% 8.57/4.52            ( heap_T2633723481742716231t_unit @ ( ref_lo7930775386976318366t_unit @ R2 )
% 8.57/4.52            @ ^ [X: product_unit] :
% 8.57/4.52                ( heap_T2633723481742716231t_unit @ ( ref_up627237114476368303t_unit @ R2 @ ( F3 @ X ) )
% 8.57/4.52                @ ^ [Uu: product_unit] : ( heap_T7507251653302230130t_unit @ ( F3 @ X ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_718_one__le__ceiling,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.52        = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_719_ceiling__less__one,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 8.57/4.52        = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_720_of__nat__nat,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.52       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 8.57/4.52          = ( ring_1_of_int_int @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_721_of__nat__nat,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.52       => ( ( semiri4939895301339042750nteger @ ( nat2 @ Z2 ) )
% 8.57/4.52          = ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_722_of__nat__nat,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.52       => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z2 ) )
% 8.57/4.52          = ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_723_one__le__floor,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.52        = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_724_power__int__decreasing,axiom,
% 8.57/4.52      ! [N: int,N4: int,A: rat] :
% 8.57/4.52        ( ( ord_less_eq_int @ N @ N4 )
% 8.57/4.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.52         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.57/4.52           => ( ( ( A != zero_zero_rat )
% 8.57/4.52                | ( N4 != zero_zero_int )
% 8.57/4.52                | ( N = zero_zero_int ) )
% 8.57/4.52             => ( ord_less_eq_rat @ ( power_int_rat @ A @ N4 ) @ ( power_int_rat @ A @ N ) ) ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_725_power__int__le__one,axiom,
% 8.57/4.52      ! [X2: rat,N: int] :
% 8.57/4.52        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.52       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 8.57/4.52         => ( ( ord_less_eq_rat @ X2 @ one_one_rat )
% 8.57/4.52           => ( ord_less_eq_rat @ ( power_int_rat @ X2 @ N ) @ one_one_rat ) ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_726_zero__le__floor,axiom,
% 8.57/4.52      ! [X2: rat] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.52        = ( ord_less_eq_rat @ zero_zero_rat @ X2 ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_727_rotate1__length01,axiom,
% 8.57/4.52      ! [Xs: list_nat] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 8.57/4.52       => ( ( rotate1_nat @ Xs )
% 8.57/4.52          = Xs ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_728_rotate1__length01,axiom,
% 8.57/4.52      ! [Xs: list_int] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 8.57/4.52       => ( ( rotate1_int @ Xs )
% 8.57/4.52          = Xs ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_729_rotate1__length01,axiom,
% 8.57/4.52      ! [Xs: list_o] :
% 8.57/4.52        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 8.57/4.52       => ( ( rotate1_o @ Xs )
% 8.57/4.52          = Xs ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_730_le__imp__0__less,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.52       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_731_bot__nat__0_Onot__eq__extremum,axiom,
% 8.57/4.52      ! [A: nat] :
% 8.57/4.52        ( ( A != zero_zero_nat )
% 8.57/4.52        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_732_neq0__conv,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( N != zero_zero_nat )
% 8.57/4.52        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_733_less__nat__zero__code,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_734_nat__add__left__cancel__less,axiom,
% 8.57/4.52      ! [K: nat,M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 8.57/4.52        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_735_not__gr__zero,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 8.57/4.52        = ( N = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_736_add__less__cancel__left,axiom,
% 8.57/4.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 8.57/4.52        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_737_add__less__cancel__left,axiom,
% 8.57/4.52      ! [C: rat,A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.57/4.52        = ( ord_less_rat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_738_add__less__cancel__left,axiom,
% 8.57/4.52      ! [C: nat,A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.57/4.52        = ( ord_less_nat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_739_add__less__cancel__left,axiom,
% 8.57/4.52      ! [C: int,A: int,B: int] :
% 8.57/4.52        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.57/4.52        = ( ord_less_int @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_740_add__less__cancel__right,axiom,
% 8.57/4.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.52        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_741_add__less__cancel__right,axiom,
% 8.57/4.52      ! [A: rat,C: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.52        = ( ord_less_rat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_742_add__less__cancel__right,axiom,
% 8.57/4.52      ! [A: nat,C: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.57/4.52        = ( ord_less_nat @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_743_add__less__cancel__right,axiom,
% 8.57/4.52      ! [A: int,C: int,B: int] :
% 8.57/4.52        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.57/4.52        = ( ord_less_int @ A @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_744_of__nat__less__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_745_of__nat__less__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.57/4.52        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_746_of__nat__less__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 8.57/4.52        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_747_of__nat__less__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.52        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_748_of__nat__less__iff,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) )
% 8.57/4.52        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_749_add__gr__0,axiom,
% 8.57/4.52      ! [M: nat,N: nat] :
% 8.57/4.52        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.52        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.52          | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_750_less__one,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( ord_less_nat @ N @ one_one_nat )
% 8.57/4.52        = ( N = zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_751_power__int__1__left,axiom,
% 8.57/4.52      ! [N: int] :
% 8.57/4.52        ( ( power_int_rat @ one_one_rat @ N )
% 8.57/4.52        = one_one_rat ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_752_nat__int,axiom,
% 8.57/4.52      ! [N: nat] :
% 8.57/4.52        ( ( nat2 @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.52        = N ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_753_floor__of__int,axiom,
% 8.57/4.52      ! [Z2: int] :
% 8.57/4.52        ( ( archim3151403230148437115or_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.52        = Z2 ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_754_length__rotate1,axiom,
% 8.57/4.52      ! [Xs: list_nat] :
% 8.57/4.52        ( ( size_size_list_nat @ ( rotate1_nat @ Xs ) )
% 8.57/4.52        = ( size_size_list_nat @ Xs ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_755_length__rotate1,axiom,
% 8.57/4.52      ! [Xs: list_int] :
% 8.57/4.52        ( ( size_size_list_int @ ( rotate1_int @ Xs ) )
% 8.57/4.52        = ( size_size_list_int @ Xs ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_756_length__rotate1,axiom,
% 8.57/4.52      ! [Xs: list_o] :
% 8.57/4.52        ( ( size_size_list_o @ ( rotate1_o @ Xs ) )
% 8.57/4.52        = ( size_size_list_o @ Xs ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_757_add__less__same__cancel1,axiom,
% 8.57/4.52      ! [B: code_natural,A: code_natural] :
% 8.57/4.52        ( ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 8.57/4.52        = ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_758_add__less__same__cancel1,axiom,
% 8.57/4.52      ! [B: code_integer,A: code_integer] :
% 8.57/4.52        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 8.57/4.52        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_759_add__less__same__cancel1,axiom,
% 8.57/4.52      ! [B: rat,A: rat] :
% 8.57/4.52        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 8.57/4.52        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_760_add__less__same__cancel1,axiom,
% 8.57/4.52      ! [B: nat,A: nat] :
% 8.57/4.52        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.57/4.52        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_761_add__less__same__cancel1,axiom,
% 8.57/4.52      ! [B: int,A: int] :
% 8.57/4.52        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.57/4.52        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_762_add__less__same__cancel2,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 8.57/4.52        = ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_763_add__less__same__cancel2,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 8.57/4.52        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_764_add__less__same__cancel2,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.57/4.52        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_765_add__less__same__cancel2,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.57/4.52        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_766_add__less__same__cancel2,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.57/4.52        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_767_less__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le5570908160329646204atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 8.57/4.52        = ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_768_less__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.57/4.52        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_769_less__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.57/4.52        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_770_less__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.57/4.52        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_771_less__add__same__cancel1,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.57/4.52        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_772_less__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: code_natural,B: code_natural] :
% 8.57/4.52        ( ( ord_le5570908160329646204atural @ A @ ( plus_p4538020629002901425atural @ B @ A ) )
% 8.57/4.52        = ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_773_less__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: code_integer,B: code_integer] :
% 8.57/4.52        ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 8.57/4.52        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_774_less__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: rat,B: rat] :
% 8.57/4.52        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 8.57/4.52        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_775_less__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: nat,B: nat] :
% 8.57/4.52        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 8.57/4.52        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_776_less__add__same__cancel2,axiom,
% 8.57/4.52      ! [A: int,B: int] :
% 8.57/4.52        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 8.57/4.52        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 8.57/4.52  
% 8.57/4.52  thf(fact_777_double__add__less__zero__iff__single__add__less__zero,axiom,
% 8.57/4.52      ! [A: code_integer] :
% 8.57/4.52        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 8.57/4.52        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_778_double__add__less__zero__iff__single__add__less__zero,axiom,
% 8.57/4.53      ! [A: rat] :
% 8.57/4.53        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 8.57/4.53        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_779_double__add__less__zero__iff__single__add__less__zero,axiom,
% 8.57/4.53      ! [A: int] :
% 8.57/4.53        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 8.57/4.53        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_780_zero__less__double__add__iff__zero__less__single__add,axiom,
% 8.57/4.53      ! [A: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 8.57/4.53        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_781_zero__less__double__add__iff__zero__less__single__add,axiom,
% 8.57/4.53      ! [A: rat] :
% 8.57/4.53        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 8.57/4.53        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_782_zero__less__double__add__iff__zero__less__single__add,axiom,
% 8.57/4.53      ! [A: int] :
% 8.57/4.53        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 8.57/4.53        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_783_of__int__less__iff,axiom,
% 8.57/4.53      ! [W2: int,Z2: int] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_784_of__int__less__iff,axiom,
% 8.57/4.53      ! [W2: int,Z2: int] :
% 8.57/4.53        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_785_of__int__less__iff,axiom,
% 8.57/4.53      ! [W2: int,Z2: int] :
% 8.57/4.53        ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_786_power__int__eq__0__iff,axiom,
% 8.57/4.53      ! [X2: rat,N: int] :
% 8.57/4.53        ( ( ( power_int_rat @ X2 @ N )
% 8.57/4.53          = zero_zero_rat )
% 8.57/4.53        = ( ( X2 = zero_zero_rat )
% 8.57/4.53          & ( N != zero_zero_int ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_787_power__int__0__left,axiom,
% 8.57/4.53      ! [M: int] :
% 8.57/4.53        ( ( M != zero_zero_int )
% 8.57/4.53       => ( ( power_int_rat @ zero_zero_rat @ M )
% 8.57/4.53          = zero_zero_rat ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_788_floor__zero,axiom,
% 8.57/4.53      ( ( archim3151403230148437115or_rat @ zero_zero_rat )
% 8.57/4.53      = zero_zero_int ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_789_power__int__0__right,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53        ( ( power_int_rat @ X2 @ zero_zero_int )
% 8.57/4.53        = one_one_rat ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_790_zless__nat__conj,axiom,
% 8.57/4.53      ! [W2: int,Z2: int] :
% 8.57/4.53        ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 8.57/4.53        = ( ( ord_less_int @ zero_zero_int @ Z2 )
% 8.57/4.53          & ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_791_floor__one,axiom,
% 8.57/4.53      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 8.57/4.53      = one_one_int ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_792_floor__of__nat,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53        ( ( archim3151403230148437115or_rat @ ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.53        = ( semiri1314217659103216013at_int @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_793_of__nat__0__less__iff,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.53        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_794_of__nat__0__less__iff,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 8.57/4.53        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_795_of__nat__0__less__iff,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) )
% 8.57/4.53        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_796_of__nat__0__less__iff,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.53        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_797_of__nat__0__less__iff,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( semiri3763490453095760265atural @ N ) )
% 8.57/4.53        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_798_nat__0__iff,axiom,
% 8.57/4.53      ! [I: int] :
% 8.57/4.53        ( ( ( nat2 @ I )
% 8.57/4.53          = zero_zero_nat )
% 8.57/4.53        = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_799_nat__le__0,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 8.57/4.53       => ( ( nat2 @ Z2 )
% 8.57/4.53          = zero_zero_nat ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_800_zero__less__nat__eq,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_801_zle__add1__eq__le,axiom,
% 8.57/4.53      ! [W2: int,Z2: int] :
% 8.57/4.53        ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 8.57/4.53        = ( ord_less_eq_int @ W2 @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_802_int__nat__eq,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.53         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 8.57/4.53            = Z2 ) )
% 8.57/4.53        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.53         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 8.57/4.53            = zero_zero_int ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_803_of__int__less__0__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ zero_z3403309356797280102nteger )
% 8.57/4.53        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_804_of__int__less__0__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 8.57/4.53        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_805_of__int__less__0__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 8.57/4.53        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_806_of__int__0__less__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_807_of__int__0__less__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_808_of__int__0__less__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_809_power__int__mono__iff,axiom,
% 8.57/4.53      ! [A: rat,B: rat,N: int] :
% 8.57/4.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.53         => ( ( ord_less_int @ zero_zero_int @ N )
% 8.57/4.53           => ( ( ord_less_eq_rat @ ( power_int_rat @ A @ N ) @ ( power_int_rat @ B @ N ) )
% 8.57/4.53              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_810_of__int__less__1__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ one_one_Code_integer )
% 8.57/4.53        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_811_of__int__less__1__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 8.57/4.53        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_812_of__int__less__1__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 8.57/4.53        = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_813_of__int__1__less__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_814_of__int__1__less__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_815_of__int__1__less__iff,axiom,
% 8.57/4.53      ! [Z2: int] :
% 8.57/4.53        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_816_floor__less__zero,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 8.57/4.53        = ( ord_less_rat @ X2 @ zero_zero_rat ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_817_zero__less__floor,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.53        = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_818_floor__le__zero,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 8.57/4.53        = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_819_zero__less__ceiling,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53        ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.53        = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_820_floor__less__one,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 8.57/4.53        = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_821_one__less__ceiling,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.53        = ( ord_less_rat @ one_one_rat @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_822_neq__if__length__neq,axiom,
% 8.57/4.53      ! [Xs: list_nat,Ys: list_nat] :
% 8.57/4.53        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.53         != ( size_size_list_nat @ Ys ) )
% 8.57/4.53       => ( Xs != Ys ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_823_neq__if__length__neq,axiom,
% 8.57/4.53      ! [Xs: list_int,Ys: list_int] :
% 8.57/4.53        ( ( ( size_size_list_int @ Xs )
% 8.57/4.53         != ( size_size_list_int @ Ys ) )
% 8.57/4.53       => ( Xs != Ys ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_824_neq__if__length__neq,axiom,
% 8.57/4.53      ! [Xs: list_o,Ys: list_o] :
% 8.57/4.53        ( ( ( size_size_list_o @ Xs )
% 8.57/4.53         != ( size_size_list_o @ Ys ) )
% 8.57/4.53       => ( Xs != Ys ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_825_Ex__list__of__length,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53      ? [Xs2: list_nat] :
% 8.57/4.53        ( ( size_size_list_nat @ Xs2 )
% 8.57/4.53        = N ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_826_Ex__list__of__length,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53      ? [Xs2: list_int] :
% 8.57/4.53        ( ( size_size_list_int @ Xs2 )
% 8.57/4.53        = N ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_827_Ex__list__of__length,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53      ? [Xs2: list_o] :
% 8.57/4.53        ( ( size_size_list_o @ Xs2 )
% 8.57/4.53        = N ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_828_length__induct,axiom,
% 8.57/4.53      ! [P: list_nat > $o,Xs: list_nat] :
% 8.57/4.53        ( ! [Xs2: list_nat] :
% 8.57/4.53            ( ! [Ys2: list_nat] :
% 8.57/4.53                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 8.57/4.53               => ( P @ Ys2 ) )
% 8.57/4.53           => ( P @ Xs2 ) )
% 8.57/4.53       => ( P @ Xs ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_829_length__induct,axiom,
% 8.57/4.53      ! [P: list_int > $o,Xs: list_int] :
% 8.57/4.53        ( ! [Xs2: list_int] :
% 8.57/4.53            ( ! [Ys2: list_int] :
% 8.57/4.53                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 8.57/4.53               => ( P @ Ys2 ) )
% 8.57/4.53           => ( P @ Xs2 ) )
% 8.57/4.53       => ( P @ Xs ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_830_length__induct,axiom,
% 8.57/4.53      ! [P: list_o > $o,Xs: list_o] :
% 8.57/4.53        ( ! [Xs2: list_o] :
% 8.57/4.53            ( ! [Ys2: list_o] :
% 8.57/4.53                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs2 ) )
% 8.57/4.53               => ( P @ Ys2 ) )
% 8.57/4.53           => ( P @ Xs2 ) )
% 8.57/4.53       => ( P @ Xs ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_831_floor__less__iff,axiom,
% 8.57/4.53      ! [X2: rat,Z2: int] :
% 8.57/4.53        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z2 )
% 8.57/4.53        = ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_832_minf_I7_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_le6747313008572928689nteger @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_833_minf_I7_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_less_rat @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_834_minf_I7_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_less_num @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_835_minf_I7_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_less_nat @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_836_minf_I7_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_less_int @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_837_minf_I5_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 8.57/4.53       => ( ord_le6747313008572928689nteger @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_838_minf_I5_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X4 @ Z4 )
% 8.57/4.53       => ( ord_less_rat @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_839_minf_I5_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ X4 @ Z4 )
% 8.57/4.53       => ( ord_less_num @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_840_minf_I5_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X4 @ Z4 )
% 8.57/4.53       => ( ord_less_nat @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_841_minf_I5_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ X4 @ Z4 )
% 8.57/4.53       => ( ord_less_int @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_842_minf_I4_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_843_minf_I4_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_844_minf_I4_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_845_minf_I4_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_846_minf_I4_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_847_minf_I3_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_848_minf_I3_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_849_minf_I3_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_850_minf_I3_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_851_minf_I3_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ X4 @ Z4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_852_minf_I2_J,axiom,
% 8.57/4.53      ! [P: code_integer > $o,P2: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 8.57/4.53        ( ? [Z5: code_integer] :
% 8.57/4.53          ! [X3: code_integer] :
% 8.57/4.53            ( ( ord_le6747313008572928689nteger @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: code_integer] :
% 8.57/4.53            ! [X3: code_integer] :
% 8.57/4.53              ( ( ord_le6747313008572928689nteger @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: code_integer] :
% 8.57/4.53            ! [X4: code_integer] :
% 8.57/4.53              ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_853_minf_I2_J,axiom,
% 8.57/4.53      ! [P: rat > $o,P2: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 8.57/4.53        ( ? [Z5: rat] :
% 8.57/4.53          ! [X3: rat] :
% 8.57/4.53            ( ( ord_less_rat @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: rat] :
% 8.57/4.53            ! [X3: rat] :
% 8.57/4.53              ( ( ord_less_rat @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: rat] :
% 8.57/4.53            ! [X4: rat] :
% 8.57/4.53              ( ( ord_less_rat @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_854_minf_I2_J,axiom,
% 8.57/4.53      ! [P: num > $o,P2: num > $o,Q: num > $o,Q3: num > $o] :
% 8.57/4.53        ( ? [Z5: num] :
% 8.57/4.53          ! [X3: num] :
% 8.57/4.53            ( ( ord_less_num @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: num] :
% 8.57/4.53            ! [X3: num] :
% 8.57/4.53              ( ( ord_less_num @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: num] :
% 8.57/4.53            ! [X4: num] :
% 8.57/4.53              ( ( ord_less_num @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_855_minf_I2_J,axiom,
% 8.57/4.53      ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 8.57/4.53        ( ? [Z5: nat] :
% 8.57/4.53          ! [X3: nat] :
% 8.57/4.53            ( ( ord_less_nat @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: nat] :
% 8.57/4.53            ! [X3: nat] :
% 8.57/4.53              ( ( ord_less_nat @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: nat] :
% 8.57/4.53            ! [X4: nat] :
% 8.57/4.53              ( ( ord_less_nat @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_856_minf_I2_J,axiom,
% 8.57/4.53      ! [P: int > $o,P2: int > $o,Q: int > $o,Q3: int > $o] :
% 8.57/4.53        ( ? [Z5: int] :
% 8.57/4.53          ! [X3: int] :
% 8.57/4.53            ( ( ord_less_int @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: int] :
% 8.57/4.53            ! [X3: int] :
% 8.57/4.53              ( ( ord_less_int @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: int] :
% 8.57/4.53            ! [X4: int] :
% 8.57/4.53              ( ( ord_less_int @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_857_minf_I1_J,axiom,
% 8.57/4.53      ! [P: code_integer > $o,P2: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 8.57/4.53        ( ? [Z5: code_integer] :
% 8.57/4.53          ! [X3: code_integer] :
% 8.57/4.53            ( ( ord_le6747313008572928689nteger @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: code_integer] :
% 8.57/4.53            ! [X3: code_integer] :
% 8.57/4.53              ( ( ord_le6747313008572928689nteger @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: code_integer] :
% 8.57/4.53            ! [X4: code_integer] :
% 8.57/4.53              ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_858_minf_I1_J,axiom,
% 8.57/4.53      ! [P: rat > $o,P2: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 8.57/4.53        ( ? [Z5: rat] :
% 8.57/4.53          ! [X3: rat] :
% 8.57/4.53            ( ( ord_less_rat @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: rat] :
% 8.57/4.53            ! [X3: rat] :
% 8.57/4.53              ( ( ord_less_rat @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: rat] :
% 8.57/4.53            ! [X4: rat] :
% 8.57/4.53              ( ( ord_less_rat @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_859_minf_I1_J,axiom,
% 8.57/4.53      ! [P: num > $o,P2: num > $o,Q: num > $o,Q3: num > $o] :
% 8.57/4.53        ( ? [Z5: num] :
% 8.57/4.53          ! [X3: num] :
% 8.57/4.53            ( ( ord_less_num @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: num] :
% 8.57/4.53            ! [X3: num] :
% 8.57/4.53              ( ( ord_less_num @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: num] :
% 8.57/4.53            ! [X4: num] :
% 8.57/4.53              ( ( ord_less_num @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_860_minf_I1_J,axiom,
% 8.57/4.53      ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 8.57/4.53        ( ? [Z5: nat] :
% 8.57/4.53          ! [X3: nat] :
% 8.57/4.53            ( ( ord_less_nat @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: nat] :
% 8.57/4.53            ! [X3: nat] :
% 8.57/4.53              ( ( ord_less_nat @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: nat] :
% 8.57/4.53            ! [X4: nat] :
% 8.57/4.53              ( ( ord_less_nat @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_861_minf_I1_J,axiom,
% 8.57/4.53      ! [P: int > $o,P2: int > $o,Q: int > $o,Q3: int > $o] :
% 8.57/4.53        ( ? [Z5: int] :
% 8.57/4.53          ! [X3: int] :
% 8.57/4.53            ( ( ord_less_int @ X3 @ Z5 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: int] :
% 8.57/4.53            ! [X3: int] :
% 8.57/4.53              ( ( ord_less_int @ X3 @ Z5 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: int] :
% 8.57/4.53            ! [X4: int] :
% 8.57/4.53              ( ( ord_less_int @ X4 @ Z4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_862_pinf_I7_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 8.57/4.53       => ( ord_le6747313008572928689nteger @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_863_pinf_I7_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ Z4 @ X4 )
% 8.57/4.53       => ( ord_less_rat @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_864_pinf_I7_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ Z4 @ X4 )
% 8.57/4.53       => ( ord_less_num @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_865_pinf_I7_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ Z4 @ X4 )
% 8.57/4.53       => ( ord_less_nat @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_866_pinf_I7_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ Z4 @ X4 )
% 8.57/4.53       => ( ord_less_int @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_867_pinf_I5_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_le6747313008572928689nteger @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_868_pinf_I5_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_less_rat @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_869_pinf_I5_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_less_num @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_870_pinf_I5_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_less_nat @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_871_pinf_I5_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_less_int @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_872_pinf_I4_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_873_pinf_I4_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_874_pinf_I4_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_875_pinf_I4_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_876_pinf_I4_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_877_pinf_I3_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_878_pinf_I3_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_879_pinf_I3_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_880_pinf_I3_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_881_pinf_I3_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ Z4 @ X4 )
% 8.57/4.53       => ( X4 != T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_882_pinf_I2_J,axiom,
% 8.57/4.53      ! [P: code_integer > $o,P2: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 8.57/4.53        ( ? [Z5: code_integer] :
% 8.57/4.53          ! [X3: code_integer] :
% 8.57/4.53            ( ( ord_le6747313008572928689nteger @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: code_integer] :
% 8.57/4.53            ! [X3: code_integer] :
% 8.57/4.53              ( ( ord_le6747313008572928689nteger @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: code_integer] :
% 8.57/4.53            ! [X4: code_integer] :
% 8.57/4.53              ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_883_pinf_I2_J,axiom,
% 8.57/4.53      ! [P: rat > $o,P2: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 8.57/4.53        ( ? [Z5: rat] :
% 8.57/4.53          ! [X3: rat] :
% 8.57/4.53            ( ( ord_less_rat @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: rat] :
% 8.57/4.53            ! [X3: rat] :
% 8.57/4.53              ( ( ord_less_rat @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: rat] :
% 8.57/4.53            ! [X4: rat] :
% 8.57/4.53              ( ( ord_less_rat @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_884_pinf_I2_J,axiom,
% 8.57/4.53      ! [P: num > $o,P2: num > $o,Q: num > $o,Q3: num > $o] :
% 8.57/4.53        ( ? [Z5: num] :
% 8.57/4.53          ! [X3: num] :
% 8.57/4.53            ( ( ord_less_num @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: num] :
% 8.57/4.53            ! [X3: num] :
% 8.57/4.53              ( ( ord_less_num @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: num] :
% 8.57/4.53            ! [X4: num] :
% 8.57/4.53              ( ( ord_less_num @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_885_pinf_I2_J,axiom,
% 8.57/4.53      ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 8.57/4.53        ( ? [Z5: nat] :
% 8.57/4.53          ! [X3: nat] :
% 8.57/4.53            ( ( ord_less_nat @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: nat] :
% 8.57/4.53            ! [X3: nat] :
% 8.57/4.53              ( ( ord_less_nat @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: nat] :
% 8.57/4.53            ! [X4: nat] :
% 8.57/4.53              ( ( ord_less_nat @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_886_pinf_I2_J,axiom,
% 8.57/4.53      ! [P: int > $o,P2: int > $o,Q: int > $o,Q3: int > $o] :
% 8.57/4.53        ( ? [Z5: int] :
% 8.57/4.53          ! [X3: int] :
% 8.57/4.53            ( ( ord_less_int @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: int] :
% 8.57/4.53            ! [X3: int] :
% 8.57/4.53              ( ( ord_less_int @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: int] :
% 8.57/4.53            ! [X4: int] :
% 8.57/4.53              ( ( ord_less_int @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  | ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  | ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_887_pinf_I1_J,axiom,
% 8.57/4.53      ! [P: code_integer > $o,P2: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 8.57/4.53        ( ? [Z5: code_integer] :
% 8.57/4.53          ! [X3: code_integer] :
% 8.57/4.53            ( ( ord_le6747313008572928689nteger @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: code_integer] :
% 8.57/4.53            ! [X3: code_integer] :
% 8.57/4.53              ( ( ord_le6747313008572928689nteger @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: code_integer] :
% 8.57/4.53            ! [X4: code_integer] :
% 8.57/4.53              ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_888_pinf_I1_J,axiom,
% 8.57/4.53      ! [P: rat > $o,P2: rat > $o,Q: rat > $o,Q3: rat > $o] :
% 8.57/4.53        ( ? [Z5: rat] :
% 8.57/4.53          ! [X3: rat] :
% 8.57/4.53            ( ( ord_less_rat @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: rat] :
% 8.57/4.53            ! [X3: rat] :
% 8.57/4.53              ( ( ord_less_rat @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: rat] :
% 8.57/4.53            ! [X4: rat] :
% 8.57/4.53              ( ( ord_less_rat @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_889_pinf_I1_J,axiom,
% 8.57/4.53      ! [P: num > $o,P2: num > $o,Q: num > $o,Q3: num > $o] :
% 8.57/4.53        ( ? [Z5: num] :
% 8.57/4.53          ! [X3: num] :
% 8.57/4.53            ( ( ord_less_num @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: num] :
% 8.57/4.53            ! [X3: num] :
% 8.57/4.53              ( ( ord_less_num @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: num] :
% 8.57/4.53            ! [X4: num] :
% 8.57/4.53              ( ( ord_less_num @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_890_pinf_I1_J,axiom,
% 8.57/4.53      ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 8.57/4.53        ( ? [Z5: nat] :
% 8.57/4.53          ! [X3: nat] :
% 8.57/4.53            ( ( ord_less_nat @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: nat] :
% 8.57/4.53            ! [X3: nat] :
% 8.57/4.53              ( ( ord_less_nat @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: nat] :
% 8.57/4.53            ! [X4: nat] :
% 8.57/4.53              ( ( ord_less_nat @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_891_pinf_I1_J,axiom,
% 8.57/4.53      ! [P: int > $o,P2: int > $o,Q: int > $o,Q3: int > $o] :
% 8.57/4.53        ( ? [Z5: int] :
% 8.57/4.53          ! [X3: int] :
% 8.57/4.53            ( ( ord_less_int @ Z5 @ X3 )
% 8.57/4.53           => ( ( P @ X3 )
% 8.57/4.53              = ( P2 @ X3 ) ) )
% 8.57/4.53       => ( ? [Z5: int] :
% 8.57/4.53            ! [X3: int] :
% 8.57/4.53              ( ( ord_less_int @ Z5 @ X3 )
% 8.57/4.53             => ( ( Q @ X3 )
% 8.57/4.53                = ( Q3 @ X3 ) ) )
% 8.57/4.53         => ? [Z4: int] :
% 8.57/4.53            ! [X4: int] :
% 8.57/4.53              ( ( ord_less_int @ Z4 @ X4 )
% 8.57/4.53             => ( ( ( P @ X4 )
% 8.57/4.53                  & ( Q @ X4 ) )
% 8.57/4.53                = ( ( P2 @ X4 )
% 8.57/4.53                  & ( Q3 @ X4 ) ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_892_lt__ex,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53      ? [Y2: rat] : ( ord_less_rat @ Y2 @ X2 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_893_lt__ex,axiom,
% 8.57/4.53      ! [X2: int] :
% 8.57/4.53      ? [Y2: int] : ( ord_less_int @ Y2 @ X2 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_894_gt__ex,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53      ? [X_12: rat] : ( ord_less_rat @ X2 @ X_12 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_895_gt__ex,axiom,
% 8.57/4.53      ! [X2: nat] :
% 8.57/4.53      ? [X_12: nat] : ( ord_less_nat @ X2 @ X_12 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_896_gt__ex,axiom,
% 8.57/4.53      ! [X2: int] :
% 8.57/4.53      ? [X_12: int] : ( ord_less_int @ X2 @ X_12 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_897_dense,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ? [Z4: rat] :
% 8.57/4.53            ( ( ord_less_rat @ X2 @ Z4 )
% 8.57/4.53            & ( ord_less_rat @ Z4 @ Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_898_less__imp__neq,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_899_less__imp__neq,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_900_less__imp__neq,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_901_less__imp__neq,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_902_less__imp__neq,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_903_order_Oasym,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ~ ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_904_order_Oasym,axiom,
% 8.57/4.53      ! [A: rat,B: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ~ ( ord_less_rat @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_905_order_Oasym,axiom,
% 8.57/4.53      ! [A: num,B: num] :
% 8.57/4.53        ( ( ord_less_num @ A @ B )
% 8.57/4.53       => ~ ( ord_less_num @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_906_order_Oasym,axiom,
% 8.57/4.53      ! [A: nat,B: nat] :
% 8.57/4.53        ( ( ord_less_nat @ A @ B )
% 8.57/4.53       => ~ ( ord_less_nat @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_907_order_Oasym,axiom,
% 8.57/4.53      ! [A: int,B: int] :
% 8.57/4.53        ( ( ord_less_int @ A @ B )
% 8.57/4.53       => ~ ( ord_less_int @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_908_ord__eq__less__trans,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( A = B )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_909_ord__eq__less__trans,axiom,
% 8.57/4.53      ! [A: rat,B: rat,C: rat] :
% 8.57/4.53        ( ( A = B )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_910_ord__eq__less__trans,axiom,
% 8.57/4.53      ! [A: num,B: num,C: num] :
% 8.57/4.53        ( ( A = B )
% 8.57/4.53       => ( ( ord_less_num @ B @ C )
% 8.57/4.53         => ( ord_less_num @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_911_ord__eq__less__trans,axiom,
% 8.57/4.53      ! [A: nat,B: nat,C: nat] :
% 8.57/4.53        ( ( A = B )
% 8.57/4.53       => ( ( ord_less_nat @ B @ C )
% 8.57/4.53         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_912_ord__eq__less__trans,axiom,
% 8.57/4.53      ! [A: int,B: int,C: int] :
% 8.57/4.53        ( ( A = B )
% 8.57/4.53       => ( ( ord_less_int @ B @ C )
% 8.57/4.53         => ( ord_less_int @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_913_ord__less__eq__trans,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( B = C )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_914_ord__less__eq__trans,axiom,
% 8.57/4.53      ! [A: rat,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( B = C )
% 8.57/4.53         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_915_ord__less__eq__trans,axiom,
% 8.57/4.53      ! [A: num,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_num @ A @ B )
% 8.57/4.53       => ( ( B = C )
% 8.57/4.53         => ( ord_less_num @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_916_ord__less__eq__trans,axiom,
% 8.57/4.53      ! [A: nat,B: nat,C: nat] :
% 8.57/4.53        ( ( ord_less_nat @ A @ B )
% 8.57/4.53       => ( ( B = C )
% 8.57/4.53         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_917_ord__less__eq__trans,axiom,
% 8.57/4.53      ! [A: int,B: int,C: int] :
% 8.57/4.53        ( ( ord_less_int @ A @ B )
% 8.57/4.53       => ( ( B = C )
% 8.57/4.53         => ( ord_less_int @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_918_less__induct,axiom,
% 8.57/4.53      ! [P: nat > $o,A: nat] :
% 8.57/4.53        ( ! [X3: nat] :
% 8.57/4.53            ( ! [Y5: nat] :
% 8.57/4.53                ( ( ord_less_nat @ Y5 @ X3 )
% 8.57/4.53               => ( P @ Y5 ) )
% 8.57/4.53           => ( P @ X3 ) )
% 8.57/4.53       => ( P @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_919_antisym__conv3,axiom,
% 8.57/4.53      ! [Y: code_integer,X2: code_integer] :
% 8.57/4.53        ( ~ ( ord_le6747313008572928689nteger @ Y @ X2 )
% 8.57/4.53       => ( ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_920_antisym__conv3,axiom,
% 8.57/4.53      ! [Y: rat,X2: rat] :
% 8.57/4.53        ( ~ ( ord_less_rat @ Y @ X2 )
% 8.57/4.53       => ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_921_antisym__conv3,axiom,
% 8.57/4.53      ! [Y: num,X2: num] :
% 8.57/4.53        ( ~ ( ord_less_num @ Y @ X2 )
% 8.57/4.53       => ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_922_antisym__conv3,axiom,
% 8.57/4.53      ! [Y: nat,X2: nat] :
% 8.57/4.53        ( ~ ( ord_less_nat @ Y @ X2 )
% 8.57/4.53       => ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_923_antisym__conv3,axiom,
% 8.57/4.53      ! [Y: int,X2: int] :
% 8.57/4.53        ( ~ ( ord_less_int @ Y @ X2 )
% 8.57/4.53       => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_924_linorder__cases,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( ( X2 != Y )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_925_linorder__cases,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ~ ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( ( X2 != Y )
% 8.57/4.53         => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_926_linorder__cases,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ~ ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( ( X2 != Y )
% 8.57/4.53         => ( ord_less_num @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_927_linorder__cases,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ~ ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( ( X2 != Y )
% 8.57/4.53         => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_928_linorder__cases,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ~ ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( ( X2 != Y )
% 8.57/4.53         => ( ord_less_int @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_929_dual__order_Oasym,axiom,
% 8.57/4.53      ! [B: code_integer,A: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.57/4.53       => ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_930_dual__order_Oasym,axiom,
% 8.57/4.53      ! [B: rat,A: rat] :
% 8.57/4.53        ( ( ord_less_rat @ B @ A )
% 8.57/4.53       => ~ ( ord_less_rat @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_931_dual__order_Oasym,axiom,
% 8.57/4.53      ! [B: num,A: num] :
% 8.57/4.53        ( ( ord_less_num @ B @ A )
% 8.57/4.53       => ~ ( ord_less_num @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_932_dual__order_Oasym,axiom,
% 8.57/4.53      ! [B: nat,A: nat] :
% 8.57/4.53        ( ( ord_less_nat @ B @ A )
% 8.57/4.53       => ~ ( ord_less_nat @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_933_dual__order_Oasym,axiom,
% 8.57/4.53      ! [B: int,A: int] :
% 8.57/4.53        ( ( ord_less_int @ B @ A )
% 8.57/4.53       => ~ ( ord_less_int @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_934_dual__order_Oirrefl,axiom,
% 8.57/4.53      ! [A: code_integer] :
% 8.57/4.53        ~ ( ord_le6747313008572928689nteger @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_935_dual__order_Oirrefl,axiom,
% 8.57/4.53      ! [A: rat] :
% 8.57/4.53        ~ ( ord_less_rat @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_936_dual__order_Oirrefl,axiom,
% 8.57/4.53      ! [A: num] :
% 8.57/4.53        ~ ( ord_less_num @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_937_dual__order_Oirrefl,axiom,
% 8.57/4.53      ! [A: nat] :
% 8.57/4.53        ~ ( ord_less_nat @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_938_dual__order_Oirrefl,axiom,
% 8.57/4.53      ! [A: int] :
% 8.57/4.53        ~ ( ord_less_int @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_939_exists__least__iff,axiom,
% 8.57/4.53      ( ( ^ [P4: nat > $o] :
% 8.57/4.53          ? [X7: nat] : ( P4 @ X7 ) )
% 8.57/4.53      = ( ^ [P5: nat > $o] :
% 8.57/4.53          ? [N3: nat] :
% 8.57/4.53            ( ( P5 @ N3 )
% 8.57/4.53            & ! [M2: nat] :
% 8.57/4.53                ( ( ord_less_nat @ M2 @ N3 )
% 8.57/4.53               => ~ ( P5 @ M2 ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_940_linorder__less__wlog,axiom,
% 8.57/4.53      ! [P: code_integer > code_integer > $o,A: code_integer,B: code_integer] :
% 8.57/4.53        ( ! [A3: code_integer,B3: code_integer] :
% 8.57/4.53            ( ( ord_le6747313008572928689nteger @ A3 @ B3 )
% 8.57/4.53           => ( P @ A3 @ B3 ) )
% 8.57/4.53       => ( ! [A3: code_integer] : ( P @ A3 @ A3 )
% 8.57/4.53         => ( ! [A3: code_integer,B3: code_integer] :
% 8.57/4.53                ( ( P @ B3 @ A3 )
% 8.57/4.53               => ( P @ A3 @ B3 ) )
% 8.57/4.53           => ( P @ A @ B ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_941_linorder__less__wlog,axiom,
% 8.57/4.53      ! [P: rat > rat > $o,A: rat,B: rat] :
% 8.57/4.53        ( ! [A3: rat,B3: rat] :
% 8.57/4.53            ( ( ord_less_rat @ A3 @ B3 )
% 8.57/4.53           => ( P @ A3 @ B3 ) )
% 8.57/4.53       => ( ! [A3: rat] : ( P @ A3 @ A3 )
% 8.57/4.53         => ( ! [A3: rat,B3: rat] :
% 8.57/4.53                ( ( P @ B3 @ A3 )
% 8.57/4.53               => ( P @ A3 @ B3 ) )
% 8.57/4.53           => ( P @ A @ B ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_942_linorder__less__wlog,axiom,
% 8.57/4.53      ! [P: num > num > $o,A: num,B: num] :
% 8.57/4.53        ( ! [A3: num,B3: num] :
% 8.57/4.53            ( ( ord_less_num @ A3 @ B3 )
% 8.57/4.53           => ( P @ A3 @ B3 ) )
% 8.57/4.53       => ( ! [A3: num] : ( P @ A3 @ A3 )
% 8.57/4.53         => ( ! [A3: num,B3: num] :
% 8.57/4.53                ( ( P @ B3 @ A3 )
% 8.57/4.53               => ( P @ A3 @ B3 ) )
% 8.57/4.53           => ( P @ A @ B ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_943_linorder__less__wlog,axiom,
% 8.57/4.53      ! [P: nat > nat > $o,A: nat,B: nat] :
% 8.57/4.53        ( ! [A3: nat,B3: nat] :
% 8.57/4.53            ( ( ord_less_nat @ A3 @ B3 )
% 8.57/4.53           => ( P @ A3 @ B3 ) )
% 8.57/4.53       => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 8.57/4.53         => ( ! [A3: nat,B3: nat] :
% 8.57/4.53                ( ( P @ B3 @ A3 )
% 8.57/4.53               => ( P @ A3 @ B3 ) )
% 8.57/4.53           => ( P @ A @ B ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_944_linorder__less__wlog,axiom,
% 8.57/4.53      ! [P: int > int > $o,A: int,B: int] :
% 8.57/4.53        ( ! [A3: int,B3: int] :
% 8.57/4.53            ( ( ord_less_int @ A3 @ B3 )
% 8.57/4.53           => ( P @ A3 @ B3 ) )
% 8.57/4.53       => ( ! [A3: int] : ( P @ A3 @ A3 )
% 8.57/4.53         => ( ! [A3: int,B3: int] :
% 8.57/4.53                ( ( P @ B3 @ A3 )
% 8.57/4.53               => ( P @ A3 @ B3 ) )
% 8.57/4.53           => ( P @ A @ B ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_945_order_Ostrict__trans,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_946_order_Ostrict__trans,axiom,
% 8.57/4.53      ! [A: rat,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_947_order_Ostrict__trans,axiom,
% 8.57/4.53      ! [A: num,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_num @ A @ B )
% 8.57/4.53       => ( ( ord_less_num @ B @ C )
% 8.57/4.53         => ( ord_less_num @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_948_order_Ostrict__trans,axiom,
% 8.57/4.53      ! [A: nat,B: nat,C: nat] :
% 8.57/4.53        ( ( ord_less_nat @ A @ B )
% 8.57/4.53       => ( ( ord_less_nat @ B @ C )
% 8.57/4.53         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_949_order_Ostrict__trans,axiom,
% 8.57/4.53      ! [A: int,B: int,C: int] :
% 8.57/4.53        ( ( ord_less_int @ A @ B )
% 8.57/4.53       => ( ( ord_less_int @ B @ C )
% 8.57/4.53         => ( ord_less_int @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_950_not__less__iff__gr__or__eq,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) )
% 8.57/4.53        = ( ( ord_le6747313008572928689nteger @ Y @ X2 )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_951_not__less__iff__gr__or__eq,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 8.57/4.53        = ( ( ord_less_rat @ Y @ X2 )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_952_not__less__iff__gr__or__eq,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 8.57/4.53        = ( ( ord_less_num @ Y @ X2 )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_953_not__less__iff__gr__or__eq,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 8.57/4.53        = ( ( ord_less_nat @ Y @ X2 )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_954_not__less__iff__gr__or__eq,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 8.57/4.53        = ( ( ord_less_int @ Y @ X2 )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_955_dual__order_Ostrict__trans,axiom,
% 8.57/4.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ C @ B )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_956_dual__order_Ostrict__trans,axiom,
% 8.57/4.53      ! [B: rat,A: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ B @ A )
% 8.57/4.53       => ( ( ord_less_rat @ C @ B )
% 8.57/4.53         => ( ord_less_rat @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_957_dual__order_Ostrict__trans,axiom,
% 8.57/4.53      ! [B: num,A: num,C: num] :
% 8.57/4.53        ( ( ord_less_num @ B @ A )
% 8.57/4.53       => ( ( ord_less_num @ C @ B )
% 8.57/4.53         => ( ord_less_num @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_958_dual__order_Ostrict__trans,axiom,
% 8.57/4.53      ! [B: nat,A: nat,C: nat] :
% 8.57/4.53        ( ( ord_less_nat @ B @ A )
% 8.57/4.53       => ( ( ord_less_nat @ C @ B )
% 8.57/4.53         => ( ord_less_nat @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_959_dual__order_Ostrict__trans,axiom,
% 8.57/4.53      ! [B: int,A: int,C: int] :
% 8.57/4.53        ( ( ord_less_int @ B @ A )
% 8.57/4.53       => ( ( ord_less_int @ C @ B )
% 8.57/4.53         => ( ord_less_int @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_960_order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_961_order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [A: rat,B: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_962_order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [A: num,B: num] :
% 8.57/4.53        ( ( ord_less_num @ A @ B )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_963_order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [A: nat,B: nat] :
% 8.57/4.53        ( ( ord_less_nat @ A @ B )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_964_order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [A: int,B: int] :
% 8.57/4.53        ( ( ord_less_int @ A @ B )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_965_dual__order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [B: code_integer,A: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_966_dual__order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [B: rat,A: rat] :
% 8.57/4.53        ( ( ord_less_rat @ B @ A )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_967_dual__order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [B: num,A: num] :
% 8.57/4.53        ( ( ord_less_num @ B @ A )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_968_dual__order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [B: nat,A: nat] :
% 8.57/4.53        ( ( ord_less_nat @ B @ A )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_969_dual__order_Ostrict__implies__not__eq,axiom,
% 8.57/4.53      ! [B: int,A: int] :
% 8.57/4.53        ( ( ord_less_int @ B @ A )
% 8.57/4.53       => ( A != B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_970_linorder__neqE,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53       => ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_971_linorder__neqE,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53       => ( ~ ( ord_less_rat @ X2 @ Y )
% 8.57/4.53         => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_972_linorder__neqE,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53       => ( ~ ( ord_less_num @ X2 @ Y )
% 8.57/4.53         => ( ord_less_num @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_973_linorder__neqE,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53       => ( ~ ( ord_less_nat @ X2 @ Y )
% 8.57/4.53         => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_974_linorder__neqE,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53       => ( ~ ( ord_less_int @ X2 @ Y )
% 8.57/4.53         => ( ord_less_int @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_975_order__less__asym,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_976_order__less__asym,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_977_order__less__asym,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_978_order__less__asym,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_979_order__less__asym,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_980_linorder__neq__iff,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53        = ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53          | ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_981_linorder__neq__iff,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53        = ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53          | ( ord_less_rat @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_982_linorder__neq__iff,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53        = ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53          | ( ord_less_num @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_983_linorder__neq__iff,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53        = ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53          | ( ord_less_nat @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_984_linorder__neq__iff,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( X2 != Y )
% 8.57/4.53        = ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53          | ( ord_less_int @ Y @ X2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_985_order__less__asym_H,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ~ ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_986_order__less__asym_H,axiom,
% 8.57/4.53      ! [A: rat,B: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ~ ( ord_less_rat @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_987_order__less__asym_H,axiom,
% 8.57/4.53      ! [A: num,B: num] :
% 8.57/4.53        ( ( ord_less_num @ A @ B )
% 8.57/4.53       => ~ ( ord_less_num @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_988_order__less__asym_H,axiom,
% 8.57/4.53      ! [A: nat,B: nat] :
% 8.57/4.53        ( ( ord_less_nat @ A @ B )
% 8.57/4.53       => ~ ( ord_less_nat @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_989_order__less__asym_H,axiom,
% 8.57/4.53      ! [A: int,B: int] :
% 8.57/4.53        ( ( ord_less_int @ A @ B )
% 8.57/4.53       => ~ ( ord_less_int @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_990_order__less__trans,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer,Z2: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ Y @ Z2 )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_991_order__less__trans,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat,Z2: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_rat @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_rat @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_992_order__less__trans,axiom,
% 8.57/4.53      ! [X2: num,Y: num,Z2: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_num @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_num @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_993_order__less__trans,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat,Z2: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_nat @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_994_order__less__trans,axiom,
% 8.57/4.53      ! [X2: int,Y: int,Z2: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_int @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_int @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_995_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: code_integer,F: code_integer > code_integer,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_996_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: rat,F: code_integer > rat,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_997_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: num,F: code_integer > num,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_998_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: nat,F: code_integer > nat,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_999_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: int,F: code_integer > int,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1000_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1001_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1002_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: num,F: rat > num,B: rat,C: rat] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1003_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1004_ord__eq__less__subst,axiom,
% 8.57/4.53      ! [A: int,F: rat > int,B: rat,C: rat] :
% 8.57/4.53        ( ( A
% 8.57/4.53          = ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1005_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1006_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > rat,C: rat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1007_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > num,C: num] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1008_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > nat,C: nat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1009_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > int,C: int] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1010_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1011_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1012_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1013_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1014_ord__less__eq__subst,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ( F @ B )
% 8.57/4.53            = C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1015_order__less__irrefl,axiom,
% 8.57/4.53      ! [X2: code_integer] :
% 8.57/4.53        ~ ( ord_le6747313008572928689nteger @ X2 @ X2 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1016_order__less__irrefl,axiom,
% 8.57/4.53      ! [X2: rat] :
% 8.57/4.53        ~ ( ord_less_rat @ X2 @ X2 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1017_order__less__irrefl,axiom,
% 8.57/4.53      ! [X2: num] :
% 8.57/4.53        ~ ( ord_less_num @ X2 @ X2 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1018_order__less__irrefl,axiom,
% 8.57/4.53      ! [X2: nat] :
% 8.57/4.53        ~ ( ord_less_nat @ X2 @ X2 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1019_order__less__irrefl,axiom,
% 8.57/4.53      ! [X2: int] :
% 8.57/4.53        ~ ( ord_less_int @ X2 @ X2 ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1020_order__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: code_integer > code_integer,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1021_order__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1022_order__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: num > code_integer,B: num,C: num] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_num @ B @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1023_order__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: nat > code_integer,B: nat,C: nat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_nat @ B @ C )
% 8.57/4.53         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.53                ( ( ord_less_nat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1024_order__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: int > code_integer,B: int,C: int] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_int @ B @ C )
% 8.57/4.53         => ( ! [X3: int,Y2: int] :
% 8.57/4.53                ( ( ord_less_int @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1025_order__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: code_integer > rat,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1026_order__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1027_order__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_num @ B @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1028_order__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_nat @ B @ C )
% 8.57/4.53         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.53                ( ( ord_less_nat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1029_order__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: int > rat,B: int,C: int] :
% 8.57/4.53        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_int @ B @ C )
% 8.57/4.53         => ( ! [X3: int,Y2: int] :
% 8.57/4.53                ( ( ord_less_int @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1030_order__less__subst2,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1031_order__less__subst2,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > rat,C: rat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1032_order__less__subst2,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > num,C: num] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ord_less_num @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1033_order__less__subst2,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > nat,C: nat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1034_order__less__subst2,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > int,C: int] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ord_less_int @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1035_order__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1036_order__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1037_order__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_num @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1038_order__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1039_order__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_int @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1040_order__less__not__sym,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1041_order__less__not__sym,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1042_order__less__not__sym,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1043_order__less__not__sym,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1044_order__less__not__sym,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1045_order__less__imp__triv,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer,P: $o] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ Y @ X2 )
% 8.57/4.53         => P ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1046_order__less__imp__triv,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat,P: $o] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_rat @ Y @ X2 )
% 8.57/4.53         => P ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1047_order__less__imp__triv,axiom,
% 8.57/4.53      ! [X2: num,Y: num,P: $o] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_num @ Y @ X2 )
% 8.57/4.53         => P ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1048_order__less__imp__triv,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat,P: $o] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_nat @ Y @ X2 )
% 8.57/4.53         => P ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1049_order__less__imp__triv,axiom,
% 8.57/4.53      ! [X2: int,Y: int,P: $o] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_int @ Y @ X2 )
% 8.57/4.53         => P ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1050_linorder__less__linear,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53        | ( X2 = Y )
% 8.57/4.53        | ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1051_linorder__less__linear,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53        | ( X2 = Y )
% 8.57/4.53        | ( ord_less_rat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1052_linorder__less__linear,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53        | ( X2 = Y )
% 8.57/4.53        | ( ord_less_num @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1053_linorder__less__linear,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53        | ( X2 = Y )
% 8.57/4.53        | ( ord_less_nat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1054_linorder__less__linear,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53        | ( X2 = Y )
% 8.57/4.53        | ( ord_less_int @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1055_order__less__imp__not__eq,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1056_order__less__imp__not__eq,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1057_order__less__imp__not__eq,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1058_order__less__imp__not__eq,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1059_order__less__imp__not__eq,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( X2 != Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1060_order__less__imp__not__eq2,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( Y != X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1061_order__less__imp__not__eq2,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( Y != X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1062_order__less__imp__not__eq2,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( Y != X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1063_order__less__imp__not__eq2,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( Y != X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1064_order__less__imp__not__eq2,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( Y != X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1065_order__less__imp__not__less,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1066_order__less__imp__not__less,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1067_order__less__imp__not__less,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1068_order__less__imp__not__less,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1069_order__less__imp__not__less,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1070_verit__comp__simplify1_I1_J,axiom,
% 8.57/4.53      ! [A: code_integer] :
% 8.57/4.53        ~ ( ord_le6747313008572928689nteger @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1071_verit__comp__simplify1_I1_J,axiom,
% 8.57/4.53      ! [A: rat] :
% 8.57/4.53        ~ ( ord_less_rat @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1072_verit__comp__simplify1_I1_J,axiom,
% 8.57/4.53      ! [A: num] :
% 8.57/4.53        ~ ( ord_less_num @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1073_verit__comp__simplify1_I1_J,axiom,
% 8.57/4.53      ! [A: nat] :
% 8.57/4.53        ~ ( ord_less_nat @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1074_verit__comp__simplify1_I1_J,axiom,
% 8.57/4.53      ! [A: int] :
% 8.57/4.53        ~ ( ord_less_int @ A @ A ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1075_floor__less__cancel,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) )
% 8.57/4.53       => ( ord_less_rat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1076_zless__nat__eq__int__zless,axiom,
% 8.57/4.53      ! [M: nat,Z2: int] :
% 8.57/4.53        ( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
% 8.57/4.53        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1077_nat__mono__iff,axiom,
% 8.57/4.53      ! [Z2: int,W2: int] :
% 8.57/4.53        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 8.57/4.53       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 8.57/4.53          = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1078_power__int__strict__increasing,axiom,
% 8.57/4.53      ! [N: int,N4: int,A: rat] :
% 8.57/4.53        ( ( ord_less_int @ N @ N4 )
% 8.57/4.53       => ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.53         => ( ord_less_rat @ ( power_int_rat @ A @ N ) @ ( power_int_rat @ A @ N4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1079_zero__less__power__int,axiom,
% 8.57/4.53      ! [X2: rat,N: int] :
% 8.57/4.53        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 8.57/4.53       => ( ord_less_rat @ zero_zero_rat @ ( power_int_rat @ X2 @ N ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1080_less__imp__of__nat__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_less_nat @ M @ N )
% 8.57/4.53       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1081_less__imp__of__nat__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_less_nat @ M @ N )
% 8.57/4.53       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1082_less__imp__of__nat__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_less_nat @ M @ N )
% 8.57/4.53       => ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1083_less__imp__of__nat__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_less_nat @ M @ N )
% 8.57/4.53       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1084_less__imp__of__nat__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_less_nat @ M @ N )
% 8.57/4.53       => ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1085_of__nat__less__imp__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.53       => ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1086_of__nat__less__imp__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.57/4.53       => ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1087_of__nat__less__imp__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 8.57/4.53       => ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1088_of__nat__less__imp__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.53       => ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1089_of__nat__less__imp__less,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) )
% 8.57/4.53       => ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1090_nat__int__comparison_I2_J,axiom,
% 8.57/4.53      ( ord_less_nat
% 8.57/4.53      = ( ^ [A2: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1091_power__int__strict__decreasing,axiom,
% 8.57/4.53      ! [N: int,N4: int,A: rat] :
% 8.57/4.53        ( ( ord_less_int @ N @ N4 )
% 8.57/4.53       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.53         => ( ( ord_less_rat @ A @ one_one_rat )
% 8.57/4.53           => ( ord_less_rat @ ( power_int_rat @ A @ N4 ) @ ( power_int_rat @ A @ N ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1092_power__int__strict__antimono,axiom,
% 8.57/4.53      ! [A: rat,B: rat,N: int] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.53         => ( ( ord_less_int @ N @ zero_zero_int )
% 8.57/4.53           => ( ord_less_rat @ ( power_int_rat @ B @ N ) @ ( power_int_rat @ A @ N ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1093_ceiling__less__cancel,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 8.57/4.53       => ( ord_less_rat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1094_one__less__power__int,axiom,
% 8.57/4.53      ! [A: rat,N: int] :
% 8.57/4.53        ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.53       => ( ( ord_less_int @ zero_zero_int @ N )
% 8.57/4.53         => ( ord_less_rat @ one_one_rat @ ( power_int_rat @ A @ N ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1095_nat__less__eq__zless,axiom,
% 8.57/4.53      ! [W2: int,Z2: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.57/4.53       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 8.57/4.53          = ( ord_less_int @ W2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1096_nat__less__as__int,axiom,
% 8.57/4.53      ( ord_less_nat
% 8.57/4.53      = ( ^ [A2: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1097_power__int__antimono,axiom,
% 8.57/4.53      ! [A: rat,B: rat,N: int] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.53         => ( ( ord_less_int @ N @ zero_zero_int )
% 8.57/4.53           => ( ord_less_eq_rat @ ( power_int_rat @ B @ N ) @ ( power_int_rat @ A @ N ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1098_power__int__strict__mono,axiom,
% 8.57/4.53      ! [A: rat,B: rat,N: int] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.53         => ( ( ord_less_int @ zero_zero_int @ N )
% 8.57/4.53           => ( ord_less_rat @ ( power_int_rat @ A @ N ) @ ( power_int_rat @ B @ N ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1099_power__int__le__imp__less__exp,axiom,
% 8.57/4.53      ! [X2: rat,M: int,N: int] :
% 8.57/4.53        ( ( ord_less_rat @ one_one_rat @ X2 )
% 8.57/4.53       => ( ( ord_less_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ X2 @ N ) )
% 8.57/4.53         => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 8.57/4.53           => ( ord_less_int @ M @ N ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1100_nat__less__iff,axiom,
% 8.57/4.53      ! [W2: int,M: nat] :
% 8.57/4.53        ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.57/4.53       => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 8.57/4.53          = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1101_less__ceiling__iff,axiom,
% 8.57/4.53      ! [Z2: int,X2: rat] :
% 8.57/4.53        ( ( ord_less_int @ Z2 @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.53        = ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1102_verit__comp__simplify1_I3_J,axiom,
% 8.57/4.53      ! [B5: code_integer,A5: code_integer] :
% 8.57/4.53        ( ( ~ ( ord_le3102999989581377725nteger @ B5 @ A5 ) )
% 8.57/4.53        = ( ord_le6747313008572928689nteger @ A5 @ B5 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1103_verit__comp__simplify1_I3_J,axiom,
% 8.57/4.53      ! [B5: rat,A5: rat] :
% 8.57/4.53        ( ( ~ ( ord_less_eq_rat @ B5 @ A5 ) )
% 8.57/4.53        = ( ord_less_rat @ A5 @ B5 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1104_verit__comp__simplify1_I3_J,axiom,
% 8.57/4.53      ! [B5: num,A5: num] :
% 8.57/4.53        ( ( ~ ( ord_less_eq_num @ B5 @ A5 ) )
% 8.57/4.53        = ( ord_less_num @ A5 @ B5 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1105_verit__comp__simplify1_I3_J,axiom,
% 8.57/4.53      ! [B5: nat,A5: nat] :
% 8.57/4.53        ( ( ~ ( ord_less_eq_nat @ B5 @ A5 ) )
% 8.57/4.53        = ( ord_less_nat @ A5 @ B5 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1106_verit__comp__simplify1_I3_J,axiom,
% 8.57/4.53      ! [B5: int,A5: int] :
% 8.57/4.53        ( ( ~ ( ord_less_eq_int @ B5 @ A5 ) )
% 8.57/4.53        = ( ord_less_int @ A5 @ B5 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1107_leD,axiom,
% 8.57/4.53      ! [Y: code_integer,X2: code_integer] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ Y @ X2 )
% 8.57/4.53       => ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1108_leD,axiom,
% 8.57/4.53      ! [Y: set_nat,X2: set_nat] :
% 8.57/4.53        ( ( ord_less_eq_set_nat @ Y @ X2 )
% 8.57/4.53       => ~ ( ord_less_set_nat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1109_leD,axiom,
% 8.57/4.53      ! [Y: rat,X2: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ Y @ X2 )
% 8.57/4.53       => ~ ( ord_less_rat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1110_leD,axiom,
% 8.57/4.53      ! [Y: num,X2: num] :
% 8.57/4.53        ( ( ord_less_eq_num @ Y @ X2 )
% 8.57/4.53       => ~ ( ord_less_num @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1111_leD,axiom,
% 8.57/4.53      ! [Y: nat,X2: nat] :
% 8.57/4.53        ( ( ord_less_eq_nat @ Y @ X2 )
% 8.57/4.53       => ~ ( ord_less_nat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1112_leD,axiom,
% 8.57/4.53      ! [Y: int,X2: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ Y @ X2 )
% 8.57/4.53       => ~ ( ord_less_int @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1113_leI,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( ord_le3102999989581377725nteger @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1114_leI,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ~ ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1115_leI,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ~ ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1116_leI,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ~ ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1117_leI,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ~ ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( ord_less_eq_int @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1118_nless__le,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer] :
% 8.57/4.53        ( ( ~ ( ord_le6747313008572928689nteger @ A @ B ) )
% 8.57/4.53        = ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.53          | ( A = B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1119_nless__le,axiom,
% 8.57/4.53      ! [A: set_nat,B: set_nat] :
% 8.57/4.53        ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 8.57/4.53        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 8.57/4.53          | ( A = B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1120_nless__le,axiom,
% 8.57/4.53      ! [A: rat,B: rat] :
% 8.57/4.53        ( ( ~ ( ord_less_rat @ A @ B ) )
% 8.57/4.53        = ( ~ ( ord_less_eq_rat @ A @ B )
% 8.57/4.53          | ( A = B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1121_nless__le,axiom,
% 8.57/4.53      ! [A: num,B: num] :
% 8.57/4.53        ( ( ~ ( ord_less_num @ A @ B ) )
% 8.57/4.53        = ( ~ ( ord_less_eq_num @ A @ B )
% 8.57/4.53          | ( A = B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1122_nless__le,axiom,
% 8.57/4.53      ! [A: nat,B: nat] :
% 8.57/4.53        ( ( ~ ( ord_less_nat @ A @ B ) )
% 8.57/4.53        = ( ~ ( ord_less_eq_nat @ A @ B )
% 8.57/4.53          | ( A = B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1123_nless__le,axiom,
% 8.57/4.53      ! [A: int,B: int] :
% 8.57/4.53        ( ( ~ ( ord_less_int @ A @ B ) )
% 8.57/4.53        = ( ~ ( ord_less_eq_int @ A @ B )
% 8.57/4.53          | ( A = B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1124_antisym__conv1,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1125_antisym__conv1,axiom,
% 8.57/4.53      ! [X2: set_nat,Y: set_nat] :
% 8.57/4.53        ( ~ ( ord_less_set_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_set_nat @ X2 @ Y )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1126_antisym__conv1,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ~ ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1127_antisym__conv1,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ~ ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1128_antisym__conv1,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ~ ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1129_antisym__conv1,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ~ ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1130_antisym__conv2,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 8.57/4.53       => ( ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1131_antisym__conv2,axiom,
% 8.57/4.53      ! [X2: set_nat,Y: set_nat] :
% 8.57/4.53        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ~ ( ord_less_set_nat @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1132_antisym__conv2,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.53       => ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1133_antisym__conv2,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.53       => ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1134_antisym__conv2,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1135_antisym__conv2,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.53       => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 8.57/4.53          = ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1136_dense__ge,axiom,
% 8.57/4.53      ! [Z2: rat,Y: rat] :
% 8.57/4.53        ( ! [X3: rat] :
% 8.57/4.53            ( ( ord_less_rat @ Z2 @ X3 )
% 8.57/4.53           => ( ord_less_eq_rat @ Y @ X3 ) )
% 8.57/4.53       => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1137_dense__le,axiom,
% 8.57/4.53      ! [Y: rat,Z2: rat] :
% 8.57/4.53        ( ! [X3: rat] :
% 8.57/4.53            ( ( ord_less_rat @ X3 @ Y )
% 8.57/4.53           => ( ord_less_eq_rat @ X3 @ Z2 ) )
% 8.57/4.53       => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1138_less__le__not__le,axiom,
% 8.57/4.53      ( ord_le6747313008572928689nteger
% 8.57/4.53      = ( ^ [X: code_integer,Y4: code_integer] :
% 8.57/4.53            ( ( ord_le3102999989581377725nteger @ X @ Y4 )
% 8.57/4.53            & ~ ( ord_le3102999989581377725nteger @ Y4 @ X ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1139_less__le__not__le,axiom,
% 8.57/4.53      ( ord_less_set_nat
% 8.57/4.53      = ( ^ [X: set_nat,Y4: set_nat] :
% 8.57/4.53            ( ( ord_less_eq_set_nat @ X @ Y4 )
% 8.57/4.53            & ~ ( ord_less_eq_set_nat @ Y4 @ X ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1140_less__le__not__le,axiom,
% 8.57/4.53      ( ord_less_rat
% 8.57/4.53      = ( ^ [X: rat,Y4: rat] :
% 8.57/4.53            ( ( ord_less_eq_rat @ X @ Y4 )
% 8.57/4.53            & ~ ( ord_less_eq_rat @ Y4 @ X ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1141_less__le__not__le,axiom,
% 8.57/4.53      ( ord_less_num
% 8.57/4.53      = ( ^ [X: num,Y4: num] :
% 8.57/4.53            ( ( ord_less_eq_num @ X @ Y4 )
% 8.57/4.53            & ~ ( ord_less_eq_num @ Y4 @ X ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1142_less__le__not__le,axiom,
% 8.57/4.53      ( ord_less_nat
% 8.57/4.53      = ( ^ [X: nat,Y4: nat] :
% 8.57/4.53            ( ( ord_less_eq_nat @ X @ Y4 )
% 8.57/4.53            & ~ ( ord_less_eq_nat @ Y4 @ X ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1143_less__le__not__le,axiom,
% 8.57/4.53      ( ord_less_int
% 8.57/4.53      = ( ^ [X: int,Y4: int] :
% 8.57/4.53            ( ( ord_less_eq_int @ X @ Y4 )
% 8.57/4.53            & ~ ( ord_less_eq_int @ Y4 @ X ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1144_not__le__imp__less,axiom,
% 8.57/4.53      ! [Y: code_integer,X2: code_integer] :
% 8.57/4.53        ( ~ ( ord_le3102999989581377725nteger @ Y @ X2 )
% 8.57/4.53       => ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1145_not__le__imp__less,axiom,
% 8.57/4.53      ! [Y: rat,X2: rat] :
% 8.57/4.53        ( ~ ( ord_less_eq_rat @ Y @ X2 )
% 8.57/4.53       => ( ord_less_rat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1146_not__le__imp__less,axiom,
% 8.57/4.53      ! [Y: num,X2: num] :
% 8.57/4.53        ( ~ ( ord_less_eq_num @ Y @ X2 )
% 8.57/4.53       => ( ord_less_num @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1147_not__le__imp__less,axiom,
% 8.57/4.53      ! [Y: nat,X2: nat] :
% 8.57/4.53        ( ~ ( ord_less_eq_nat @ Y @ X2 )
% 8.57/4.53       => ( ord_less_nat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1148_not__le__imp__less,axiom,
% 8.57/4.53      ! [Y: int,X2: int] :
% 8.57/4.53        ( ~ ( ord_less_eq_int @ Y @ X2 )
% 8.57/4.53       => ( ord_less_int @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1149_order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_le3102999989581377725nteger
% 8.57/4.53      = ( ^ [A2: code_integer,B2: code_integer] :
% 8.57/4.53            ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1150_order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_set_nat
% 8.57/4.53      = ( ^ [A2: set_nat,B2: set_nat] :
% 8.57/4.53            ( ( ord_less_set_nat @ A2 @ B2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1151_order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_rat
% 8.57/4.53      = ( ^ [A2: rat,B2: rat] :
% 8.57/4.53            ( ( ord_less_rat @ A2 @ B2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1152_order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_num
% 8.57/4.53      = ( ^ [A2: num,B2: num] :
% 8.57/4.53            ( ( ord_less_num @ A2 @ B2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1153_order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_nat
% 8.57/4.53      = ( ^ [A2: nat,B2: nat] :
% 8.57/4.53            ( ( ord_less_nat @ A2 @ B2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1154_order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_int
% 8.57/4.53      = ( ^ [A2: int,B2: int] :
% 8.57/4.53            ( ( ord_less_int @ A2 @ B2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1155_order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_le6747313008572928689nteger
% 8.57/4.53      = ( ^ [A2: code_integer,B2: code_integer] :
% 8.57/4.53            ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1156_order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_set_nat
% 8.57/4.53      = ( ^ [A2: set_nat,B2: set_nat] :
% 8.57/4.53            ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1157_order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_rat
% 8.57/4.53      = ( ^ [A2: rat,B2: rat] :
% 8.57/4.53            ( ( ord_less_eq_rat @ A2 @ B2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1158_order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_num
% 8.57/4.53      = ( ^ [A2: num,B2: num] :
% 8.57/4.53            ( ( ord_less_eq_num @ A2 @ B2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1159_order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_nat
% 8.57/4.53      = ( ^ [A2: nat,B2: nat] :
% 8.57/4.53            ( ( ord_less_eq_nat @ A2 @ B2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1160_order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_int
% 8.57/4.53      = ( ^ [A2: int,B2: int] :
% 8.57/4.53            ( ( ord_less_eq_int @ A2 @ B2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1161_order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1162_order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [A: set_nat,B: set_nat,C: set_nat] :
% 8.57/4.53        ( ( ord_less_eq_set_nat @ A @ B )
% 8.57/4.53       => ( ( ord_less_set_nat @ B @ C )
% 8.57/4.53         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1163_order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [A: rat,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1164_order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [A: num,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.53       => ( ( ord_less_num @ B @ C )
% 8.57/4.53         => ( ord_less_num @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1165_order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [A: nat,B: nat,C: nat] :
% 8.57/4.53        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.53       => ( ( ord_less_nat @ B @ C )
% 8.57/4.53         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1166_order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [A: int,B: int,C: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.53       => ( ( ord_less_int @ B @ C )
% 8.57/4.53         => ( ord_less_int @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1167_order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1168_order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [A: set_nat,B: set_nat,C: set_nat] :
% 8.57/4.53        ( ( ord_less_set_nat @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_set_nat @ B @ C )
% 8.57/4.53         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1169_order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.53         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1170_order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [A: num,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_num @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.53         => ( ord_less_num @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1171_order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [A: nat,B: nat,C: nat] :
% 8.57/4.53        ( ( ord_less_nat @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.53         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1172_order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [A: int,B: int,C: int] :
% 8.57/4.53        ( ( ord_less_int @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_int @ B @ C )
% 8.57/4.53         => ( ord_less_int @ A @ C ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1173_order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_le6747313008572928689nteger
% 8.57/4.53      = ( ^ [A2: code_integer,B2: code_integer] :
% 8.57/4.53            ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 8.57/4.53            & ~ ( ord_le3102999989581377725nteger @ B2 @ A2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1174_order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_set_nat
% 8.57/4.53      = ( ^ [A2: set_nat,B2: set_nat] :
% 8.57/4.53            ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 8.57/4.53            & ~ ( ord_less_eq_set_nat @ B2 @ A2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1175_order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_rat
% 8.57/4.53      = ( ^ [A2: rat,B2: rat] :
% 8.57/4.53            ( ( ord_less_eq_rat @ A2 @ B2 )
% 8.57/4.53            & ~ ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1176_order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_num
% 8.57/4.53      = ( ^ [A2: num,B2: num] :
% 8.57/4.53            ( ( ord_less_eq_num @ A2 @ B2 )
% 8.57/4.53            & ~ ( ord_less_eq_num @ B2 @ A2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1177_order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_nat
% 8.57/4.53      = ( ^ [A2: nat,B2: nat] :
% 8.57/4.53            ( ( ord_less_eq_nat @ A2 @ B2 )
% 8.57/4.53            & ~ ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1178_order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_int
% 8.57/4.53      = ( ^ [A2: int,B2: int] :
% 8.57/4.53            ( ( ord_less_eq_int @ A2 @ B2 )
% 8.57/4.53            & ~ ( ord_less_eq_int @ B2 @ A2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1179_dense__ge__bounded,axiom,
% 8.57/4.53      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ Z2 @ X2 )
% 8.57/4.53       => ( ! [W3: rat] :
% 8.57/4.53              ( ( ord_less_rat @ Z2 @ W3 )
% 8.57/4.53             => ( ( ord_less_rat @ W3 @ X2 )
% 8.57/4.53               => ( ord_less_eq_rat @ Y @ W3 ) ) )
% 8.57/4.53         => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1180_dense__le__bounded,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat,Z2: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( ! [W3: rat] :
% 8.57/4.53              ( ( ord_less_rat @ X2 @ W3 )
% 8.57/4.53             => ( ( ord_less_rat @ W3 @ Y )
% 8.57/4.53               => ( ord_less_eq_rat @ W3 @ Z2 ) ) )
% 8.57/4.53         => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1181_dual__order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_le3102999989581377725nteger
% 8.57/4.53      = ( ^ [B2: code_integer,A2: code_integer] :
% 8.57/4.53            ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1182_dual__order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_set_nat
% 8.57/4.53      = ( ^ [B2: set_nat,A2: set_nat] :
% 8.57/4.53            ( ( ord_less_set_nat @ B2 @ A2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1183_dual__order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_rat
% 8.57/4.53      = ( ^ [B2: rat,A2: rat] :
% 8.57/4.53            ( ( ord_less_rat @ B2 @ A2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1184_dual__order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_num
% 8.57/4.53      = ( ^ [B2: num,A2: num] :
% 8.57/4.53            ( ( ord_less_num @ B2 @ A2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1185_dual__order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_nat
% 8.57/4.53      = ( ^ [B2: nat,A2: nat] :
% 8.57/4.53            ( ( ord_less_nat @ B2 @ A2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1186_dual__order_Oorder__iff__strict,axiom,
% 8.57/4.53      ( ord_less_eq_int
% 8.57/4.53      = ( ^ [B2: int,A2: int] :
% 8.57/4.53            ( ( ord_less_int @ B2 @ A2 )
% 8.57/4.53            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1187_dual__order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_le6747313008572928689nteger
% 8.57/4.53      = ( ^ [B2: code_integer,A2: code_integer] :
% 8.57/4.53            ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1188_dual__order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_set_nat
% 8.57/4.53      = ( ^ [B2: set_nat,A2: set_nat] :
% 8.57/4.53            ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1189_dual__order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_rat
% 8.57/4.53      = ( ^ [B2: rat,A2: rat] :
% 8.57/4.53            ( ( ord_less_eq_rat @ B2 @ A2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1190_dual__order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_num
% 8.57/4.53      = ( ^ [B2: num,A2: num] :
% 8.57/4.53            ( ( ord_less_eq_num @ B2 @ A2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1191_dual__order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_nat
% 8.57/4.53      = ( ^ [B2: nat,A2: nat] :
% 8.57/4.53            ( ( ord_less_eq_nat @ B2 @ A2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1192_dual__order_Ostrict__iff__order,axiom,
% 8.57/4.53      ( ord_less_int
% 8.57/4.53      = ( ^ [B2: int,A2: int] :
% 8.57/4.53            ( ( ord_less_eq_int @ B2 @ A2 )
% 8.57/4.53            & ( A2 != B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1193_dual__order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ C @ B )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1194_dual__order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [B: set_nat,A: set_nat,C: set_nat] :
% 8.57/4.53        ( ( ord_less_eq_set_nat @ B @ A )
% 8.57/4.53       => ( ( ord_less_set_nat @ C @ B )
% 8.57/4.53         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1195_dual__order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [B: rat,A: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.53       => ( ( ord_less_rat @ C @ B )
% 8.57/4.53         => ( ord_less_rat @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1196_dual__order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [B: num,A: num,C: num] :
% 8.57/4.53        ( ( ord_less_eq_num @ B @ A )
% 8.57/4.53       => ( ( ord_less_num @ C @ B )
% 8.57/4.53         => ( ord_less_num @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1197_dual__order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [B: nat,A: nat,C: nat] :
% 8.57/4.53        ( ( ord_less_eq_nat @ B @ A )
% 8.57/4.53       => ( ( ord_less_nat @ C @ B )
% 8.57/4.53         => ( ord_less_nat @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1198_dual__order_Ostrict__trans1,axiom,
% 8.57/4.53      ! [B: int,A: int,C: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ B @ A )
% 8.57/4.53       => ( ( ord_less_int @ C @ B )
% 8.57/4.53         => ( ord_less_int @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1199_dual__order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ C @ B )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1200_dual__order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [B: set_nat,A: set_nat,C: set_nat] :
% 8.57/4.53        ( ( ord_less_set_nat @ B @ A )
% 8.57/4.53       => ( ( ord_less_eq_set_nat @ C @ B )
% 8.57/4.53         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1201_dual__order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [B: rat,A: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ B @ A )
% 8.57/4.53       => ( ( ord_less_eq_rat @ C @ B )
% 8.57/4.53         => ( ord_less_rat @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1202_dual__order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [B: num,A: num,C: num] :
% 8.57/4.53        ( ( ord_less_num @ B @ A )
% 8.57/4.53       => ( ( ord_less_eq_num @ C @ B )
% 8.57/4.53         => ( ord_less_num @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1203_dual__order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [B: nat,A: nat,C: nat] :
% 8.57/4.53        ( ( ord_less_nat @ B @ A )
% 8.57/4.53       => ( ( ord_less_eq_nat @ C @ B )
% 8.57/4.53         => ( ord_less_nat @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1204_dual__order_Ostrict__trans2,axiom,
% 8.57/4.53      ! [B: int,A: int,C: int] :
% 8.57/4.53        ( ( ord_less_int @ B @ A )
% 8.57/4.53       => ( ( ord_less_eq_int @ C @ B )
% 8.57/4.53         => ( ord_less_int @ C @ A ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1205_dual__order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_le6747313008572928689nteger
% 8.57/4.53      = ( ^ [B2: code_integer,A2: code_integer] :
% 8.57/4.53            ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 8.57/4.53            & ~ ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1206_dual__order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_set_nat
% 8.57/4.53      = ( ^ [B2: set_nat,A2: set_nat] :
% 8.57/4.53            ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 8.57/4.53            & ~ ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1207_dual__order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_rat
% 8.57/4.53      = ( ^ [B2: rat,A2: rat] :
% 8.57/4.53            ( ( ord_less_eq_rat @ B2 @ A2 )
% 8.57/4.53            & ~ ( ord_less_eq_rat @ A2 @ B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1208_dual__order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_num
% 8.57/4.53      = ( ^ [B2: num,A2: num] :
% 8.57/4.53            ( ( ord_less_eq_num @ B2 @ A2 )
% 8.57/4.53            & ~ ( ord_less_eq_num @ A2 @ B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1209_dual__order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_nat
% 8.57/4.53      = ( ^ [B2: nat,A2: nat] :
% 8.57/4.53            ( ( ord_less_eq_nat @ B2 @ A2 )
% 8.57/4.53            & ~ ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1210_dual__order_Ostrict__iff__not,axiom,
% 8.57/4.53      ( ord_less_int
% 8.57/4.53      = ( ^ [B2: int,A2: int] :
% 8.57/4.53            ( ( ord_less_eq_int @ B2 @ A2 )
% 8.57/4.53            & ~ ( ord_less_eq_int @ A2 @ B2 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1211_order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1212_order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [A: set_nat,B: set_nat] :
% 8.57/4.53        ( ( ord_less_set_nat @ A @ B )
% 8.57/4.53       => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1213_order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [A: rat,B: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1214_order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [A: num,B: num] :
% 8.57/4.53        ( ( ord_less_num @ A @ B )
% 8.57/4.53       => ( ord_less_eq_num @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1215_order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [A: nat,B: nat] :
% 8.57/4.53        ( ( ord_less_nat @ A @ B )
% 8.57/4.53       => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1216_order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [A: int,B: int] :
% 8.57/4.53        ( ( ord_less_int @ A @ B )
% 8.57/4.53       => ( ord_less_eq_int @ A @ B ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1217_dual__order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [B: code_integer,A: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.57/4.53       => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1218_dual__order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [B: set_nat,A: set_nat] :
% 8.57/4.53        ( ( ord_less_set_nat @ B @ A )
% 8.57/4.53       => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1219_dual__order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [B: rat,A: rat] :
% 8.57/4.53        ( ( ord_less_rat @ B @ A )
% 8.57/4.53       => ( ord_less_eq_rat @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1220_dual__order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [B: num,A: num] :
% 8.57/4.53        ( ( ord_less_num @ B @ A )
% 8.57/4.53       => ( ord_less_eq_num @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1221_dual__order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [B: nat,A: nat] :
% 8.57/4.53        ( ( ord_less_nat @ B @ A )
% 8.57/4.53       => ( ord_less_eq_nat @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1222_dual__order_Ostrict__implies__order,axiom,
% 8.57/4.53      ! [B: int,A: int] :
% 8.57/4.53        ( ( ord_less_int @ B @ A )
% 8.57/4.53       => ( ord_less_eq_int @ B @ A ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1223_order__le__less,axiom,
% 8.57/4.53      ( ord_le3102999989581377725nteger
% 8.57/4.53      = ( ^ [X: code_integer,Y4: code_integer] :
% 8.57/4.53            ( ( ord_le6747313008572928689nteger @ X @ Y4 )
% 8.57/4.53            | ( X = Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1224_order__le__less,axiom,
% 8.57/4.53      ( ord_less_eq_set_nat
% 8.57/4.53      = ( ^ [X: set_nat,Y4: set_nat] :
% 8.57/4.53            ( ( ord_less_set_nat @ X @ Y4 )
% 8.57/4.53            | ( X = Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1225_order__le__less,axiom,
% 8.57/4.53      ( ord_less_eq_rat
% 8.57/4.53      = ( ^ [X: rat,Y4: rat] :
% 8.57/4.53            ( ( ord_less_rat @ X @ Y4 )
% 8.57/4.53            | ( X = Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1226_order__le__less,axiom,
% 8.57/4.53      ( ord_less_eq_num
% 8.57/4.53      = ( ^ [X: num,Y4: num] :
% 8.57/4.53            ( ( ord_less_num @ X @ Y4 )
% 8.57/4.53            | ( X = Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1227_order__le__less,axiom,
% 8.57/4.53      ( ord_less_eq_nat
% 8.57/4.53      = ( ^ [X: nat,Y4: nat] :
% 8.57/4.53            ( ( ord_less_nat @ X @ Y4 )
% 8.57/4.53            | ( X = Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1228_order__le__less,axiom,
% 8.57/4.53      ( ord_less_eq_int
% 8.57/4.53      = ( ^ [X: int,Y4: int] :
% 8.57/4.53            ( ( ord_less_int @ X @ Y4 )
% 8.57/4.53            | ( X = Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1229_order__less__le,axiom,
% 8.57/4.53      ( ord_le6747313008572928689nteger
% 8.57/4.53      = ( ^ [X: code_integer,Y4: code_integer] :
% 8.57/4.53            ( ( ord_le3102999989581377725nteger @ X @ Y4 )
% 8.57/4.53            & ( X != Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1230_order__less__le,axiom,
% 8.57/4.53      ( ord_less_set_nat
% 8.57/4.53      = ( ^ [X: set_nat,Y4: set_nat] :
% 8.57/4.53            ( ( ord_less_eq_set_nat @ X @ Y4 )
% 8.57/4.53            & ( X != Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1231_order__less__le,axiom,
% 8.57/4.53      ( ord_less_rat
% 8.57/4.53      = ( ^ [X: rat,Y4: rat] :
% 8.57/4.53            ( ( ord_less_eq_rat @ X @ Y4 )
% 8.57/4.53            & ( X != Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1232_order__less__le,axiom,
% 8.57/4.53      ( ord_less_num
% 8.57/4.53      = ( ^ [X: num,Y4: num] :
% 8.57/4.53            ( ( ord_less_eq_num @ X @ Y4 )
% 8.57/4.53            & ( X != Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1233_order__less__le,axiom,
% 8.57/4.53      ( ord_less_nat
% 8.57/4.53      = ( ^ [X: nat,Y4: nat] :
% 8.57/4.53            ( ( ord_less_eq_nat @ X @ Y4 )
% 8.57/4.53            & ( X != Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1234_order__less__le,axiom,
% 8.57/4.53      ( ord_less_int
% 8.57/4.53      = ( ^ [X: int,Y4: int] :
% 8.57/4.53            ( ( ord_less_eq_int @ X @ Y4 )
% 8.57/4.53            & ( X != Y4 ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1235_linorder__not__le,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ~ ( ord_le3102999989581377725nteger @ X2 @ Y ) )
% 8.57/4.53        = ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1236_linorder__not__le,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ~ ( ord_less_eq_rat @ X2 @ Y ) )
% 8.57/4.53        = ( ord_less_rat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1237_linorder__not__le,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ~ ( ord_less_eq_num @ X2 @ Y ) )
% 8.57/4.53        = ( ord_less_num @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1238_linorder__not__le,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ~ ( ord_less_eq_nat @ X2 @ Y ) )
% 8.57/4.53        = ( ord_less_nat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1239_linorder__not__le,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ~ ( ord_less_eq_int @ X2 @ Y ) )
% 8.57/4.53        = ( ord_less_int @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1240_linorder__not__less,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ~ ( ord_le6747313008572928689nteger @ X2 @ Y ) )
% 8.57/4.53        = ( ord_le3102999989581377725nteger @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1241_linorder__not__less,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 8.57/4.53        = ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1242_linorder__not__less,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 8.57/4.53        = ( ord_less_eq_num @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1243_linorder__not__less,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 8.57/4.53        = ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1244_linorder__not__less,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 8.57/4.53        = ( ord_less_eq_int @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1245_order__less__imp__le,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( ord_le3102999989581377725nteger @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1246_order__less__imp__le,axiom,
% 8.57/4.53      ! [X2: set_nat,Y: set_nat] :
% 8.57/4.53        ( ( ord_less_set_nat @ X2 @ Y )
% 8.57/4.53       => ( ord_less_eq_set_nat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1247_order__less__imp__le,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1248_order__less__imp__le,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1249_order__less__imp__le,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1250_order__less__imp__le,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( ord_less_eq_int @ X2 @ Y ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1251_order__le__neq__trans,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.53       => ( ( A != B )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1252_order__le__neq__trans,axiom,
% 8.57/4.53      ! [A: set_nat,B: set_nat] :
% 8.57/4.53        ( ( ord_less_eq_set_nat @ A @ B )
% 8.57/4.53       => ( ( A != B )
% 8.57/4.53         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1253_order__le__neq__trans,axiom,
% 8.57/4.53      ! [A: rat,B: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.53       => ( ( A != B )
% 8.57/4.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1254_order__le__neq__trans,axiom,
% 8.57/4.53      ! [A: num,B: num] :
% 8.57/4.53        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.53       => ( ( A != B )
% 8.57/4.53         => ( ord_less_num @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1255_order__le__neq__trans,axiom,
% 8.57/4.53      ! [A: nat,B: nat] :
% 8.57/4.53        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.53       => ( ( A != B )
% 8.57/4.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1256_order__le__neq__trans,axiom,
% 8.57/4.53      ! [A: int,B: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.53       => ( ( A != B )
% 8.57/4.53         => ( ord_less_int @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1257_order__neq__le__trans,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer] :
% 8.57/4.53        ( ( A != B )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1258_order__neq__le__trans,axiom,
% 8.57/4.53      ! [A: set_nat,B: set_nat] :
% 8.57/4.53        ( ( A != B )
% 8.57/4.53       => ( ( ord_less_eq_set_nat @ A @ B )
% 8.57/4.53         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1259_order__neq__le__trans,axiom,
% 8.57/4.53      ! [A: rat,B: rat] :
% 8.57/4.53        ( ( A != B )
% 8.57/4.53       => ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1260_order__neq__le__trans,axiom,
% 8.57/4.53      ! [A: num,B: num] :
% 8.57/4.53        ( ( A != B )
% 8.57/4.53       => ( ( ord_less_eq_num @ A @ B )
% 8.57/4.53         => ( ord_less_num @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1261_order__neq__le__trans,axiom,
% 8.57/4.53      ! [A: nat,B: nat] :
% 8.57/4.53        ( ( A != B )
% 8.57/4.53       => ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1262_order__neq__le__trans,axiom,
% 8.57/4.53      ! [A: int,B: int] :
% 8.57/4.53        ( ( A != B )
% 8.57/4.53       => ( ( ord_less_eq_int @ A @ B )
% 8.57/4.53         => ( ord_less_int @ A @ B ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1263_order__le__less__trans,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer,Z2: code_integer] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ Y @ Z2 )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1264_order__le__less__trans,axiom,
% 8.57/4.53      ! [X2: set_nat,Y: set_nat,Z2: set_nat] :
% 8.57/4.53        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_set_nat @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_set_nat @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1265_order__le__less__trans,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat,Z2: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_rat @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_rat @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1266_order__le__less__trans,axiom,
% 8.57/4.53      ! [X2: num,Y: num,Z2: num] :
% 8.57/4.53        ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_num @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_num @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1267_order__le__less__trans,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat,Z2: nat] :
% 8.57/4.53        ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_nat @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1268_order__le__less__trans,axiom,
% 8.57/4.53      ! [X2: int,Y: int,Z2: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_int @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_int @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1269_order__less__le__trans,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer,Z2: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ Y @ Z2 )
% 8.57/4.53         => ( ord_le6747313008572928689nteger @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1270_order__less__le__trans,axiom,
% 8.57/4.53      ! [X2: set_nat,Y: set_nat,Z2: set_nat] :
% 8.57/4.53        ( ( ord_less_set_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_set_nat @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_set_nat @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1271_order__less__le__trans,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat,Z2: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_rat @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_rat @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1272_order__less__le__trans,axiom,
% 8.57/4.53      ! [X2: num,Y: num,Z2: num] :
% 8.57/4.53        ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_num @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_num @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1273_order__less__le__trans,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat,Z2: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_nat @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1274_order__less__le__trans,axiom,
% 8.57/4.53      ! [X2: int,Y: int,Z2: int] :
% 8.57/4.53        ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_eq_int @ Y @ Z2 )
% 8.57/4.53         => ( ord_less_int @ X2 @ Z2 ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1275_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: code_integer > code_integer,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1276_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1277_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: num > code_integer,B: num,C: num] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_num @ B @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1278_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: nat > code_integer,B: nat,C: nat] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_nat @ B @ C )
% 8.57/4.53         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.53                ( ( ord_less_nat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1279_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: int > code_integer,B: int,C: int] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_int @ B @ C )
% 8.57/4.53         => ( ! [X3: int,Y2: int] :
% 8.57/4.53                ( ( ord_less_int @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1280_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: code_integer > rat,B: code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1281_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1282_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_num @ B @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1283_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_nat @ B @ C )
% 8.57/4.53         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.53                ( ( ord_less_nat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1284_order__le__less__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: int > rat,B: int,C: int] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_int @ B @ C )
% 8.57/4.53         => ( ! [X3: int,Y2: int] :
% 8.57/4.53                ( ( ord_less_int @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1285_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1286_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1287_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_num @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1288_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1289_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.57/4.53        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_int @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1290_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: num,B: num,F: num > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1291_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: num,B: num,F: num > rat,C: rat] :
% 8.57/4.53        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.53       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1292_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: num,B: num,F: num > num,C: num] :
% 8.57/4.53        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.53       => ( ( ord_less_num @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1293_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: num,B: num,F: num > nat,C: nat] :
% 8.57/4.53        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.53       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1294_order__le__less__subst2,axiom,
% 8.57/4.53      ! [A: num,B: num,F: num > int,C: int] :
% 8.57/4.53        ( ( ord_less_eq_num @ A @ B )
% 8.57/4.53       => ( ( ord_less_int @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1295_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1296_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1297_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: num,F: rat > num,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_num @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1298_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_nat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1299_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: int,F: rat > int,B: rat,C: rat] :
% 8.57/4.53        ( ( ord_less_int @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_eq_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1300_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: code_integer,F: num > code_integer,B: num,C: num] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1301_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1302_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: num,F: num > num,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_num @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1303_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: nat,F: num > nat,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_nat @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1304_order__less__le__subst1,axiom,
% 8.57/4.53      ! [A: int,F: num > int,B: num,C: num] :
% 8.57/4.53        ( ( ord_less_int @ A @ ( F @ B ) )
% 8.57/4.53       => ( ( ord_less_eq_num @ B @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_eq_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1305_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1306_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1307_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: num,B: num,F: num > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_num @ A @ B )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1308_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: nat,B: nat,F: nat > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_nat @ A @ B )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.53                ( ( ord_less_nat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1309_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: int,B: int,F: int > code_integer,C: code_integer] :
% 8.57/4.53        ( ( ord_less_int @ A @ B )
% 8.57/4.53       => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: int,Y2: int] :
% 8.57/4.53                ( ( ord_less_int @ X3 @ Y2 )
% 8.57/4.53               => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_le6747313008572928689nteger @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1310_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: code_integer,B: code_integer,F: code_integer > rat,C: rat] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: code_integer,Y2: code_integer] :
% 8.57/4.53                ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1311_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.57/4.53        ( ( ord_less_rat @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: rat,Y2: rat] :
% 8.57/4.53                ( ( ord_less_rat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1312_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: num,B: num,F: num > rat,C: rat] :
% 8.57/4.53        ( ( ord_less_num @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: num,Y2: num] :
% 8.57/4.53                ( ( ord_less_num @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1313_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 8.57/4.53        ( ( ord_less_nat @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.53                ( ( ord_less_nat @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1314_order__less__le__subst2,axiom,
% 8.57/4.53      ! [A: int,B: int,F: int > rat,C: rat] :
% 8.57/4.53        ( ( ord_less_int @ A @ B )
% 8.57/4.53       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.57/4.53         => ( ! [X3: int,Y2: int] :
% 8.57/4.53                ( ( ord_less_int @ X3 @ Y2 )
% 8.57/4.53               => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 8.57/4.53           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1315_linorder__le__less__linear,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 8.57/4.53        | ( ord_le6747313008572928689nteger @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1316_linorder__le__less__linear,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.53        | ( ord_less_rat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1317_linorder__le__less__linear,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.53        | ( ord_less_num @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1318_linorder__le__less__linear,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.53        | ( ord_less_nat @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1319_linorder__le__less__linear,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.53        | ( ord_less_int @ Y @ X2 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1320_order__le__imp__less__or__eq,axiom,
% 8.57/4.53      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.53        ( ( ord_le3102999989581377725nteger @ X2 @ Y )
% 8.57/4.53       => ( ( ord_le6747313008572928689nteger @ X2 @ Y )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1321_order__le__imp__less__or__eq,axiom,
% 8.57/4.53      ! [X2: set_nat,Y: set_nat] :
% 8.57/4.53        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_set_nat @ X2 @ Y )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1322_order__le__imp__less__or__eq,axiom,
% 8.57/4.53      ! [X2: rat,Y: rat] :
% 8.57/4.53        ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1323_order__le__imp__less__or__eq,axiom,
% 8.57/4.53      ! [X2: num,Y: num] :
% 8.57/4.53        ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_num @ X2 @ Y )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1324_order__le__imp__less__or__eq,axiom,
% 8.57/4.53      ! [X2: nat,Y: nat] :
% 8.57/4.53        ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1325_order__le__imp__less__or__eq,axiom,
% 8.57/4.53      ! [X2: int,Y: int] :
% 8.57/4.53        ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.53       => ( ( ord_less_int @ X2 @ Y )
% 8.57/4.53          | ( X2 = Y ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1326_minf_I8_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_le3102999989581377725nteger @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1327_minf_I8_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_less_eq_rat @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1328_minf_I8_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_less_eq_num @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1329_minf_I8_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_less_eq_nat @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1330_minf_I8_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ X4 @ Z4 )
% 8.57/4.53       => ~ ( ord_less_eq_int @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1331_minf_I6_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 8.57/4.53       => ( ord_le3102999989581377725nteger @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1332_minf_I6_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ X4 @ Z4 )
% 8.57/4.53       => ( ord_less_eq_rat @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1333_minf_I6_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ X4 @ Z4 )
% 8.57/4.53       => ( ord_less_eq_num @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1334_minf_I6_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ X4 @ Z4 )
% 8.57/4.53       => ( ord_less_eq_nat @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1335_minf_I6_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ X4 @ Z4 )
% 8.57/4.53       => ( ord_less_eq_int @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1336_pinf_I8_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 8.57/4.53       => ( ord_le3102999989581377725nteger @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1337_pinf_I8_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ Z4 @ X4 )
% 8.57/4.53       => ( ord_less_eq_rat @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1338_pinf_I8_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ Z4 @ X4 )
% 8.57/4.53       => ( ord_less_eq_num @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1339_pinf_I8_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ Z4 @ X4 )
% 8.57/4.53       => ( ord_less_eq_nat @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1340_pinf_I8_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ Z4 @ X4 )
% 8.57/4.53       => ( ord_less_eq_int @ T @ X4 ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1341_pinf_I6_J,axiom,
% 8.57/4.53      ! [T: code_integer] :
% 8.57/4.53      ? [Z4: code_integer] :
% 8.57/4.53      ! [X4: code_integer] :
% 8.57/4.53        ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_le3102999989581377725nteger @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1342_pinf_I6_J,axiom,
% 8.57/4.53      ! [T: rat] :
% 8.57/4.53      ? [Z4: rat] :
% 8.57/4.53      ! [X4: rat] :
% 8.57/4.53        ( ( ord_less_rat @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_less_eq_rat @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1343_pinf_I6_J,axiom,
% 8.57/4.53      ! [T: num] :
% 8.57/4.53      ? [Z4: num] :
% 8.57/4.53      ! [X4: num] :
% 8.57/4.53        ( ( ord_less_num @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_less_eq_num @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1344_pinf_I6_J,axiom,
% 8.57/4.53      ! [T: nat] :
% 8.57/4.53      ? [Z4: nat] :
% 8.57/4.53      ! [X4: nat] :
% 8.57/4.53        ( ( ord_less_nat @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_less_eq_nat @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1345_pinf_I6_J,axiom,
% 8.57/4.53      ! [T: int] :
% 8.57/4.53      ? [Z4: int] :
% 8.57/4.53      ! [X4: int] :
% 8.57/4.53        ( ( ord_less_int @ Z4 @ X4 )
% 8.57/4.53       => ~ ( ord_less_eq_int @ X4 @ T ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1346_zero__less__iff__neq__zero,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.53        = ( N != zero_zero_nat ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1347_gr__implies__not__zero,axiom,
% 8.57/4.53      ! [M: nat,N: nat] :
% 8.57/4.53        ( ( ord_less_nat @ M @ N )
% 8.57/4.53       => ( N != zero_zero_nat ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1348_not__less__zero,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1349_gr__zeroI,axiom,
% 8.57/4.53      ! [N: nat] :
% 8.57/4.53        ( ( N != zero_zero_nat )
% 8.57/4.53       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1350_less__numeral__extra_I3_J,axiom,
% 8.57/4.53      ~ ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ zero_z2226904508553997617atural ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1351_less__numeral__extra_I3_J,axiom,
% 8.57/4.53      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1352_less__numeral__extra_I3_J,axiom,
% 8.57/4.53      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1353_less__numeral__extra_I3_J,axiom,
% 8.57/4.53      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1354_less__numeral__extra_I3_J,axiom,
% 8.57/4.53      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1355_add__mono__thms__linordered__field_I5_J,axiom,
% 8.57/4.53      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 8.57/4.53        ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 8.57/4.53          & ( ord_le6747313008572928689nteger @ K @ L ) )
% 8.57/4.53       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1356_add__mono__thms__linordered__field_I5_J,axiom,
% 8.57/4.53      ! [I: rat,J: rat,K: rat,L: rat] :
% 8.57/4.53        ( ( ( ord_less_rat @ I @ J )
% 8.57/4.53          & ( ord_less_rat @ K @ L ) )
% 8.57/4.53       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1357_add__mono__thms__linordered__field_I5_J,axiom,
% 8.57/4.53      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.53        ( ( ( ord_less_nat @ I @ J )
% 8.57/4.53          & ( ord_less_nat @ K @ L ) )
% 8.57/4.53       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1358_add__mono__thms__linordered__field_I5_J,axiom,
% 8.57/4.53      ! [I: int,J: int,K: int,L: int] :
% 8.57/4.53        ( ( ( ord_less_int @ I @ J )
% 8.57/4.53          & ( ord_less_int @ K @ L ) )
% 8.57/4.53       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1359_add__mono__thms__linordered__field_I2_J,axiom,
% 8.57/4.53      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 8.57/4.53        ( ( ( I = J )
% 8.57/4.53          & ( ord_le6747313008572928689nteger @ K @ L ) )
% 8.57/4.53       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 8.57/4.53  
% 8.57/4.53  thf(fact_1360_add__mono__thms__linordered__field_I2_J,axiom,
% 8.57/4.53      ! [I: rat,J: rat,K: rat,L: rat] :
% 8.57/4.54        ( ( ( I = J )
% 8.57/4.54          & ( ord_less_rat @ K @ L ) )
% 8.57/4.54       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1361_add__mono__thms__linordered__field_I2_J,axiom,
% 8.57/4.54      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.54        ( ( ( I = J )
% 8.57/4.54          & ( ord_less_nat @ K @ L ) )
% 8.57/4.54       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1362_add__mono__thms__linordered__field_I2_J,axiom,
% 8.57/4.54      ! [I: int,J: int,K: int,L: int] :
% 8.57/4.54        ( ( ( I = J )
% 8.57/4.54          & ( ord_less_int @ K @ L ) )
% 8.57/4.54       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1363_add__mono__thms__linordered__field_I1_J,axiom,
% 8.57/4.54      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 8.57/4.54        ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 8.57/4.54          & ( K = L ) )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1364_add__mono__thms__linordered__field_I1_J,axiom,
% 8.57/4.54      ! [I: rat,J: rat,K: rat,L: rat] :
% 8.57/4.54        ( ( ( ord_less_rat @ I @ J )
% 8.57/4.54          & ( K = L ) )
% 8.57/4.54       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1365_add__mono__thms__linordered__field_I1_J,axiom,
% 8.57/4.54      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.54        ( ( ( ord_less_nat @ I @ J )
% 8.57/4.54          & ( K = L ) )
% 8.57/4.54       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1366_add__mono__thms__linordered__field_I1_J,axiom,
% 8.57/4.54      ! [I: int,J: int,K: int,L: int] :
% 8.57/4.54        ( ( ( ord_less_int @ I @ J )
% 8.57/4.54          & ( K = L ) )
% 8.57/4.54       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1367_add__strict__mono,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1368_add__strict__mono,axiom,
% 8.57/4.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ B )
% 8.57/4.54       => ( ( ord_less_rat @ C @ D )
% 8.57/4.54         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1369_add__strict__mono,axiom,
% 8.57/4.54      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.54        ( ( ord_less_nat @ A @ B )
% 8.57/4.54       => ( ( ord_less_nat @ C @ D )
% 8.57/4.54         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1370_add__strict__mono,axiom,
% 8.57/4.54      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ B )
% 8.57/4.54       => ( ( ord_less_int @ C @ D )
% 8.57/4.54         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1371_add__strict__left__mono,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1372_add__strict__left__mono,axiom,
% 8.57/4.54      ! [A: rat,B: rat,C: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ B )
% 8.57/4.54       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1373_add__strict__left__mono,axiom,
% 8.57/4.54      ! [A: nat,B: nat,C: nat] :
% 8.57/4.54        ( ( ord_less_nat @ A @ B )
% 8.57/4.54       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1374_add__strict__left__mono,axiom,
% 8.57/4.54      ! [A: int,B: int,C: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ B )
% 8.57/4.54       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1375_add__strict__right__mono,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1376_add__strict__right__mono,axiom,
% 8.57/4.54      ! [A: rat,B: rat,C: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ B )
% 8.57/4.54       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1377_add__strict__right__mono,axiom,
% 8.57/4.54      ! [A: nat,B: nat,C: nat] :
% 8.57/4.54        ( ( ord_less_nat @ A @ B )
% 8.57/4.54       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1378_add__strict__right__mono,axiom,
% 8.57/4.54      ! [A: int,B: int,C: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ B )
% 8.57/4.54       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1379_add__less__imp__less__left,axiom,
% 8.57/4.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1380_add__less__imp__less__left,axiom,
% 8.57/4.54      ! [C: rat,A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.57/4.54       => ( ord_less_rat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1381_add__less__imp__less__left,axiom,
% 8.57/4.54      ! [C: nat,A: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.57/4.54       => ( ord_less_nat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1382_add__less__imp__less__left,axiom,
% 8.57/4.54      ! [C: int,A: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.57/4.54       => ( ord_less_int @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1383_add__less__imp__less__right,axiom,
% 8.57/4.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1384_add__less__imp__less__right,axiom,
% 8.57/4.54      ! [A: rat,C: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.54       => ( ord_less_rat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1385_add__less__imp__less__right,axiom,
% 8.57/4.54      ! [A: nat,C: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.57/4.54       => ( ord_less_nat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1386_add__less__imp__less__right,axiom,
% 8.57/4.54      ! [A: int,C: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.57/4.54       => ( ord_less_int @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1387_less__numeral__extra_I4_J,axiom,
% 8.57/4.54      ~ ( ord_le5570908160329646204atural @ one_one_Code_natural @ one_one_Code_natural ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1388_less__numeral__extra_I4_J,axiom,
% 8.57/4.54      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1389_less__numeral__extra_I4_J,axiom,
% 8.57/4.54      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1390_less__numeral__extra_I4_J,axiom,
% 8.57/4.54      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1391_less__numeral__extra_I4_J,axiom,
% 8.57/4.54      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1392_bot__nat__0_Oextremum__strict,axiom,
% 8.57/4.54      ! [A: nat] :
% 8.57/4.54        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1393_gr0I,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( N != zero_zero_nat )
% 8.57/4.54       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1394_not__gr0,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 8.57/4.54        = ( N = zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1395_not__less0,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1396_less__zeroE,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1397_gr__implies__not0,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ N )
% 8.57/4.54       => ( N != zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1398_infinite__descent0,axiom,
% 8.57/4.54      ! [P: nat > $o,N: nat] :
% 8.57/4.54        ( ( P @ zero_zero_nat )
% 8.57/4.54       => ( ! [N2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 8.57/4.54             => ( ~ ( P @ N2 )
% 8.57/4.54               => ? [M6: nat] :
% 8.57/4.54                    ( ( ord_less_nat @ M6 @ N2 )
% 8.57/4.54                    & ~ ( P @ M6 ) ) ) )
% 8.57/4.54         => ( P @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1399_reals__Archimedean2,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54      ? [N2: nat] : ( ord_less_rat @ X2 @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1400_less__int__code_I1_J,axiom,
% 8.57/4.54      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1401_exists__leI,axiom,
% 8.57/4.54      ! [N: nat,P: nat > $o] :
% 8.57/4.54        ( ( ! [N5: nat] :
% 8.57/4.54              ( ( ord_less_nat @ N5 @ N )
% 8.57/4.54             => ~ ( P @ N5 ) )
% 8.57/4.54         => ( P @ N ) )
% 8.57/4.54       => ? [N6: nat] :
% 8.57/4.54            ( ( ord_less_eq_nat @ N6 @ N )
% 8.57/4.54            & ( P @ N6 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1402_nat__less__le,axiom,
% 8.57/4.54      ( ord_less_nat
% 8.57/4.54      = ( ^ [M2: nat,N3: nat] :
% 8.57/4.54            ( ( ord_less_eq_nat @ M2 @ N3 )
% 8.57/4.54            & ( M2 != N3 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1403_less__imp__le__nat,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ N )
% 8.57/4.54       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1404_le__eq__less__or__eq,axiom,
% 8.57/4.54      ( ord_less_eq_nat
% 8.57/4.54      = ( ^ [M2: nat,N3: nat] :
% 8.57/4.54            ( ( ord_less_nat @ M2 @ N3 )
% 8.57/4.54            | ( M2 = N3 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1405_less__or__eq__imp__le,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ( ord_less_nat @ M @ N )
% 8.57/4.54          | ( M = N ) )
% 8.57/4.54       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1406_le__neq__implies__less,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.54       => ( ( M != N )
% 8.57/4.54         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1407_less__mono__imp__le__mono,axiom,
% 8.57/4.54      ! [F: nat > nat,I: nat,J: nat] :
% 8.57/4.54        ( ! [I3: nat,J2: nat] :
% 8.57/4.54            ( ( ord_less_nat @ I3 @ J2 )
% 8.57/4.54           => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.54         => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1408_add__lessD1,axiom,
% 8.57/4.54      ! [I: nat,J: nat,K: nat] :
% 8.57/4.54        ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 8.57/4.54       => ( ord_less_nat @ I @ K ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1409_add__less__mono,axiom,
% 8.57/4.54      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.54        ( ( ord_less_nat @ I @ J )
% 8.57/4.54       => ( ( ord_less_nat @ K @ L )
% 8.57/4.54         => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1410_not__add__less1,axiom,
% 8.57/4.54      ! [I: nat,J: nat] :
% 8.57/4.54        ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1411_not__add__less2,axiom,
% 8.57/4.54      ! [J: nat,I: nat] :
% 8.57/4.54        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1412_add__less__mono1,axiom,
% 8.57/4.54      ! [I: nat,J: nat,K: nat] :
% 8.57/4.54        ( ( ord_less_nat @ I @ J )
% 8.57/4.54       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1413_trans__less__add1,axiom,
% 8.57/4.54      ! [I: nat,J: nat,M: nat] :
% 8.57/4.54        ( ( ord_less_nat @ I @ J )
% 8.57/4.54       => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1414_trans__less__add2,axiom,
% 8.57/4.54      ! [I: nat,J: nat,M: nat] :
% 8.57/4.54        ( ( ord_less_nat @ I @ J )
% 8.57/4.54       => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1415_less__add__eq__less,axiom,
% 8.57/4.54      ! [K: nat,L: nat,M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ K @ L )
% 8.57/4.54       => ( ( ( plus_plus_nat @ M @ L )
% 8.57/4.54            = ( plus_plus_nat @ K @ N ) )
% 8.57/4.54         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1416_ex__less__of__int,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54      ? [Z4: int] : ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z4 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1417_ex__of__int__less,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54      ? [Z4: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z4 ) @ X2 ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1418_of__nat__floor,axiom,
% 8.57/4.54      ! [R: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 8.57/4.54       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R ) ) ) @ R ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1419_nat__le__eq__zle,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 8.57/4.54          | ( ord_less_eq_int @ zero_zero_int @ Z2 ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z2 ) )
% 8.57/4.54          = ( ord_less_eq_int @ W2 @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1420_split__nat,axiom,
% 8.57/4.54      ! [P: nat > $o,I: int] :
% 8.57/4.54        ( ( P @ ( nat2 @ I ) )
% 8.57/4.54        = ( ! [N3: nat] :
% 8.57/4.54              ( ( I
% 8.57/4.54                = ( semiri1314217659103216013at_int @ N3 ) )
% 8.57/4.54             => ( P @ N3 ) )
% 8.57/4.54          & ( ( ord_less_int @ I @ zero_zero_int )
% 8.57/4.54           => ( P @ zero_zero_nat ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1421_of__int__pos,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1422_of__int__pos,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 8.57/4.54       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1423_of__int__pos,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 8.57/4.54       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1424_zero__less__imp__eq__int,axiom,
% 8.57/4.54      ! [K: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.54       => ? [N2: nat] :
% 8.57/4.54            ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 8.57/4.54            & ( K
% 8.57/4.54              = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1425_pos__int__cases,axiom,
% 8.57/4.54      ! [K: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.54       => ~ ! [N2: nat] :
% 8.57/4.54              ( ( K
% 8.57/4.54                = ( semiri1314217659103216013at_int @ N2 ) )
% 8.57/4.54             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1426_of__nat__less__of__int__iff,axiom,
% 8.57/4.54      ! [N: nat,X2: int] :
% 8.57/4.54        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X2 ) )
% 8.57/4.54        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1427_of__nat__less__of__int__iff,axiom,
% 8.57/4.54      ! [N: nat,X2: int] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N ) @ ( ring_18347121197199848620nteger @ X2 ) )
% 8.57/4.54        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1428_of__nat__less__of__int__iff,axiom,
% 8.57/4.54      ! [N: nat,X2: int] :
% 8.57/4.54        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X2 ) )
% 8.57/4.54        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1429_zero__le__power__int,axiom,
% 8.57/4.54      ! [X2: rat,N: int] :
% 8.57/4.54        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.54       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_int_rat @ X2 @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1430_power__int__le__imp__le__exp,axiom,
% 8.57/4.54      ! [X2: rat,M: int,N: int] :
% 8.57/4.54        ( ( ord_less_rat @ one_one_rat @ X2 )
% 8.57/4.54       => ( ( ord_less_eq_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ X2 @ N ) )
% 8.57/4.54         => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 8.57/4.54           => ( ord_less_eq_int @ M @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1431_floor__split,axiom,
% 8.57/4.54      ! [P: int > $o,T: rat] :
% 8.57/4.54        ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 8.57/4.54        = ( ! [I2: int] :
% 8.57/4.54              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I2 ) @ T )
% 8.57/4.54                & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) ) )
% 8.57/4.54             => ( P @ I2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1432_floor__eq__iff,axiom,
% 8.57/4.54      ! [X2: rat,A: int] :
% 8.57/4.54        ( ( ( archim3151403230148437115or_rat @ X2 )
% 8.57/4.54          = A )
% 8.57/4.54        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X2 )
% 8.57/4.54          & ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1433_floor__unique,axiom,
% 8.57/4.54      ! [Z2: int,X2: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 )
% 8.57/4.54       => ( ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) )
% 8.57/4.54         => ( ( archim3151403230148437115or_rat @ X2 )
% 8.57/4.54            = Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1434_less__floor__iff,axiom,
% 8.57/4.54      ! [Z2: int,X2: rat] :
% 8.57/4.54        ( ( ord_less_int @ Z2 @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.54        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1435_power__int__not__zero,axiom,
% 8.57/4.54      ! [X2: rat,N: int] :
% 8.57/4.54        ( ( ( X2 != zero_zero_rat )
% 8.57/4.54          | ( N = zero_zero_int ) )
% 8.57/4.54       => ( ( power_int_rat @ X2 @ N )
% 8.57/4.54         != zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1436_floor__le__iff,axiom,
% 8.57/4.54      ! [X2: rat,Z2: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z2 )
% 8.57/4.54        = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1437_floor__correct,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 )
% 8.57/4.54        & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1438_floor__mono,axiom,
% 8.57/4.54      ! [X2: rat,Y: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.54       => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1439_nat__zero__as__int,axiom,
% 8.57/4.54      ( zero_zero_nat
% 8.57/4.54      = ( nat2 @ zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1440_of__int__floor__le,axiom,
% 8.57/4.54      ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1441_nat__mono,axiom,
% 8.57/4.54      ! [X2: int,Y: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.54       => ( ord_less_eq_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1442_ex__nat,axiom,
% 8.57/4.54      ( ( ^ [P4: nat > $o] :
% 8.57/4.54          ? [X7: nat] : ( P4 @ X7 ) )
% 8.57/4.54      = ( ^ [P5: nat > $o] :
% 8.57/4.54          ? [X: int] :
% 8.57/4.54            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.57/4.54            & ( P5 @ ( nat2 @ X ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1443_all__nat,axiom,
% 8.57/4.54      ( ( ^ [P4: nat > $o] :
% 8.57/4.54          ! [X7: nat] : ( P4 @ X7 ) )
% 8.57/4.54      = ( ^ [P5: nat > $o] :
% 8.57/4.54          ! [X: int] :
% 8.57/4.54            ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.57/4.54           => ( P5 @ ( nat2 @ X ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1444_eq__nat__nat__iff,axiom,
% 8.57/4.54      ! [Z2: int,Z6: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.54       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 8.57/4.54         => ( ( ( nat2 @ Z2 )
% 8.57/4.54              = ( nat2 @ Z6 ) )
% 8.57/4.54            = ( Z2 = Z6 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1445_nat__one__as__int,axiom,
% 8.57/4.54      ( one_one_nat
% 8.57/4.54      = ( nat2 @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1446_add__less__le__mono,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.54       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1447_add__less__le__mono,axiom,
% 8.57/4.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ B )
% 8.57/4.54       => ( ( ord_less_eq_rat @ C @ D )
% 8.57/4.54         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1448_add__less__le__mono,axiom,
% 8.57/4.54      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.54        ( ( ord_less_nat @ A @ B )
% 8.57/4.54       => ( ( ord_less_eq_nat @ C @ D )
% 8.57/4.54         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1449_add__less__le__mono,axiom,
% 8.57/4.54      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ B )
% 8.57/4.54       => ( ( ord_less_eq_int @ C @ D )
% 8.57/4.54         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1450_add__le__less__mono,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1451_add__le__less__mono,axiom,
% 8.57/4.54      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.54       => ( ( ord_less_rat @ C @ D )
% 8.57/4.54         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1452_add__le__less__mono,axiom,
% 8.57/4.54      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.54       => ( ( ord_less_nat @ C @ D )
% 8.57/4.54         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1453_add__le__less__mono,axiom,
% 8.57/4.54      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.54       => ( ( ord_less_int @ C @ D )
% 8.57/4.54         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1454_add__mono__thms__linordered__field_I3_J,axiom,
% 8.57/4.54      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 8.57/4.54        ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 8.57/4.54          & ( ord_le3102999989581377725nteger @ K @ L ) )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1455_add__mono__thms__linordered__field_I3_J,axiom,
% 8.57/4.54      ! [I: rat,J: rat,K: rat,L: rat] :
% 8.57/4.54        ( ( ( ord_less_rat @ I @ J )
% 8.57/4.54          & ( ord_less_eq_rat @ K @ L ) )
% 8.57/4.54       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1456_add__mono__thms__linordered__field_I3_J,axiom,
% 8.57/4.54      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.54        ( ( ( ord_less_nat @ I @ J )
% 8.57/4.54          & ( ord_less_eq_nat @ K @ L ) )
% 8.57/4.54       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1457_add__mono__thms__linordered__field_I3_J,axiom,
% 8.57/4.54      ! [I: int,J: int,K: int,L: int] :
% 8.57/4.54        ( ( ( ord_less_int @ I @ J )
% 8.57/4.54          & ( ord_less_eq_int @ K @ L ) )
% 8.57/4.54       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1458_add__mono__thms__linordered__field_I4_J,axiom,
% 8.57/4.54      ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 8.57/4.54        ( ( ( ord_le3102999989581377725nteger @ I @ J )
% 8.57/4.54          & ( ord_le6747313008572928689nteger @ K @ L ) )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1459_add__mono__thms__linordered__field_I4_J,axiom,
% 8.57/4.54      ! [I: rat,J: rat,K: rat,L: rat] :
% 8.57/4.54        ( ( ( ord_less_eq_rat @ I @ J )
% 8.57/4.54          & ( ord_less_rat @ K @ L ) )
% 8.57/4.54       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1460_add__mono__thms__linordered__field_I4_J,axiom,
% 8.57/4.54      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.54        ( ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.54          & ( ord_less_nat @ K @ L ) )
% 8.57/4.54       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1461_add__mono__thms__linordered__field_I4_J,axiom,
% 8.57/4.54      ! [I: int,J: int,K: int,L: int] :
% 8.57/4.54        ( ( ( ord_less_eq_int @ I @ J )
% 8.57/4.54          & ( ord_less_int @ K @ L ) )
% 8.57/4.54       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1462_add__less__zeroD,axiom,
% 8.57/4.54      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ X2 @ Y ) @ zero_z3403309356797280102nteger )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ X2 @ zero_z3403309356797280102nteger )
% 8.57/4.54          | ( ord_le6747313008572928689nteger @ Y @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1463_add__less__zeroD,axiom,
% 8.57/4.54      ! [X2: rat,Y: rat] :
% 8.57/4.54        ( ( ord_less_rat @ ( plus_plus_rat @ X2 @ Y ) @ zero_zero_rat )
% 8.57/4.54       => ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 8.57/4.54          | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1464_add__less__zeroD,axiom,
% 8.57/4.54      ! [X2: int,Y: int] :
% 8.57/4.54        ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y ) @ zero_zero_int )
% 8.57/4.54       => ( ( ord_less_int @ X2 @ zero_zero_int )
% 8.57/4.54          | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1465_add__neg__neg,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.54       => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 8.57/4.54         => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1466_add__neg__neg,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1467_add__neg__neg,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.54       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.57/4.54         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1468_add__neg__neg,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_nat @ A @ zero_zero_nat )
% 8.57/4.54       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.57/4.54         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1469_add__neg__neg,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ zero_zero_int )
% 8.57/4.54       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.54         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1470_add__pos__pos,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.54       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.54         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1471_add__pos__pos,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1472_add__pos__pos,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.54       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.57/4.54         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1473_add__pos__pos,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.54       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.54         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1474_add__pos__pos,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.54       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.54         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1475_canonically__ordered__monoid__add__class_OlessE,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_nat @ A @ B )
% 8.57/4.54       => ~ ! [C3: nat] :
% 8.57/4.54              ( ( B
% 8.57/4.54                = ( plus_plus_nat @ A @ C3 ) )
% 8.57/4.54             => ( C3 = zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1476_pos__add__strict,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.54        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.54       => ( ( ord_le5570908160329646204atural @ B @ C )
% 8.57/4.54         => ( ord_le5570908160329646204atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1477_pos__add__strict,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1478_pos__add__strict,axiom,
% 8.57/4.54      ! [A: rat,B: rat,C: rat] :
% 8.57/4.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.54       => ( ( ord_less_rat @ B @ C )
% 8.57/4.54         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1479_pos__add__strict,axiom,
% 8.57/4.54      ! [A: nat,B: nat,C: nat] :
% 8.57/4.54        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.54       => ( ( ord_less_nat @ B @ C )
% 8.57/4.54         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1480_pos__add__strict,axiom,
% 8.57/4.54      ! [A: int,B: int,C: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.54       => ( ( ord_less_int @ B @ C )
% 8.57/4.54         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1481_zero__less__one,axiom,
% 8.57/4.54      ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1482_zero__less__one,axiom,
% 8.57/4.54      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1483_zero__less__one,axiom,
% 8.57/4.54      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1484_zero__less__one,axiom,
% 8.57/4.54      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1485_zero__less__one,axiom,
% 8.57/4.54      ord_less_int @ zero_zero_int @ one_one_int ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1486_not__one__less__zero,axiom,
% 8.57/4.54      ~ ( ord_le5570908160329646204atural @ one_one_Code_natural @ zero_z2226904508553997617atural ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1487_not__one__less__zero,axiom,
% 8.57/4.54      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1488_not__one__less__zero,axiom,
% 8.57/4.54      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1489_not__one__less__zero,axiom,
% 8.57/4.54      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1490_not__one__less__zero,axiom,
% 8.57/4.54      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1491_less__numeral__extra_I1_J,axiom,
% 8.57/4.54      ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1492_less__numeral__extra_I1_J,axiom,
% 8.57/4.54      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1493_less__numeral__extra_I1_J,axiom,
% 8.57/4.54      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1494_less__numeral__extra_I1_J,axiom,
% 8.57/4.54      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1495_less__numeral__extra_I1_J,axiom,
% 8.57/4.54      ord_less_int @ zero_zero_int @ one_one_int ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1496_less__add__one,axiom,
% 8.57/4.54      ! [A: code_natural] : ( ord_le5570908160329646204atural @ A @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1497_less__add__one,axiom,
% 8.57/4.54      ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1498_less__add__one,axiom,
% 8.57/4.54      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1499_less__add__one,axiom,
% 8.57/4.54      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1500_less__add__one,axiom,
% 8.57/4.54      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1501_add__mono1,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ord_le5570908160329646204atural @ A @ B )
% 8.57/4.54       => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ B @ one_one_Code_natural ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1502_add__mono1,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1503_add__mono1,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ B )
% 8.57/4.54       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1504_add__mono1,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_nat @ A @ B )
% 8.57/4.54       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1505_add__mono1,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ B )
% 8.57/4.54       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1506_floor__le__ceiling,axiom,
% 8.57/4.54      ! [X2: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1507_of__nat__less__0__iff,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1508_of__nat__less__0__iff,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1509_of__nat__less__0__iff,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ~ ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1510_of__nat__less__0__iff,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1511_of__nat__less__0__iff,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ~ ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ M ) @ zero_z2226904508553997617atural ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1512_ex__least__nat__le,axiom,
% 8.57/4.54      ! [P: nat > $o,N: nat] :
% 8.57/4.54        ( ( P @ N )
% 8.57/4.54       => ( ~ ( P @ zero_zero_nat )
% 8.57/4.54         => ? [K3: nat] :
% 8.57/4.54              ( ( ord_less_eq_nat @ K3 @ N )
% 8.57/4.54              & ! [I4: nat] :
% 8.57/4.54                  ( ( ord_less_nat @ I4 @ K3 )
% 8.57/4.54                 => ~ ( P @ I4 ) )
% 8.57/4.54              & ( P @ K3 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1513_less__imp__add__positive,axiom,
% 8.57/4.54      ! [I: nat,J: nat] :
% 8.57/4.54        ( ( ord_less_nat @ I @ J )
% 8.57/4.54       => ? [K3: nat] :
% 8.57/4.54            ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 8.57/4.54            & ( ( plus_plus_nat @ I @ K3 )
% 8.57/4.54              = J ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1514_mono__nat__linear__lb,axiom,
% 8.57/4.54      ! [F: nat > nat,M: nat,K: nat] :
% 8.57/4.54        ( ! [M4: nat,N2: nat] :
% 8.57/4.54            ( ( ord_less_nat @ M4 @ N2 )
% 8.57/4.54           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 8.57/4.54       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1515_zless__add1__eq,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 8.57/4.54        = ( ( ord_less_int @ W2 @ Z2 )
% 8.57/4.54          | ( W2 = Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1516_int__gr__induct,axiom,
% 8.57/4.54      ! [K: int,I: int,P: int > $o] :
% 8.57/4.54        ( ( ord_less_int @ K @ I )
% 8.57/4.54       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 8.57/4.54         => ( ! [I3: int] :
% 8.57/4.54                ( ( ord_less_int @ K @ I3 )
% 8.57/4.54               => ( ( P @ I3 )
% 8.57/4.54                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 8.57/4.54           => ( P @ I ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1517_power__int__0__left__If,axiom,
% 8.57/4.54      ! [M: int] :
% 8.57/4.54        ( ( ( M = zero_zero_int )
% 8.57/4.54         => ( ( power_int_rat @ zero_zero_rat @ M )
% 8.57/4.54            = one_one_rat ) )
% 8.57/4.54        & ( ( M != zero_zero_int )
% 8.57/4.54         => ( ( power_int_rat @ zero_zero_rat @ M )
% 8.57/4.54            = zero_zero_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1518_power__int__increasing,axiom,
% 8.57/4.54      ! [N: int,N4: int,A: rat] :
% 8.57/4.54        ( ( ord_less_eq_int @ N @ N4 )
% 8.57/4.54       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.57/4.54         => ( ord_less_eq_rat @ ( power_int_rat @ A @ N ) @ ( power_int_rat @ A @ N4 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1519_le__floor__iff,axiom,
% 8.57/4.54      ! [Z2: int,X2: rat] :
% 8.57/4.54        ( ( ord_less_eq_int @ Z2 @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.54        = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1520_le__floor__add,axiom,
% 8.57/4.54      ! [X2: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1521_int__add__floor,axiom,
% 8.57/4.54      ! [Z2: int,X2: rat] :
% 8.57/4.54        ( ( plus_plus_int @ Z2 @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.54        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1522_floor__add__int,axiom,
% 8.57/4.54      ! [X2: rat,Z2: int] :
% 8.57/4.54        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z2 )
% 8.57/4.54        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1523_nat__le__iff,axiom,
% 8.57/4.54      ! [X2: int,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( nat2 @ X2 ) @ N )
% 8.57/4.54        = ( ord_less_eq_int @ X2 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1524_nat__0__le,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.54       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 8.57/4.54          = Z2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1525_int__eq__iff,axiom,
% 8.57/4.54      ! [M: nat,Z2: int] :
% 8.57/4.54        ( ( ( semiri1314217659103216013at_int @ M )
% 8.57/4.54          = Z2 )
% 8.57/4.54        = ( ( M
% 8.57/4.54            = ( nat2 @ Z2 ) )
% 8.57/4.54          & ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1526_of__nat__ceiling,axiom,
% 8.57/4.54      ! [R: rat] : ( ord_less_eq_rat @ R @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1527_nat__int__add,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 8.57/4.54        = ( plus_plus_nat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1528_add__neg__nonpos,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.54       => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 8.57/4.54         => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1529_add__neg__nonpos,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.54       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1530_add__neg__nonpos,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.54       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.57/4.54         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1531_add__neg__nonpos,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_nat @ A @ zero_zero_nat )
% 8.57/4.54       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.57/4.54         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1532_add__neg__nonpos,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ zero_zero_int )
% 8.57/4.54       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.57/4.54         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1533_add__nonneg__pos,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.54       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.54         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1534_add__nonneg__pos,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1535_add__nonneg__pos,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.54       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.57/4.54         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1536_add__nonneg__pos,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.54       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.54         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1537_add__nonneg__pos,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.54       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.54         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1538_add__nonpos__neg,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.54       => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 8.57/4.54         => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1539_add__nonpos__neg,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1540_add__nonpos__neg,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.54       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.57/4.54         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1541_add__nonpos__neg,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.57/4.54       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.57/4.54         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1542_add__nonpos__neg,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.54       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.54         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1543_add__pos__nonneg,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.54       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.54         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1544_add__pos__nonneg,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.54       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1545_add__pos__nonneg,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.54         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1546_add__pos__nonneg,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.54         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1547_add__pos__nonneg,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.54       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.54         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1548_add__strict__increasing,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.54        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.54       => ( ( ord_le1926595141338095240atural @ B @ C )
% 8.57/4.54         => ( ord_le5570908160329646204atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1549_add__strict__increasing,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.54       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1550_add__strict__increasing,axiom,
% 8.57/4.54      ! [A: rat,B: rat,C: rat] :
% 8.57/4.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.54       => ( ( ord_less_eq_rat @ B @ C )
% 8.57/4.54         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1551_add__strict__increasing,axiom,
% 8.57/4.54      ! [A: nat,B: nat,C: nat] :
% 8.57/4.54        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.54       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.54         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1552_add__strict__increasing,axiom,
% 8.57/4.54      ! [A: int,B: int,C: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.54       => ( ( ord_less_eq_int @ B @ C )
% 8.57/4.54         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1553_add__strict__increasing2,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.54        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.54       => ( ( ord_le5570908160329646204atural @ B @ C )
% 8.57/4.54         => ( ord_le5570908160329646204atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1554_add__strict__increasing2,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1555_add__strict__increasing2,axiom,
% 8.57/4.54      ! [A: rat,B: rat,C: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.54       => ( ( ord_less_rat @ B @ C )
% 8.57/4.54         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1556_add__strict__increasing2,axiom,
% 8.57/4.54      ! [A: nat,B: nat,C: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.54       => ( ( ord_less_nat @ B @ C )
% 8.57/4.54         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1557_add__strict__increasing2,axiom,
% 8.57/4.54      ! [A: int,B: int,C: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.54       => ( ( ord_less_int @ B @ C )
% 8.57/4.54         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1558_zero__less__two,axiom,
% 8.57/4.54      ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1559_zero__less__two,axiom,
% 8.57/4.54      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1560_zero__less__two,axiom,
% 8.57/4.54      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1561_zero__less__two,axiom,
% 8.57/4.54      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1562_zero__less__two,axiom,
% 8.57/4.54      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1563_int__one__le__iff__zero__less,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ one_one_int @ Z2 )
% 8.57/4.54        = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1564_odd__less__0__iff,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 ) @ zero_zero_int )
% 8.57/4.54        = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1565_add1__zle__eq,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 )
% 8.57/4.54        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1566_zless__imp__add1__zle,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ord_less_int @ W2 @ Z2 )
% 8.57/4.54       => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1567_nat__plus__as__int,axiom,
% 8.57/4.54      ( plus_plus_nat
% 8.57/4.54      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1568_power__int__mono,axiom,
% 8.57/4.54      ! [X2: rat,Y: rat,N: int] :
% 8.57/4.54        ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.54       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 8.57/4.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.54           => ( ord_less_eq_rat @ ( power_int_rat @ X2 @ N ) @ ( power_int_rat @ Y @ N ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1569_one__le__power__int,axiom,
% 8.57/4.54      ! [X2: rat,N: int] :
% 8.57/4.54        ( ( ord_less_eq_rat @ one_one_rat @ X2 )
% 8.57/4.54       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 8.57/4.54         => ( ord_less_eq_rat @ one_one_rat @ ( power_int_rat @ X2 @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1570_one__add__floor,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 8.57/4.54        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1571_nat__eq__iff2,axiom,
% 8.57/4.54      ! [M: nat,W2: int] :
% 8.57/4.54        ( ( M
% 8.57/4.54          = ( nat2 @ W2 ) )
% 8.57/4.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.57/4.54           => ( W2
% 8.57/4.54              = ( semiri1314217659103216013at_int @ M ) ) )
% 8.57/4.54          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.57/4.54           => ( M = zero_zero_nat ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1572_nat__eq__iff,axiom,
% 8.57/4.54      ! [W2: int,M: nat] :
% 8.57/4.54        ( ( ( nat2 @ W2 )
% 8.57/4.54          = M )
% 8.57/4.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.57/4.54           => ( W2
% 8.57/4.54              = ( semiri1314217659103216013at_int @ M ) ) )
% 8.57/4.54          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.57/4.54           => ( M = zero_zero_nat ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1573_le__nat__iff,axiom,
% 8.57/4.54      ! [K: int,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 8.57/4.54          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1574_nat__add__distrib,axiom,
% 8.57/4.54      ! [Z2: int,Z6: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.54       => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 8.57/4.54         => ( ( nat2 @ ( plus_plus_int @ Z2 @ Z6 ) )
% 8.57/4.54            = ( plus_plus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1575_ceiling__altdef,axiom,
% 8.57/4.54      ( archim2889992004027027881ng_rat
% 8.57/4.54      = ( ^ [X: rat] :
% 8.57/4.54            ( if_int
% 8.57/4.54            @ ( X
% 8.57/4.54              = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 8.57/4.54            @ ( archim3151403230148437115or_rat @ X )
% 8.57/4.54            @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1576_floor__exists,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54      ? [Z4: int] :
% 8.57/4.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X2 )
% 8.57/4.54        & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1577_floor__exists1,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54      ? [X3: int] :
% 8.57/4.54        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X2 )
% 8.57/4.54        & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 8.57/4.54        & ! [Y5: int] :
% 8.57/4.54            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X2 )
% 8.57/4.54              & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 8.57/4.54           => ( Y5 = X3 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1578_discrete,axiom,
% 8.57/4.54      ( ord_le6747313008572928689nteger
% 8.57/4.54      = ( ^ [A2: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1579_discrete,axiom,
% 8.57/4.54      ( ord_less_nat
% 8.57/4.54      = ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1580_discrete,axiom,
% 8.57/4.54      ( ord_less_int
% 8.57/4.54      = ( ^ [A2: int] : ( ord_less_eq_int @ ( plus_plus_int @ A2 @ one_one_int ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1581_field__le__epsilon,axiom,
% 8.57/4.54      ! [X2: rat,Y: rat] :
% 8.57/4.54        ( ! [E3: rat] :
% 8.57/4.54            ( ( ord_less_rat @ zero_zero_rat @ E3 )
% 8.57/4.54           => ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ Y @ E3 ) ) )
% 8.57/4.54       => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1582_floor__add,axiom,
% 8.57/4.54      ! [X2: rat,Y: rat] :
% 8.57/4.54        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 8.57/4.54         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 8.57/4.54            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 8.57/4.54        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 8.57/4.54         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 8.57/4.54            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1583_complete__interval,axiom,
% 8.57/4.54      ! [A: nat,B: nat,P: nat > $o] :
% 8.57/4.54        ( ( ord_less_nat @ A @ B )
% 8.57/4.54       => ( ( P @ A )
% 8.57/4.54         => ( ~ ( P @ B )
% 8.57/4.54           => ? [C3: nat] :
% 8.57/4.54                ( ( ord_less_eq_nat @ A @ C3 )
% 8.57/4.54                & ( ord_less_eq_nat @ C3 @ B )
% 8.57/4.54                & ! [X4: nat] :
% 8.57/4.54                    ( ( ( ord_less_eq_nat @ A @ X4 )
% 8.57/4.54                      & ( ord_less_nat @ X4 @ C3 ) )
% 8.57/4.54                   => ( P @ X4 ) )
% 8.57/4.54                & ! [D2: nat] :
% 8.57/4.54                    ( ! [X3: nat] :
% 8.57/4.54                        ( ( ( ord_less_eq_nat @ A @ X3 )
% 8.57/4.54                          & ( ord_less_nat @ X3 @ D2 ) )
% 8.57/4.54                       => ( P @ X3 ) )
% 8.57/4.54                   => ( ord_less_eq_nat @ D2 @ C3 ) ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1584_complete__interval,axiom,
% 8.57/4.54      ! [A: int,B: int,P: int > $o] :
% 8.57/4.54        ( ( ord_less_int @ A @ B )
% 8.57/4.54       => ( ( P @ A )
% 8.57/4.54         => ( ~ ( P @ B )
% 8.57/4.54           => ? [C3: int] :
% 8.57/4.54                ( ( ord_less_eq_int @ A @ C3 )
% 8.57/4.54                & ( ord_less_eq_int @ C3 @ B )
% 8.57/4.54                & ! [X4: int] :
% 8.57/4.54                    ( ( ( ord_less_eq_int @ A @ X4 )
% 8.57/4.54                      & ( ord_less_int @ X4 @ C3 ) )
% 8.57/4.54                   => ( P @ X4 ) )
% 8.57/4.54                & ! [D2: int] :
% 8.57/4.54                    ( ! [X3: int] :
% 8.57/4.54                        ( ( ( ord_less_eq_int @ A @ X3 )
% 8.57/4.54                          & ( ord_less_int @ X3 @ D2 ) )
% 8.57/4.54                       => ( P @ X3 ) )
% 8.57/4.54                   => ( ord_less_eq_int @ D2 @ C3 ) ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1585_zero__le__ceiling,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.54        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1586_ceiling__less__zero,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 8.57/4.54        = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1587_time__array__of__list,axiom,
% 8.57/4.54      ! [Xs: list_nat,H: heap_e7401611519738050253t_unit] :
% 8.57/4.54        ( ( time_time_array_nat @ ( array_of_list_nat @ Xs ) @ H )
% 8.57/4.54        = ( plus_plus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1588_time__array__of__list,axiom,
% 8.57/4.54      ! [Xs: list_int,H: heap_e7401611519738050253t_unit] :
% 8.57/4.54        ( ( time_time_array_int @ ( array_of_list_int @ Xs ) @ H )
% 8.57/4.54        = ( plus_plus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1589_time__array__of__list,axiom,
% 8.57/4.54      ! [Xs: list_o,H: heap_e7401611519738050253t_unit] :
% 8.57/4.54        ( ( time_time_array_o @ ( array_of_list_o @ Xs ) @ H )
% 8.57/4.54        = ( plus_plus_nat @ ( size_size_list_o @ Xs ) @ one_one_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1590_Suc__nat__eq__nat__zadd1,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.54       => ( ( suc @ ( nat2 @ Z2 ) )
% 8.57/4.54          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1591_gen__length__def,axiom,
% 8.57/4.54      ( gen_length_nat
% 8.57/4.54      = ( ^ [N3: nat,Xs3: list_nat] : ( plus_plus_nat @ N3 @ ( size_size_list_nat @ Xs3 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1592_gen__length__def,axiom,
% 8.57/4.54      ( gen_length_int
% 8.57/4.54      = ( ^ [N3: nat,Xs3: list_int] : ( plus_plus_nat @ N3 @ ( size_size_list_int @ Xs3 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1593_gen__length__def,axiom,
% 8.57/4.54      ( gen_length_o
% 8.57/4.54      = ( ^ [N3: nat,Xs3: list_o] : ( plus_plus_nat @ N3 @ ( size_size_list_o @ Xs3 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1594_verit__minus__simplify_I4_J,axiom,
% 8.57/4.54      ! [B: int] :
% 8.57/4.54        ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1595_verit__minus__simplify_I4_J,axiom,
% 8.57/4.54      ! [B: code_integer] :
% 8.57/4.54        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1596_verit__minus__simplify_I4_J,axiom,
% 8.57/4.54      ! [B: rat] :
% 8.57/4.54        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1597_neg__equal__iff__equal,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ( uminus_uminus_int @ A )
% 8.57/4.54          = ( uminus_uminus_int @ B ) )
% 8.57/4.54        = ( A = B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1598_neg__equal__iff__equal,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ( uminus1351360451143612070nteger @ A )
% 8.57/4.54          = ( uminus1351360451143612070nteger @ B ) )
% 8.57/4.54        = ( A = B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1599_neg__equal__iff__equal,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ( uminus_uminus_rat @ A )
% 8.57/4.54          = ( uminus_uminus_rat @ B ) )
% 8.57/4.54        = ( A = B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1600_add_Oinverse__inverse,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1601_add_Oinverse__inverse,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1602_add_Oinverse__inverse,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1603_old_Onat_Oinject,axiom,
% 8.57/4.54      ! [Nat: nat,Nat2: nat] :
% 8.57/4.54        ( ( ( suc @ Nat )
% 8.57/4.54          = ( suc @ Nat2 ) )
% 8.57/4.54        = ( Nat = Nat2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1604_nat_Oinject,axiom,
% 8.57/4.54      ! [X22: nat,Y22: nat] :
% 8.57/4.54        ( ( ( suc @ X22 )
% 8.57/4.54          = ( suc @ Y22 ) )
% 8.57/4.54        = ( X22 = Y22 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1605_neg__le__iff__le,axiom,
% 8.57/4.54      ! [B: code_integer,A: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1606_neg__le__iff__le,axiom,
% 8.57/4.54      ! [B: rat,A: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = ( ord_less_eq_rat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1607_neg__le__iff__le,axiom,
% 8.57/4.54      ! [B: int,A: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 8.57/4.54        = ( ord_less_eq_int @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1608_add_Oinverse__neutral,axiom,
% 8.57/4.54      ( ( uminus_uminus_int @ zero_zero_int )
% 8.57/4.54      = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1609_add_Oinverse__neutral,axiom,
% 8.57/4.54      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 8.57/4.54      = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1610_add_Oinverse__neutral,axiom,
% 8.57/4.54      ( ( uminus_uminus_rat @ zero_zero_rat )
% 8.57/4.54      = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1611_neg__0__equal__iff__equal,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( zero_zero_int
% 8.57/4.54          = ( uminus_uminus_int @ A ) )
% 8.57/4.54        = ( zero_zero_int = A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1612_neg__0__equal__iff__equal,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( zero_z3403309356797280102nteger
% 8.57/4.54          = ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = ( zero_z3403309356797280102nteger = A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1613_neg__0__equal__iff__equal,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( zero_zero_rat
% 8.57/4.54          = ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = ( zero_zero_rat = A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1614_neg__equal__0__iff__equal,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ( uminus_uminus_int @ A )
% 8.57/4.54          = zero_zero_int )
% 8.57/4.54        = ( A = zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1615_neg__equal__0__iff__equal,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ( uminus1351360451143612070nteger @ A )
% 8.57/4.54          = zero_z3403309356797280102nteger )
% 8.57/4.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1616_neg__equal__0__iff__equal,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ( uminus_uminus_rat @ A )
% 8.57/4.54          = zero_zero_rat )
% 8.57/4.54        = ( A = zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1617_equal__neg__zero,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( A
% 8.57/4.54          = ( uminus_uminus_int @ A ) )
% 8.57/4.54        = ( A = zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1618_equal__neg__zero,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( A
% 8.57/4.54          = ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1619_equal__neg__zero,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( A
% 8.57/4.54          = ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = ( A = zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1620_neg__equal__zero,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ( uminus_uminus_int @ A )
% 8.57/4.54          = A )
% 8.57/4.54        = ( A = zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1621_neg__equal__zero,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ( uminus1351360451143612070nteger @ A )
% 8.57/4.54          = A )
% 8.57/4.54        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1622_neg__equal__zero,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ( uminus_uminus_rat @ A )
% 8.57/4.54          = A )
% 8.57/4.54        = ( A = zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1623_neg__less__iff__less,axiom,
% 8.57/4.54      ! [B: int,A: int] :
% 8.57/4.54        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 8.57/4.54        = ( ord_less_int @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1624_neg__less__iff__less,axiom,
% 8.57/4.54      ! [B: code_integer,A: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1625_neg__less__iff__less,axiom,
% 8.57/4.54      ! [B: rat,A: rat] :
% 8.57/4.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = ( ord_less_rat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1626_minus__add__distrib,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 8.57/4.54        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1627_minus__add__distrib,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.57/4.54        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1628_minus__add__distrib,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 8.57/4.54        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1629_minus__add__cancel,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1630_minus__add__cancel,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1631_minus__add__cancel,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1632_add__minus__cancel,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1633_add__minus__cancel,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1634_add__minus__cancel,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1635_lessI,axiom,
% 8.57/4.54      ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1636_Suc__mono,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ N )
% 8.57/4.54       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1637_Suc__less__eq,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.57/4.54        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1638_Suc__le__mono,axiom,
% 8.57/4.54      ! [N: nat,M: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 8.57/4.54        = ( ord_less_eq_nat @ N @ M ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1639_add__Suc__right,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 8.57/4.54        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1640_negative__eq__positive,axiom,
% 8.57/4.54      ! [N: nat,M: nat] :
% 8.57/4.54        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.54          = ( semiri1314217659103216013at_int @ M ) )
% 8.57/4.54        = ( ( N = zero_zero_nat )
% 8.57/4.54          & ( M = zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1641_of__int__minus,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z2 ) )
% 8.57/4.54        = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1642_of__int__minus,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z2 ) )
% 8.57/4.54        = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1643_of__int__minus,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z2 ) )
% 8.57/4.54        = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1644_negative__zle,axiom,
% 8.57/4.54      ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1645_neg__less__eq__nonneg,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.57/4.54        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1646_neg__less__eq__nonneg,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.57/4.54        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1647_neg__less__eq__nonneg,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 8.57/4.54        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1648_less__eq__neg__nonpos,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1649_less__eq__neg__nonpos,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1650_less__eq__neg__nonpos,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 8.57/4.54        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1651_neg__le__0__iff__le,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 8.57/4.54        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1652_neg__le__0__iff__le,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 8.57/4.54        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1653_neg__le__0__iff__le,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 8.57/4.54        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1654_neg__0__le__iff__le,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1655_neg__0__le__iff__le,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1656_neg__0__le__iff__le,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 8.57/4.54        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1657_neg__less__0__iff__less,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 8.57/4.54        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1658_neg__less__0__iff__less,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 8.57/4.54        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1659_neg__less__0__iff__less,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 8.57/4.54        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1660_neg__0__less__iff__less,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 8.57/4.54        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1661_neg__0__less__iff__less,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1662_neg__0__less__iff__less,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1663_neg__less__pos,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 8.57/4.54        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1664_neg__less__pos,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.57/4.54        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1665_neg__less__pos,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.57/4.54        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1666_less__neg__neg,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 8.57/4.54        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1667_less__neg__neg,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1668_less__neg__neg,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1669_ab__left__minus,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 8.57/4.54        = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1670_ab__left__minus,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.57/4.54        = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1671_ab__left__minus,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.57/4.54        = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1672_add_Oright__inverse,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 8.57/4.54        = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1673_add_Oright__inverse,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.54        = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1674_add_Oright__inverse,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 8.57/4.54        = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1675_zero__less__Suc,axiom,
% 8.57/4.54      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1676_less__Suc0,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.57/4.54        = ( N = zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1677_negative__zless,axiom,
% 8.57/4.54      ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1678_nat__zminus__int,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.57/4.54        = zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1679_floor__uminus__of__int,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z2 ) ) )
% 8.57/4.54        = ( uminus_uminus_int @ Z2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1680_frac__of__int,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.54        = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1681_dbl__inc__simps_I4_J,axiom,
% 8.57/4.54      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.54      = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1682_dbl__inc__simps_I4_J,axiom,
% 8.57/4.54      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.57/4.54      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1683_dbl__inc__simps_I4_J,axiom,
% 8.57/4.54      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.57/4.54      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1684_add__neg__numeral__special_I8_J,axiom,
% 8.57/4.54      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 8.57/4.54      = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1685_add__neg__numeral__special_I8_J,axiom,
% 8.57/4.54      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 8.57/4.54      = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1686_add__neg__numeral__special_I8_J,axiom,
% 8.57/4.54      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 8.57/4.54      = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1687_add__neg__numeral__special_I7_J,axiom,
% 8.57/4.54      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.54      = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1688_add__neg__numeral__special_I7_J,axiom,
% 8.57/4.54      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.57/4.54      = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1689_add__neg__numeral__special_I7_J,axiom,
% 8.57/4.54      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.57/4.54      = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1690_of__nat__Suc,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 8.57/4.54        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1691_of__nat__Suc,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 8.57/4.54        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1692_of__nat__Suc,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 8.57/4.54        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1693_of__nat__Suc,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 8.57/4.54        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1694_of__nat__Suc,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( ( semiri3763490453095760265atural @ ( suc @ M ) )
% 8.57/4.54        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( semiri3763490453095760265atural @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1695_nat__1,axiom,
% 8.57/4.54      ( ( nat2 @ one_one_int )
% 8.57/4.54      = ( suc @ zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1696_one__less__nat__eq,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
% 8.57/4.54        = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1697_Nat_OlessE,axiom,
% 8.57/4.54      ! [I: nat,K: nat] :
% 8.57/4.54        ( ( ord_less_nat @ I @ K )
% 8.57/4.54       => ( ( K
% 8.57/4.54           != ( suc @ I ) )
% 8.57/4.54         => ~ ! [J2: nat] :
% 8.57/4.54                ( ( ord_less_nat @ I @ J2 )
% 8.57/4.54               => ( K
% 8.57/4.54                 != ( suc @ J2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1698_Suc__lessD,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ ( suc @ M ) @ N )
% 8.57/4.54       => ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1699_Suc__lessE,axiom,
% 8.57/4.54      ! [I: nat,K: nat] :
% 8.57/4.54        ( ( ord_less_nat @ ( suc @ I ) @ K )
% 8.57/4.54       => ~ ! [J2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ I @ J2 )
% 8.57/4.54             => ( K
% 8.57/4.54               != ( suc @ J2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1700_Suc__lessI,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ N )
% 8.57/4.54       => ( ( ( suc @ M )
% 8.57/4.54           != N )
% 8.57/4.54         => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1701_less__SucE,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 8.57/4.54       => ( ~ ( ord_less_nat @ M @ N )
% 8.57/4.54         => ( M = N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1702_less__SucI,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ N )
% 8.57/4.54       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1703_Ex__less__Suc,axiom,
% 8.57/4.54      ! [N: nat,P: nat > $o] :
% 8.57/4.54        ( ( ? [I2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 8.57/4.54              & ( P @ I2 ) ) )
% 8.57/4.54        = ( ( P @ N )
% 8.57/4.54          | ? [I2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ I2 @ N )
% 8.57/4.54              & ( P @ I2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1704_less__Suc__eq,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 8.57/4.54        = ( ( ord_less_nat @ M @ N )
% 8.57/4.54          | ( M = N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1705_nat__neq__iff,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( M != N )
% 8.57/4.54        = ( ( ord_less_nat @ M @ N )
% 8.57/4.54          | ( ord_less_nat @ N @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1706_not__less__eq,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ~ ( ord_less_nat @ M @ N ) )
% 8.57/4.54        = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1707_All__less__Suc,axiom,
% 8.57/4.54      ! [N: nat,P: nat > $o] :
% 8.57/4.54        ( ( ! [I2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 8.57/4.54             => ( P @ I2 ) ) )
% 8.57/4.54        = ( ( P @ N )
% 8.57/4.54          & ! [I2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ I2 @ N )
% 8.57/4.54             => ( P @ I2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1708_Suc__less__eq2,axiom,
% 8.57/4.54      ! [N: nat,M: nat] :
% 8.57/4.54        ( ( ord_less_nat @ ( suc @ N ) @ M )
% 8.57/4.54        = ( ? [M7: nat] :
% 8.57/4.54              ( ( M
% 8.57/4.54                = ( suc @ M7 ) )
% 8.57/4.54              & ( ord_less_nat @ N @ M7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1709_less__antisym,axiom,
% 8.57/4.54      ! [N: nat,M: nat] :
% 8.57/4.54        ( ~ ( ord_less_nat @ N @ M )
% 8.57/4.54       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 8.57/4.54         => ( M = N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1710_Suc__less__SucD,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.57/4.54       => ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1711_less__not__refl,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ~ ( ord_less_nat @ N @ N ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1712_less__not__refl2,axiom,
% 8.57/4.54      ! [N: nat,M: nat] :
% 8.57/4.54        ( ( ord_less_nat @ N @ M )
% 8.57/4.54       => ( M != N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1713_less__not__refl3,axiom,
% 8.57/4.54      ! [S: nat,T: nat] :
% 8.57/4.54        ( ( ord_less_nat @ S @ T )
% 8.57/4.54       => ( S != T ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1714_less__trans__Suc,axiom,
% 8.57/4.54      ! [I: nat,J: nat,K: nat] :
% 8.57/4.54        ( ( ord_less_nat @ I @ J )
% 8.57/4.54       => ( ( ord_less_nat @ J @ K )
% 8.57/4.54         => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1715_less__Suc__induct,axiom,
% 8.57/4.54      ! [I: nat,J: nat,P: nat > nat > $o] :
% 8.57/4.54        ( ( ord_less_nat @ I @ J )
% 8.57/4.54       => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 8.57/4.54         => ( ! [I3: nat,J2: nat,K3: nat] :
% 8.57/4.54                ( ( ord_less_nat @ I3 @ J2 )
% 8.57/4.54               => ( ( ord_less_nat @ J2 @ K3 )
% 8.57/4.54                 => ( ( P @ I3 @ J2 )
% 8.57/4.54                   => ( ( P @ J2 @ K3 )
% 8.57/4.54                     => ( P @ I3 @ K3 ) ) ) ) )
% 8.57/4.54           => ( P @ I @ J ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1716_less__irrefl__nat,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ~ ( ord_less_nat @ N @ N ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1717_nat__less__induct,axiom,
% 8.57/4.54      ! [P: nat > $o,N: nat] :
% 8.57/4.54        ( ! [N2: nat] :
% 8.57/4.54            ( ! [M6: nat] :
% 8.57/4.54                ( ( ord_less_nat @ M6 @ N2 )
% 8.57/4.54               => ( P @ M6 ) )
% 8.57/4.54           => ( P @ N2 ) )
% 8.57/4.54       => ( P @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1718_infinite__descent,axiom,
% 8.57/4.54      ! [P: nat > $o,N: nat] :
% 8.57/4.54        ( ! [N2: nat] :
% 8.57/4.54            ( ~ ( P @ N2 )
% 8.57/4.54           => ? [M6: nat] :
% 8.57/4.54                ( ( ord_less_nat @ M6 @ N2 )
% 8.57/4.54                & ~ ( P @ M6 ) ) )
% 8.57/4.54       => ( P @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1719_linorder__neqE__nat,axiom,
% 8.57/4.54      ! [X2: nat,Y: nat] :
% 8.57/4.54        ( ( X2 != Y )
% 8.57/4.54       => ( ~ ( ord_less_nat @ X2 @ Y )
% 8.57/4.54         => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1720_strict__inc__induct,axiom,
% 8.57/4.54      ! [I: nat,J: nat,P: nat > $o] :
% 8.57/4.54        ( ( ord_less_nat @ I @ J )
% 8.57/4.54       => ( ! [I3: nat] :
% 8.57/4.54              ( ( J
% 8.57/4.54                = ( suc @ I3 ) )
% 8.57/4.54             => ( P @ I3 ) )
% 8.57/4.54         => ( ! [I3: nat] :
% 8.57/4.54                ( ( ord_less_nat @ I3 @ J )
% 8.57/4.54               => ( ( P @ ( suc @ I3 ) )
% 8.57/4.54                 => ( P @ I3 ) ) )
% 8.57/4.54           => ( P @ I ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1721_not__less__less__Suc__eq,axiom,
% 8.57/4.54      ! [N: nat,M: nat] :
% 8.57/4.54        ( ~ ( ord_less_nat @ N @ M )
% 8.57/4.54       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 8.57/4.54          = ( N = M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1722_verit__negate__coefficient_I3_J,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( A = B )
% 8.57/4.54       => ( ( uminus_uminus_int @ A )
% 8.57/4.54          = ( uminus_uminus_int @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1723_verit__negate__coefficient_I3_J,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( A = B )
% 8.57/4.54       => ( ( uminus1351360451143612070nteger @ A )
% 8.57/4.54          = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1724_verit__negate__coefficient_I3_J,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( A = B )
% 8.57/4.54       => ( ( uminus_uminus_rat @ A )
% 8.57/4.54          = ( uminus_uminus_rat @ B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1725_n__not__Suc__n,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( N
% 8.57/4.54       != ( suc @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1726_Suc__inject,axiom,
% 8.57/4.54      ! [X2: nat,Y: nat] :
% 8.57/4.54        ( ( ( suc @ X2 )
% 8.57/4.54          = ( suc @ Y ) )
% 8.57/4.54       => ( X2 = Y ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1727_minus__equation__iff,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ( uminus_uminus_int @ A )
% 8.57/4.54          = B )
% 8.57/4.54        = ( ( uminus_uminus_int @ B )
% 8.57/4.54          = A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1728_minus__equation__iff,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ( uminus1351360451143612070nteger @ A )
% 8.57/4.54          = B )
% 8.57/4.54        = ( ( uminus1351360451143612070nteger @ B )
% 8.57/4.54          = A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1729_minus__equation__iff,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ( uminus_uminus_rat @ A )
% 8.57/4.54          = B )
% 8.57/4.54        = ( ( uminus_uminus_rat @ B )
% 8.57/4.54          = A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1730_equation__minus__iff,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( A
% 8.57/4.54          = ( uminus_uminus_int @ B ) )
% 8.57/4.54        = ( B
% 8.57/4.54          = ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1731_equation__minus__iff,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( A
% 8.57/4.54          = ( uminus1351360451143612070nteger @ B ) )
% 8.57/4.54        = ( B
% 8.57/4.54          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1732_equation__minus__iff,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( A
% 8.57/4.54          = ( uminus_uminus_rat @ B ) )
% 8.57/4.54        = ( B
% 8.57/4.54          = ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1733_int__of__nat__induct,axiom,
% 8.57/4.54      ! [P: int > $o,Z2: int] :
% 8.57/4.54        ( ! [N2: nat] : ( P @ ( semiri1314217659103216013at_int @ N2 ) )
% 8.57/4.54       => ( ! [N2: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
% 8.57/4.54         => ( P @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1734_int__cases,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ! [N2: nat] :
% 8.57/4.54            ( Z2
% 8.57/4.54           != ( semiri1314217659103216013at_int @ N2 ) )
% 8.57/4.54       => ~ ! [N2: nat] :
% 8.57/4.54              ( Z2
% 8.57/4.54             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1735_ceiling__def,axiom,
% 8.57/4.54      ( archim2889992004027027881ng_rat
% 8.57/4.54      = ( ^ [X: rat] : ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1736_floor__minus,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X2 ) )
% 8.57/4.54        = ( uminus_uminus_int @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1737_ceiling__minus,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ X2 ) )
% 8.57/4.54        = ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ X2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1738_le__imp__neg__le,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.54       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1739_le__imp__neg__le,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.54       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1740_le__imp__neg__le,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.54       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1741_minus__le__iff,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.57/4.54        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1742_minus__le__iff,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.57/4.54        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1743_minus__le__iff,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 8.57/4.54        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1744_le__minus__iff,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.57/4.54        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1745_le__minus__iff,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.57/4.54        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1746_le__minus__iff,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 8.57/4.54        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1747_verit__negate__coefficient_I2_J,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ B )
% 8.57/4.54       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1748_verit__negate__coefficient_I2_J,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.54       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1749_verit__negate__coefficient_I2_J,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ B )
% 8.57/4.54       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1750_minus__less__iff,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 8.57/4.54        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1751_minus__less__iff,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.57/4.54        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1752_minus__less__iff,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.57/4.54        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1753_less__minus__iff,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 8.57/4.54        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1754_less__minus__iff,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.57/4.54        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1755_less__minus__iff,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.57/4.54        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1756_add_Oinverse__distrib__swap,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 8.57/4.54        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1757_add_Oinverse__distrib__swap,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.57/4.54        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1758_add_Oinverse__distrib__swap,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 8.57/4.54        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1759_group__cancel_Oneg1,axiom,
% 8.57/4.54      ! [A4: int,K: int,A: int] :
% 8.57/4.54        ( ( A4
% 8.57/4.54          = ( plus_plus_int @ K @ A ) )
% 8.57/4.54       => ( ( uminus_uminus_int @ A4 )
% 8.57/4.54          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1760_group__cancel_Oneg1,axiom,
% 8.57/4.54      ! [A4: code_integer,K: code_integer,A: code_integer] :
% 8.57/4.54        ( ( A4
% 8.57/4.54          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 8.57/4.54       => ( ( uminus1351360451143612070nteger @ A4 )
% 8.57/4.54          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1761_group__cancel_Oneg1,axiom,
% 8.57/4.54      ! [A4: rat,K: rat,A: rat] :
% 8.57/4.54        ( ( A4
% 8.57/4.54          = ( plus_plus_rat @ K @ A ) )
% 8.57/4.54       => ( ( uminus_uminus_rat @ A4 )
% 8.57/4.54          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1762_is__num__normalize_I8_J,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 8.57/4.54        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1763_is__num__normalize_I8_J,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.57/4.54        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1764_is__num__normalize_I8_J,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 8.57/4.54        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1765_one__neq__neg__one,axiom,
% 8.57/4.54      ( one_one_int
% 8.57/4.54     != ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1766_one__neq__neg__one,axiom,
% 8.57/4.54      ( one_one_Code_integer
% 8.57/4.54     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1767_one__neq__neg__one,axiom,
% 8.57/4.54      ( one_one_rat
% 8.57/4.54     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1768_lift__Suc__mono__less__iff,axiom,
% 8.57/4.54      ! [F: nat > code_integer,N: nat,M: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_le6747313008572928689nteger @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_le6747313008572928689nteger @ ( F @ N ) @ ( F @ M ) )
% 8.57/4.54          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1769_lift__Suc__mono__less__iff,axiom,
% 8.57/4.54      ! [F: nat > rat,N: nat,M: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 8.57/4.54          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1770_lift__Suc__mono__less__iff,axiom,
% 8.57/4.54      ! [F: nat > num,N: nat,M: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 8.57/4.54          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1771_lift__Suc__mono__less__iff,axiom,
% 8.57/4.54      ! [F: nat > nat,N: nat,M: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 8.57/4.54          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1772_lift__Suc__mono__less__iff,axiom,
% 8.57/4.54      ! [F: nat > int,N: nat,M: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 8.57/4.54          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1773_lift__Suc__mono__less,axiom,
% 8.57/4.54      ! [F: nat > code_integer,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_le6747313008572928689nteger @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_nat @ N @ N7 )
% 8.57/4.54         => ( ord_le6747313008572928689nteger @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1774_lift__Suc__mono__less,axiom,
% 8.57/4.54      ! [F: nat > rat,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_rat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1775_lift__Suc__mono__less,axiom,
% 8.57/4.54      ! [F: nat > num,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_num @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1776_lift__Suc__mono__less,axiom,
% 8.57/4.54      ! [F: nat > nat,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1777_lift__Suc__mono__less,axiom,
% 8.57/4.54      ! [F: nat > int,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1778_not0__implies__Suc,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( N != zero_zero_nat )
% 8.57/4.54       => ? [M4: nat] :
% 8.57/4.54            ( N
% 8.57/4.54            = ( suc @ M4 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1779_Zero__not__Suc,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( zero_zero_nat
% 8.57/4.54       != ( suc @ M ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1780_Zero__neq__Suc,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( zero_zero_nat
% 8.57/4.54       != ( suc @ M ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1781_Suc__neq__Zero,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( ( suc @ M )
% 8.57/4.54       != zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1782_zero__induct,axiom,
% 8.57/4.54      ! [P: nat > $o,K: nat] :
% 8.57/4.54        ( ( P @ K )
% 8.57/4.54       => ( ! [N2: nat] :
% 8.57/4.54              ( ( P @ ( suc @ N2 ) )
% 8.57/4.54             => ( P @ N2 ) )
% 8.57/4.54         => ( P @ zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1783_diff__induct,axiom,
% 8.57/4.54      ! [P: nat > nat > $o,M: nat,N: nat] :
% 8.57/4.54        ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 8.57/4.54       => ( ! [Y2: nat] : ( P @ zero_zero_nat @ ( suc @ Y2 ) )
% 8.57/4.54         => ( ! [X3: nat,Y2: nat] :
% 8.57/4.54                ( ( P @ X3 @ Y2 )
% 8.57/4.54               => ( P @ ( suc @ X3 ) @ ( suc @ Y2 ) ) )
% 8.57/4.54           => ( P @ M @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1784_nat__induct,axiom,
% 8.57/4.54      ! [P: nat > $o,N: nat] :
% 8.57/4.54        ( ( P @ zero_zero_nat )
% 8.57/4.54       => ( ! [N2: nat] :
% 8.57/4.54              ( ( P @ N2 )
% 8.57/4.54             => ( P @ ( suc @ N2 ) ) )
% 8.57/4.54         => ( P @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1785_old_Onat_Oexhaust,axiom,
% 8.57/4.54      ! [Y: nat] :
% 8.57/4.54        ( ( Y != zero_zero_nat )
% 8.57/4.54       => ~ ! [Nat3: nat] :
% 8.57/4.54              ( Y
% 8.57/4.54             != ( suc @ Nat3 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1786_nat_OdiscI,axiom,
% 8.57/4.54      ! [Nat: nat,X22: nat] :
% 8.57/4.54        ( ( Nat
% 8.57/4.54          = ( suc @ X22 ) )
% 8.57/4.54       => ( Nat != zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1787_old_Onat_Odistinct_I1_J,axiom,
% 8.57/4.54      ! [Nat2: nat] :
% 8.57/4.54        ( zero_zero_nat
% 8.57/4.54       != ( suc @ Nat2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1788_old_Onat_Odistinct_I2_J,axiom,
% 8.57/4.54      ! [Nat2: nat] :
% 8.57/4.54        ( ( suc @ Nat2 )
% 8.57/4.54       != zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1789_nat_Odistinct_I1_J,axiom,
% 8.57/4.54      ! [X22: nat] :
% 8.57/4.54        ( zero_zero_nat
% 8.57/4.54       != ( suc @ X22 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1790_exists__least__lemma,axiom,
% 8.57/4.54      ! [P: nat > $o] :
% 8.57/4.54        ( ~ ( P @ zero_zero_nat )
% 8.57/4.54       => ( ? [X_1: nat] : ( P @ X_1 )
% 8.57/4.54         => ? [N2: nat] :
% 8.57/4.54              ( ~ ( P @ N2 )
% 8.57/4.54              & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1791_less__Suc__eq__0__disj,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 8.57/4.54        = ( ( M = zero_zero_nat )
% 8.57/4.54          | ? [J3: nat] :
% 8.57/4.54              ( ( M
% 8.57/4.54                = ( suc @ J3 ) )
% 8.57/4.54              & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1792_gr0__implies__Suc,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.54       => ? [M4: nat] :
% 8.57/4.54            ( N
% 8.57/4.54            = ( suc @ M4 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1793_All__less__Suc2,axiom,
% 8.57/4.54      ! [N: nat,P: nat > $o] :
% 8.57/4.54        ( ( ! [I2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 8.57/4.54             => ( P @ I2 ) ) )
% 8.57/4.54        = ( ( P @ zero_zero_nat )
% 8.57/4.54          & ! [I2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ I2 @ N )
% 8.57/4.54             => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1794_gr0__conv__Suc,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.54        = ( ? [M2: nat] :
% 8.57/4.54              ( N
% 8.57/4.54              = ( suc @ M2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1795_Ex__less__Suc2,axiom,
% 8.57/4.54      ! [N: nat,P: nat > $o] :
% 8.57/4.54        ( ( ? [I2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 8.57/4.54              & ( P @ I2 ) ) )
% 8.57/4.54        = ( ( P @ zero_zero_nat )
% 8.57/4.54          | ? [I2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ I2 @ N )
% 8.57/4.54              & ( P @ ( suc @ I2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1796_uminus__int__code_I1_J,axiom,
% 8.57/4.54      ( ( uminus_uminus_int @ zero_zero_int )
% 8.57/4.54      = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1797_transitive__stepwise__le,axiom,
% 8.57/4.54      ! [M: nat,N: nat,R3: nat > nat > $o] :
% 8.57/4.54        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.54       => ( ! [X3: nat] : ( R3 @ X3 @ X3 )
% 8.57/4.54         => ( ! [X3: nat,Y2: nat,Z4: nat] :
% 8.57/4.54                ( ( R3 @ X3 @ Y2 )
% 8.57/4.54               => ( ( R3 @ Y2 @ Z4 )
% 8.57/4.54                 => ( R3 @ X3 @ Z4 ) ) )
% 8.57/4.54           => ( ! [N2: nat] : ( R3 @ N2 @ ( suc @ N2 ) )
% 8.57/4.54             => ( R3 @ M @ N ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1798_nat__induct__at__least,axiom,
% 8.57/4.54      ! [M: nat,N: nat,P: nat > $o] :
% 8.57/4.54        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.54       => ( ( P @ M )
% 8.57/4.54         => ( ! [N2: nat] :
% 8.57/4.54                ( ( ord_less_eq_nat @ M @ N2 )
% 8.57/4.54               => ( ( P @ N2 )
% 8.57/4.54                 => ( P @ ( suc @ N2 ) ) ) )
% 8.57/4.54           => ( P @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1799_full__nat__induct,axiom,
% 8.57/4.54      ! [P: nat > $o,N: nat] :
% 8.57/4.54        ( ! [N2: nat] :
% 8.57/4.54            ( ! [M6: nat] :
% 8.57/4.54                ( ( ord_less_eq_nat @ ( suc @ M6 ) @ N2 )
% 8.57/4.54               => ( P @ M6 ) )
% 8.57/4.54           => ( P @ N2 ) )
% 8.57/4.54       => ( P @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1800_not__less__eq__eq,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 8.57/4.54        = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1801_Suc__n__not__le__n,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1802_le__Suc__eq,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.57/4.54        = ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.54          | ( M
% 8.57/4.54            = ( suc @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1803_Suc__le__D,axiom,
% 8.57/4.54      ! [N: nat,M5: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( suc @ N ) @ M5 )
% 8.57/4.54       => ? [M4: nat] :
% 8.57/4.54            ( M5
% 8.57/4.54            = ( suc @ M4 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1804_le__SucI,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.54       => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1805_le__SucE,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.57/4.54       => ( ~ ( ord_less_eq_nat @ M @ N )
% 8.57/4.54         => ( M
% 8.57/4.54            = ( suc @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1806_Suc__leD,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 8.57/4.54       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1807_Suc__leI,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ N )
% 8.57/4.54       => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1808_Suc__le__eq,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 8.57/4.54        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1809_dec__induct,axiom,
% 8.57/4.54      ! [I: nat,J: nat,P: nat > $o] :
% 8.57/4.54        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.54       => ( ( P @ I )
% 8.57/4.54         => ( ! [N2: nat] :
% 8.57/4.54                ( ( ord_less_eq_nat @ I @ N2 )
% 8.57/4.54               => ( ( ord_less_nat @ N2 @ J )
% 8.57/4.54                 => ( ( P @ N2 )
% 8.57/4.54                   => ( P @ ( suc @ N2 ) ) ) ) )
% 8.57/4.54           => ( P @ J ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1810_inc__induct,axiom,
% 8.57/4.54      ! [I: nat,J: nat,P: nat > $o] :
% 8.57/4.54        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.54       => ( ( P @ J )
% 8.57/4.54         => ( ! [N2: nat] :
% 8.57/4.54                ( ( ord_less_eq_nat @ I @ N2 )
% 8.57/4.54               => ( ( ord_less_nat @ N2 @ J )
% 8.57/4.54                 => ( ( P @ ( suc @ N2 ) )
% 8.57/4.54                   => ( P @ N2 ) ) ) )
% 8.57/4.54           => ( P @ I ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1811_Suc__le__lessD,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 8.57/4.54       => ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1812_le__less__Suc__eq,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.54       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 8.57/4.54          = ( N = M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1813_less__Suc__eq__le,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 8.57/4.54        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1814_less__eq__Suc__le,axiom,
% 8.57/4.54      ( ord_less_nat
% 8.57/4.54      = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1815_le__imp__less__Suc,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.54       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1816_nat__in__between__eq_I1_J,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ( ord_less_nat @ A @ B )
% 8.57/4.54          & ( ord_less_eq_nat @ B @ ( suc @ A ) ) )
% 8.57/4.54        = ( B
% 8.57/4.54          = ( suc @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1817_nat__in__between__eq_I2_J,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.54          & ( ord_less_nat @ B @ ( suc @ A ) ) )
% 8.57/4.54        = ( B = A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1818_add__Suc__shift,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 8.57/4.54        = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1819_add__Suc,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 8.57/4.54        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1820_nat__arith_Osuc1,axiom,
% 8.57/4.54      ! [A4: nat,K: nat,A: nat] :
% 8.57/4.54        ( ( A4
% 8.57/4.54          = ( plus_plus_nat @ K @ A ) )
% 8.57/4.54       => ( ( suc @ A4 )
% 8.57/4.54          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1821_less__imp__Suc__add,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ N )
% 8.57/4.54       => ? [K3: nat] :
% 8.57/4.54            ( N
% 8.57/4.54            = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1822_less__iff__Suc__add,axiom,
% 8.57/4.54      ( ord_less_nat
% 8.57/4.54      = ( ^ [M2: nat,N3: nat] :
% 8.57/4.54          ? [K2: nat] :
% 8.57/4.54            ( N3
% 8.57/4.54            = ( suc @ ( plus_plus_nat @ M2 @ K2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1823_less__add__Suc2,axiom,
% 8.57/4.54      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1824_less__add__Suc1,axiom,
% 8.57/4.54      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1825_less__natE,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ M @ N )
% 8.57/4.54       => ~ ! [Q4: nat] :
% 8.57/4.54              ( N
% 8.57/4.54             != ( suc @ ( plus_plus_nat @ M @ Q4 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1826_int__cases2,axiom,
% 8.57/4.54      ! [Z2: int] :
% 8.57/4.54        ( ! [N2: nat] :
% 8.57/4.54            ( Z2
% 8.57/4.54           != ( semiri1314217659103216013at_int @ N2 ) )
% 8.57/4.54       => ~ ! [N2: nat] :
% 8.57/4.54              ( Z2
% 8.57/4.54             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1827_not__zle__0__negative,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1828_negD,axiom,
% 8.57/4.54      ! [X2: int] :
% 8.57/4.54        ( ( ord_less_int @ X2 @ zero_zero_int )
% 8.57/4.54       => ? [N2: nat] :
% 8.57/4.54            ( X2
% 8.57/4.54            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1829_negative__zless__0,axiom,
% 8.57/4.54      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1830_neg__eq__iff__add__eq__0,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ( uminus_uminus_int @ A )
% 8.57/4.54          = B )
% 8.57/4.54        = ( ( plus_plus_int @ A @ B )
% 8.57/4.54          = zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1831_neg__eq__iff__add__eq__0,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ( uminus1351360451143612070nteger @ A )
% 8.57/4.54          = B )
% 8.57/4.54        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.57/4.54          = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1832_neg__eq__iff__add__eq__0,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ( uminus_uminus_rat @ A )
% 8.57/4.54          = B )
% 8.57/4.54        = ( ( plus_plus_rat @ A @ B )
% 8.57/4.54          = zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1833_eq__neg__iff__add__eq__0,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( A
% 8.57/4.54          = ( uminus_uminus_int @ B ) )
% 8.57/4.54        = ( ( plus_plus_int @ A @ B )
% 8.57/4.54          = zero_zero_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1834_eq__neg__iff__add__eq__0,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( A
% 8.57/4.54          = ( uminus1351360451143612070nteger @ B ) )
% 8.57/4.54        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.57/4.54          = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1835_eq__neg__iff__add__eq__0,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( A
% 8.57/4.54          = ( uminus_uminus_rat @ B ) )
% 8.57/4.54        = ( ( plus_plus_rat @ A @ B )
% 8.57/4.54          = zero_zero_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1836_add_Oinverse__unique,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ( plus_plus_int @ A @ B )
% 8.57/4.54          = zero_zero_int )
% 8.57/4.54       => ( ( uminus_uminus_int @ A )
% 8.57/4.54          = B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1837_add_Oinverse__unique,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.57/4.54          = zero_z3403309356797280102nteger )
% 8.57/4.54       => ( ( uminus1351360451143612070nteger @ A )
% 8.57/4.54          = B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1838_add_Oinverse__unique,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ( plus_plus_rat @ A @ B )
% 8.57/4.54          = zero_zero_rat )
% 8.57/4.54       => ( ( uminus_uminus_rat @ A )
% 8.57/4.54          = B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1839_ab__group__add__class_Oab__left__minus,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 8.57/4.54        = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1840_ab__group__add__class_Oab__left__minus,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.57/4.54        = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1841_ab__group__add__class_Oab__left__minus,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.57/4.54        = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1842_add__eq__0__iff,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ( plus_plus_int @ A @ B )
% 8.57/4.54          = zero_zero_int )
% 8.57/4.54        = ( B
% 8.57/4.54          = ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1843_add__eq__0__iff,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.57/4.54          = zero_z3403309356797280102nteger )
% 8.57/4.54        = ( B
% 8.57/4.54          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1844_add__eq__0__iff,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ( plus_plus_rat @ A @ B )
% 8.57/4.54          = zero_zero_rat )
% 8.57/4.54        = ( B
% 8.57/4.54          = ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1845_le__minus__one__simps_I4_J,axiom,
% 8.57/4.54      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1846_le__minus__one__simps_I4_J,axiom,
% 8.57/4.54      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1847_le__minus__one__simps_I4_J,axiom,
% 8.57/4.54      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1848_le__minus__one__simps_I2_J,axiom,
% 8.57/4.54      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1849_le__minus__one__simps_I2_J,axiom,
% 8.57/4.54      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1850_le__minus__one__simps_I2_J,axiom,
% 8.57/4.54      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1851_zero__neq__neg__one,axiom,
% 8.57/4.54      ( zero_zero_int
% 8.57/4.54     != ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1852_zero__neq__neg__one,axiom,
% 8.57/4.54      ( zero_z3403309356797280102nteger
% 8.57/4.54     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1853_zero__neq__neg__one,axiom,
% 8.57/4.54      ( zero_zero_rat
% 8.57/4.54     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1854_less__minus__one__simps_I2_J,axiom,
% 8.57/4.54      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1855_less__minus__one__simps_I2_J,axiom,
% 8.57/4.54      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1856_less__minus__one__simps_I2_J,axiom,
% 8.57/4.54      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1857_less__minus__one__simps_I4_J,axiom,
% 8.57/4.54      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1858_less__minus__one__simps_I4_J,axiom,
% 8.57/4.54      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1859_less__minus__one__simps_I4_J,axiom,
% 8.57/4.54      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1860_lift__Suc__antimono__le,axiom,
% 8.57/4.54      ! [F: nat > set_nat,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_set_nat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1861_lift__Suc__antimono__le,axiom,
% 8.57/4.54      ! [F: nat > rat,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_rat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1862_lift__Suc__antimono__le,axiom,
% 8.57/4.54      ! [F: nat > num,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_num @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1863_lift__Suc__antimono__le,axiom,
% 8.57/4.54      ! [F: nat > nat,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_nat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1864_lift__Suc__antimono__le,axiom,
% 8.57/4.54      ! [F: nat > int,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_int @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1865_lift__Suc__mono__le,axiom,
% 8.57/4.54      ! [F: nat > set_nat,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1866_lift__Suc__mono__le,axiom,
% 8.57/4.54      ! [F: nat > rat,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1867_lift__Suc__mono__le,axiom,
% 8.57/4.54      ! [F: nat > num,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1868_lift__Suc__mono__le,axiom,
% 8.57/4.54      ! [F: nat > nat,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1869_lift__Suc__mono__le,axiom,
% 8.57/4.54      ! [F: nat > int,N: nat,N7: nat] :
% 8.57/4.54        ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.57/4.54       => ( ( ord_less_eq_nat @ N @ N7 )
% 8.57/4.54         => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1870_of__nat__neq__0,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 8.57/4.54       != zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1871_of__nat__neq__0,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 8.57/4.54       != zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1872_of__nat__neq__0,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( semiri4939895301339042750nteger @ ( suc @ N ) )
% 8.57/4.54       != zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1873_of__nat__neq__0,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 8.57/4.54       != zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1874_of__nat__neq__0,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( semiri3763490453095760265atural @ ( suc @ N ) )
% 8.57/4.54       != zero_z2226904508553997617atural ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1875_nat__compl__induct_H,axiom,
% 8.57/4.54      ! [P: nat > $o,N: nat] :
% 8.57/4.54        ( ( P @ zero_zero_nat )
% 8.57/4.54       => ( ! [N2: nat] :
% 8.57/4.54              ( ! [Nn: nat] :
% 8.57/4.54                  ( ( ord_less_eq_nat @ Nn @ N2 )
% 8.57/4.54                 => ( P @ Nn ) )
% 8.57/4.54             => ( P @ ( suc @ N2 ) ) )
% 8.57/4.54         => ( P @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1876_nat__compl__induct,axiom,
% 8.57/4.54      ! [P: nat > $o,N: nat] :
% 8.57/4.54        ( ( P @ zero_zero_nat )
% 8.57/4.54       => ( ! [N2: nat] :
% 8.57/4.54              ( ! [Nn: nat] :
% 8.57/4.54                  ( ( ord_less_eq_nat @ Nn @ N2 )
% 8.57/4.54                 => ( P @ Nn ) )
% 8.57/4.54             => ( P @ ( suc @ N2 ) ) )
% 8.57/4.54         => ( P @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1877_ex__least__nat__less,axiom,
% 8.57/4.54      ! [P: nat > $o,N: nat] :
% 8.57/4.54        ( ( P @ N )
% 8.57/4.54       => ( ~ ( P @ zero_zero_nat )
% 8.57/4.54         => ? [K3: nat] :
% 8.57/4.54              ( ( ord_less_nat @ K3 @ N )
% 8.57/4.54              & ! [I4: nat] :
% 8.57/4.54                  ( ( ord_less_eq_nat @ I4 @ K3 )
% 8.57/4.54                 => ~ ( P @ I4 ) )
% 8.57/4.54              & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1878_one__is__add,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ( suc @ zero_zero_nat )
% 8.57/4.54          = ( plus_plus_nat @ M @ N ) )
% 8.57/4.54        = ( ( ( M
% 8.57/4.54              = ( suc @ zero_zero_nat ) )
% 8.57/4.54            & ( N = zero_zero_nat ) )
% 8.57/4.54          | ( ( M = zero_zero_nat )
% 8.57/4.54            & ( N
% 8.57/4.54              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1879_add__is__1,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ( plus_plus_nat @ M @ N )
% 8.57/4.54          = ( suc @ zero_zero_nat ) )
% 8.57/4.54        = ( ( ( M
% 8.57/4.54              = ( suc @ zero_zero_nat ) )
% 8.57/4.54            & ( N = zero_zero_nat ) )
% 8.57/4.54          | ( ( M = zero_zero_nat )
% 8.57/4.54            & ( N
% 8.57/4.54              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1880_One__nat__def,axiom,
% 8.57/4.54      ( one_one_nat
% 8.57/4.54      = ( suc @ zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1881_nat__induct__non__zero,axiom,
% 8.57/4.54      ! [N: nat,P: nat > $o] :
% 8.57/4.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.54       => ( ( P @ one_one_nat )
% 8.57/4.54         => ( ! [N2: nat] :
% 8.57/4.54                ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 8.57/4.54               => ( ( P @ N2 )
% 8.57/4.54                 => ( P @ ( suc @ N2 ) ) ) )
% 8.57/4.54           => ( P @ N ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1882_int__cases4,axiom,
% 8.57/4.54      ! [M: int] :
% 8.57/4.54        ( ! [N2: nat] :
% 8.57/4.54            ( M
% 8.57/4.54           != ( semiri1314217659103216013at_int @ N2 ) )
% 8.57/4.54       => ~ ! [N2: nat] :
% 8.57/4.54              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 8.57/4.54             => ( M
% 8.57/4.54               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1883_Suc__eq__plus1__left,axiom,
% 8.57/4.54      ( suc
% 8.57/4.54      = ( plus_plus_nat @ one_one_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1884_plus__1__eq__Suc,axiom,
% 8.57/4.54      ( ( plus_plus_nat @ one_one_nat )
% 8.57/4.54      = suc ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1885_Suc__eq__plus1,axiom,
% 8.57/4.54      ( suc
% 8.57/4.54      = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1886_not__int__zless__negative,axiom,
% 8.57/4.54      ! [N: nat,M: nat] :
% 8.57/4.54        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1887_of__int__of__nat,axiom,
% 8.57/4.54      ( ring_1_of_int_int
% 8.57/4.54      = ( ^ [K2: int] : ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1888_of__int__of__nat,axiom,
% 8.57/4.54      ( ring_18347121197199848620nteger
% 8.57/4.54      = ( ^ [K2: int] : ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1889_of__int__of__nat,axiom,
% 8.57/4.54      ( ring_1_of_int_rat
% 8.57/4.54      = ( ^ [K2: int] : ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K2 ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1890_frac__ge__0,axiom,
% 8.57/4.54      ! [X2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1891_frac__lt__1,axiom,
% 8.57/4.54      ! [X2: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X2 ) @ one_one_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1892_frac__1__eq,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 8.57/4.54        = ( archimedean_frac_rat @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1893_le__minus__one__simps_I1_J,axiom,
% 8.57/4.54      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1894_le__minus__one__simps_I1_J,axiom,
% 8.57/4.54      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1895_le__minus__one__simps_I1_J,axiom,
% 8.57/4.54      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1896_le__minus__one__simps_I3_J,axiom,
% 8.57/4.54      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1897_le__minus__one__simps_I3_J,axiom,
% 8.57/4.54      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1898_le__minus__one__simps_I3_J,axiom,
% 8.57/4.54      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1899_less__minus__one__simps_I1_J,axiom,
% 8.57/4.54      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1900_less__minus__one__simps_I1_J,axiom,
% 8.57/4.54      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1901_less__minus__one__simps_I1_J,axiom,
% 8.57/4.54      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1902_less__minus__one__simps_I3_J,axiom,
% 8.57/4.54      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1903_less__minus__one__simps_I3_J,axiom,
% 8.57/4.54      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1904_less__minus__one__simps_I3_J,axiom,
% 8.57/4.54      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1905_int__cases3,axiom,
% 8.57/4.54      ! [K: int] :
% 8.57/4.54        ( ( K != zero_zero_int )
% 8.57/4.54       => ( ! [N2: nat] :
% 8.57/4.54              ( ( K
% 8.57/4.54                = ( semiri1314217659103216013at_int @ N2 ) )
% 8.57/4.54             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 8.57/4.54         => ~ ! [N2: nat] :
% 8.57/4.54                ( ( K
% 8.57/4.54                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 8.57/4.54               => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1906_int__zle__neg,axiom,
% 8.57/4.54      ! [N: nat,M: nat] :
% 8.57/4.54        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 8.57/4.54        = ( ( N = zero_zero_nat )
% 8.57/4.54          & ( M = zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1907_nonpos__int__cases,axiom,
% 8.57/4.54      ! [K: int] :
% 8.57/4.54        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 8.57/4.54       => ~ ! [N2: nat] :
% 8.57/4.54              ( K
% 8.57/4.54             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1908_negative__zle__0,axiom,
% 8.57/4.54      ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1909_zless__iff__Suc__zadd,axiom,
% 8.57/4.54      ( ord_less_int
% 8.57/4.54      = ( ^ [W: int,Z3: int] :
% 8.57/4.54          ? [N3: nat] :
% 8.57/4.54            ( Z3
% 8.57/4.54            = ( plus_plus_int @ W @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1910_int__Suc,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 8.57/4.54        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1911_int__ops_I4_J,axiom,
% 8.57/4.54      ! [A: nat] :
% 8.57/4.54        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 8.57/4.54        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1912_neg__int__cases,axiom,
% 8.57/4.54      ! [K: int] :
% 8.57/4.54        ( ( ord_less_int @ K @ zero_zero_int )
% 8.57/4.54       => ~ ! [N2: nat] :
% 8.57/4.54              ( ( K
% 8.57/4.54                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 8.57/4.54             => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1913_Suc__as__int,axiom,
% 8.57/4.54      ( suc
% 8.57/4.54      = ( ^ [A2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A2 ) @ one_one_int ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1914_frac__eq,axiom,
% 8.57/4.54      ! [X2: rat] :
% 8.57/4.54        ( ( ( archimedean_frac_rat @ X2 )
% 8.57/4.54          = X2 )
% 8.57/4.54        = ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.54          & ( ord_less_rat @ X2 @ one_one_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1915_length__code,axiom,
% 8.57/4.54      ( size_size_list_nat
% 8.57/4.54      = ( gen_length_nat @ zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1916_length__code,axiom,
% 8.57/4.54      ( size_size_list_int
% 8.57/4.54      = ( gen_length_int @ zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1917_length__code,axiom,
% 8.57/4.54      ( size_size_list_o
% 8.57/4.54      = ( gen_length_o @ zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1918_compl__le__compl__iff,axiom,
% 8.57/4.54      ! [X2: set_nat,Y: set_nat] :
% 8.57/4.54        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 8.57/4.54        = ( ord_less_eq_set_nat @ Y @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1919_power__int__minus__one__minus,axiom,
% 8.57/4.54      ! [N: int] :
% 8.57/4.54        ( ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_int @ N ) )
% 8.57/4.54        = ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1920_dbl__dec__simps_I2_J,axiom,
% 8.57/4.54      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 8.57/4.54      = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1921_dbl__dec__simps_I2_J,axiom,
% 8.57/4.54      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 8.57/4.54      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1922_dbl__dec__simps_I2_J,axiom,
% 8.57/4.54      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 8.57/4.54      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1923_nat__descend__induct,axiom,
% 8.57/4.54      ! [N: nat,P: nat > $o,M: nat] :
% 8.57/4.54        ( ! [K3: nat] :
% 8.57/4.54            ( ( ord_less_nat @ N @ K3 )
% 8.57/4.54           => ( P @ K3 ) )
% 8.57/4.54       => ( ! [K3: nat] :
% 8.57/4.54              ( ( ord_less_eq_nat @ K3 @ N )
% 8.57/4.54             => ( ! [I4: nat] :
% 8.57/4.54                    ( ( ord_less_nat @ K3 @ I4 )
% 8.57/4.54                   => ( P @ I4 ) )
% 8.57/4.54               => ( P @ K3 ) ) )
% 8.57/4.54         => ( P @ M ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1924_list__decode_Ocases,axiom,
% 8.57/4.54      ! [X2: nat] :
% 8.57/4.54        ( ( X2 != zero_zero_nat )
% 8.57/4.54       => ~ ! [N2: nat] :
% 8.57/4.54              ( X2
% 8.57/4.54             != ( suc @ N2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1925_compl__le__swap2,axiom,
% 8.57/4.54      ! [Y: set_nat,X2: set_nat] :
% 8.57/4.54        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X2 )
% 8.57/4.54       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ Y ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1926_compl__le__swap1,axiom,
% 8.57/4.54      ! [Y: set_nat,X2: set_nat] :
% 8.57/4.54        ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X2 ) )
% 8.57/4.54       => ( ord_less_eq_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1927_compl__mono,axiom,
% 8.57/4.54      ! [X2: set_nat,Y: set_nat] :
% 8.57/4.54        ( ( ord_less_eq_set_nat @ X2 @ Y )
% 8.57/4.54       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1928_dbl__dec__simps_I3_J,axiom,
% 8.57/4.54      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 8.57/4.54      = one_one_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1929_dbl__dec__simps_I3_J,axiom,
% 8.57/4.54      ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 8.57/4.54      = one_one_Code_integer ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1930_dbl__dec__simps_I3_J,axiom,
% 8.57/4.54      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 8.57/4.54      = one_one_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1931_triangle__Suc,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( nat_triangle @ ( suc @ N ) )
% 8.57/4.54        = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1932_bot__nat__0_Oordering__top__axioms,axiom,
% 8.57/4.54      ( ordering_top_nat
% 8.57/4.54      @ ^ [X: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X )
% 8.57/4.54      @ ^ [X: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X )
% 8.57/4.54      @ zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1933_power__int__add__1_H,axiom,
% 8.57/4.54      ! [X2: rat,M: int] :
% 8.57/4.54        ( ( ( X2 != zero_zero_rat )
% 8.57/4.54          | ( M
% 8.57/4.54           != ( uminus_uminus_int @ one_one_int ) ) )
% 8.57/4.54       => ( ( power_int_rat @ X2 @ ( plus_plus_int @ M @ one_one_int ) )
% 8.57/4.54          = ( times_times_rat @ X2 @ ( power_int_rat @ X2 @ M ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1934_power__int__add__1,axiom,
% 8.57/4.54      ! [X2: rat,M: int] :
% 8.57/4.54        ( ( ( X2 != zero_zero_rat )
% 8.57/4.54          | ( M
% 8.57/4.54           != ( uminus_uminus_int @ one_one_int ) ) )
% 8.57/4.54       => ( ( power_int_rat @ X2 @ ( plus_plus_int @ M @ one_one_int ) )
% 8.57/4.54          = ( times_times_rat @ ( power_int_rat @ X2 @ M ) @ X2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1935_length__ge__1__conv,axiom,
% 8.57/4.54      ! [L: list_char] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_char @ L ) )
% 8.57/4.54        = ( L != nil_char ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1936_length__ge__1__conv,axiom,
% 8.57/4.54      ! [L: list_nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_nat @ L ) )
% 8.57/4.54        = ( L != nil_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1937_length__ge__1__conv,axiom,
% 8.57/4.54      ! [L: list_int] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_int @ L ) )
% 8.57/4.54        = ( L != nil_int ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1938_length__ge__1__conv,axiom,
% 8.57/4.54      ! [L: list_o] :
% 8.57/4.54        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_o @ L ) )
% 8.57/4.54        = ( L != nil_o ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1939_foldr__length,axiom,
% 8.57/4.54      ! [L: list_nat] :
% 8.57/4.54        ( ( foldr_nat_nat
% 8.57/4.54          @ ^ [X: nat] : suc
% 8.57/4.54          @ L
% 8.57/4.54          @ zero_zero_nat )
% 8.57/4.54        = ( size_size_list_nat @ L ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1940_foldr__length,axiom,
% 8.57/4.54      ! [L: list_int] :
% 8.57/4.54        ( ( foldr_int_nat
% 8.57/4.54          @ ^ [X: int] : suc
% 8.57/4.54          @ L
% 8.57/4.54          @ zero_zero_nat )
% 8.57/4.54        = ( size_size_list_int @ L ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1941_foldr__length,axiom,
% 8.57/4.54      ! [L: list_o] :
% 8.57/4.54        ( ( foldr_o_nat
% 8.57/4.54          @ ^ [X: $o] : suc
% 8.57/4.54          @ L
% 8.57/4.54          @ zero_zero_nat )
% 8.57/4.54        = ( size_size_list_o @ L ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1942_le__ceiling__iff,axiom,
% 8.57/4.54      ! [Z2: int,X2: rat] :
% 8.57/4.54        ( ( ord_less_eq_int @ Z2 @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.54        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) @ X2 ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1943_diff__self__eq__0,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ M @ M )
% 8.57/4.54        = zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1944_diff__0__eq__0,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ zero_zero_nat @ N )
% 8.57/4.54        = zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1945_mult__cancel2,axiom,
% 8.57/4.54      ! [M: nat,K: nat,N: nat] :
% 8.57/4.54        ( ( ( times_times_nat @ M @ K )
% 8.57/4.54          = ( times_times_nat @ N @ K ) )
% 8.57/4.54        = ( ( M = N )
% 8.57/4.54          | ( K = zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1946_mult__cancel1,axiom,
% 8.57/4.54      ! [K: nat,M: nat,N: nat] :
% 8.57/4.54        ( ( ( times_times_nat @ K @ M )
% 8.57/4.54          = ( times_times_nat @ K @ N ) )
% 8.57/4.54        = ( ( M = N )
% 8.57/4.54          | ( K = zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1947_mult__0__right,axiom,
% 8.57/4.54      ! [M: nat] :
% 8.57/4.54        ( ( times_times_nat @ M @ zero_zero_nat )
% 8.57/4.54        = zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1948_mult__is__0,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ( times_times_nat @ M @ N )
% 8.57/4.54          = zero_zero_nat )
% 8.57/4.54        = ( ( M = zero_zero_nat )
% 8.57/4.54          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1949_Suc__diff__diff,axiom,
% 8.57/4.54      ! [M: nat,N: nat,K: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 8.57/4.54        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1950_diff__Suc__Suc,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.57/4.54        = ( minus_minus_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1951_diff__diff__cancel,axiom,
% 8.57/4.54      ! [I: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ I @ N )
% 8.57/4.54       => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 8.57/4.54          = I ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1952_diff__diff__left,axiom,
% 8.57/4.54      ! [I: nat,J: nat,K: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 8.57/4.54        = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1953_nat__1__eq__mult__iff,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( one_one_nat
% 8.57/4.54          = ( times_times_nat @ M @ N ) )
% 8.57/4.54        = ( ( M = one_one_nat )
% 8.57/4.54          & ( N = one_one_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1954_nat__mult__eq__1__iff,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ( times_times_nat @ M @ N )
% 8.57/4.54          = one_one_nat )
% 8.57/4.54        = ( ( M = one_one_nat )
% 8.57/4.54          & ( N = one_one_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1955_mult__zero__left,axiom,
% 8.57/4.54      ! [A: code_natural] :
% 8.57/4.54        ( ( times_2397367101498566445atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.54        = zero_z2226904508553997617atural ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1956_mult__zero__left,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.54        = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1957_mult__zero__left,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( times_times_rat @ zero_zero_rat @ A )
% 8.57/4.54        = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1958_mult__zero__left,axiom,
% 8.57/4.54      ! [A: nat] :
% 8.57/4.54        ( ( times_times_nat @ zero_zero_nat @ A )
% 8.57/4.54        = zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1959_mult__zero__left,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( times_times_int @ zero_zero_int @ A )
% 8.57/4.54        = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1960_mult__zero__right,axiom,
% 8.57/4.54      ! [A: code_natural] :
% 8.57/4.54        ( ( times_2397367101498566445atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.54        = zero_z2226904508553997617atural ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1961_mult__zero__right,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( times_3573771949741848930nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.54        = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1962_mult__zero__right,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( times_times_rat @ A @ zero_zero_rat )
% 8.57/4.54        = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1963_mult__zero__right,axiom,
% 8.57/4.54      ! [A: nat] :
% 8.57/4.54        ( ( times_times_nat @ A @ zero_zero_nat )
% 8.57/4.54        = zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1964_mult__zero__right,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( times_times_int @ A @ zero_zero_int )
% 8.57/4.54        = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1965_mult__eq__0__iff,axiom,
% 8.57/4.54      ! [A: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ( times_2397367101498566445atural @ A @ B )
% 8.57/4.54          = zero_z2226904508553997617atural )
% 8.57/4.54        = ( ( A = zero_z2226904508553997617atural )
% 8.57/4.54          | ( B = zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1966_mult__eq__0__iff,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ( times_3573771949741848930nteger @ A @ B )
% 8.57/4.54          = zero_z3403309356797280102nteger )
% 8.57/4.54        = ( ( A = zero_z3403309356797280102nteger )
% 8.57/4.54          | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1967_mult__eq__0__iff,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( ( times_times_rat @ A @ B )
% 8.57/4.54          = zero_zero_rat )
% 8.57/4.54        = ( ( A = zero_zero_rat )
% 8.57/4.54          | ( B = zero_zero_rat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1968_mult__eq__0__iff,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( ( times_times_nat @ A @ B )
% 8.57/4.54          = zero_zero_nat )
% 8.57/4.54        = ( ( A = zero_zero_nat )
% 8.57/4.54          | ( B = zero_zero_nat ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1969_mult__eq__0__iff,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( ( times_times_int @ A @ B )
% 8.57/4.54          = zero_zero_int )
% 8.57/4.54        = ( ( A = zero_zero_int )
% 8.57/4.54          | ( B = zero_zero_int ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1970_mult__cancel__left,axiom,
% 8.57/4.54      ! [C: code_natural,A: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ( times_2397367101498566445atural @ C @ A )
% 8.57/4.54          = ( times_2397367101498566445atural @ C @ B ) )
% 8.57/4.54        = ( ( C = zero_z2226904508553997617atural )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1971_mult__cancel__left,axiom,
% 8.57/4.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ( times_3573771949741848930nteger @ C @ A )
% 8.57/4.54          = ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.54        = ( ( C = zero_z3403309356797280102nteger )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1972_mult__cancel__left,axiom,
% 8.57/4.54      ! [C: rat,A: rat,B: rat] :
% 8.57/4.54        ( ( ( times_times_rat @ C @ A )
% 8.57/4.54          = ( times_times_rat @ C @ B ) )
% 8.57/4.54        = ( ( C = zero_zero_rat )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1973_mult__cancel__left,axiom,
% 8.57/4.54      ! [C: nat,A: nat,B: nat] :
% 8.57/4.54        ( ( ( times_times_nat @ C @ A )
% 8.57/4.54          = ( times_times_nat @ C @ B ) )
% 8.57/4.54        = ( ( C = zero_zero_nat )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1974_mult__cancel__left,axiom,
% 8.57/4.54      ! [C: int,A: int,B: int] :
% 8.57/4.54        ( ( ( times_times_int @ C @ A )
% 8.57/4.54          = ( times_times_int @ C @ B ) )
% 8.57/4.54        = ( ( C = zero_zero_int )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1975_mult__cancel__right,axiom,
% 8.57/4.54      ! [A: code_natural,C: code_natural,B: code_natural] :
% 8.57/4.54        ( ( ( times_2397367101498566445atural @ A @ C )
% 8.57/4.54          = ( times_2397367101498566445atural @ B @ C ) )
% 8.57/4.54        = ( ( C = zero_z2226904508553997617atural )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1976_mult__cancel__right,axiom,
% 8.57/4.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ( times_3573771949741848930nteger @ A @ C )
% 8.57/4.54          = ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.54        = ( ( C = zero_z3403309356797280102nteger )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1977_mult__cancel__right,axiom,
% 8.57/4.54      ! [A: rat,C: rat,B: rat] :
% 8.57/4.54        ( ( ( times_times_rat @ A @ C )
% 8.57/4.54          = ( times_times_rat @ B @ C ) )
% 8.57/4.54        = ( ( C = zero_zero_rat )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1978_mult__cancel__right,axiom,
% 8.57/4.54      ! [A: nat,C: nat,B: nat] :
% 8.57/4.54        ( ( ( times_times_nat @ A @ C )
% 8.57/4.54          = ( times_times_nat @ B @ C ) )
% 8.57/4.54        = ( ( C = zero_zero_nat )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1979_mult__cancel__right,axiom,
% 8.57/4.54      ! [A: int,C: int,B: int] :
% 8.57/4.54        ( ( ( times_times_int @ A @ C )
% 8.57/4.54          = ( times_times_int @ B @ C ) )
% 8.57/4.54        = ( ( C = zero_zero_int )
% 8.57/4.54          | ( A = B ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1980_diff__self,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( minus_8373710615458151222nteger @ A @ A )
% 8.57/4.54        = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1981_diff__self,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( minus_minus_rat @ A @ A )
% 8.57/4.54        = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1982_diff__self,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( minus_minus_int @ A @ A )
% 8.57/4.54        = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1983_diff__0__right,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1984_diff__0__right,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1985_diff__0__right,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( minus_minus_int @ A @ zero_zero_int )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1986_zero__diff,axiom,
% 8.57/4.54      ! [A: code_natural] :
% 8.57/4.54        ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.54        = zero_z2226904508553997617atural ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1987_zero__diff,axiom,
% 8.57/4.54      ! [A: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 8.57/4.54        = zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1988_diff__zero,axiom,
% 8.57/4.54      ! [A: code_natural] :
% 8.57/4.54        ( ( minus_7197305767214868737atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1989_diff__zero,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1990_diff__zero,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1991_diff__zero,axiom,
% 8.57/4.54      ! [A: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1992_diff__zero,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( minus_minus_int @ A @ zero_zero_int )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1993_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.57/4.54      ! [A: code_natural] :
% 8.57/4.54        ( ( minus_7197305767214868737atural @ A @ A )
% 8.57/4.54        = zero_z2226904508553997617atural ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1994_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( minus_8373710615458151222nteger @ A @ A )
% 8.57/4.54        = zero_z3403309356797280102nteger ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1995_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( minus_minus_rat @ A @ A )
% 8.57/4.54        = zero_zero_rat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1996_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.57/4.54      ! [A: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ A @ A )
% 8.57/4.54        = zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1997_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( minus_minus_int @ A @ A )
% 8.57/4.54        = zero_zero_int ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1998_mult__1,axiom,
% 8.57/4.54      ! [A: code_natural] :
% 8.57/4.54        ( ( times_2397367101498566445atural @ one_one_Code_natural @ A )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_1999_mult__1,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2000_mult__1,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( times_times_rat @ one_one_rat @ A )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2001_mult__1,axiom,
% 8.57/4.54      ! [A: nat] :
% 8.57/4.54        ( ( times_times_nat @ one_one_nat @ A )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2002_mult__1,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( times_times_int @ one_one_int @ A )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2003_mult_Oright__neutral,axiom,
% 8.57/4.54      ! [A: code_natural] :
% 8.57/4.54        ( ( times_2397367101498566445atural @ A @ one_one_Code_natural )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2004_mult_Oright__neutral,axiom,
% 8.57/4.54      ! [A: code_integer] :
% 8.57/4.54        ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2005_mult_Oright__neutral,axiom,
% 8.57/4.54      ! [A: rat] :
% 8.57/4.54        ( ( times_times_rat @ A @ one_one_rat )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2006_mult_Oright__neutral,axiom,
% 8.57/4.54      ! [A: nat] :
% 8.57/4.54        ( ( times_times_nat @ A @ one_one_nat )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2007_mult_Oright__neutral,axiom,
% 8.57/4.54      ! [A: int] :
% 8.57/4.54        ( ( times_times_int @ A @ one_one_int )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2008_add__diff__cancel__right_H,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2009_add__diff__cancel__right_H,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2010_add__diff__cancel__right_H,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2011_add__diff__cancel__right_H,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2012_add__diff__cancel__right,axiom,
% 8.57/4.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.54        = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2013_add__diff__cancel__right,axiom,
% 8.57/4.54      ! [A: rat,C: rat,B: rat] :
% 8.57/4.54        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.54        = ( minus_minus_rat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2014_add__diff__cancel__right,axiom,
% 8.57/4.54      ! [A: nat,C: nat,B: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.57/4.54        = ( minus_minus_nat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2015_add__diff__cancel__right,axiom,
% 8.57/4.54      ! [A: int,C: int,B: int] :
% 8.57/4.54        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.57/4.54        = ( minus_minus_int @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2016_add__diff__cancel__left_H,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ A )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2017_add__diff__cancel__left_H,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2018_add__diff__cancel__left_H,axiom,
% 8.57/4.54      ! [A: nat,B: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2019_add__diff__cancel__left_H,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 8.57/4.54        = B ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2020_add__diff__cancel__left,axiom,
% 8.57/4.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 8.57/4.54        = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2021_add__diff__cancel__left,axiom,
% 8.57/4.54      ! [C: rat,A: rat,B: rat] :
% 8.57/4.54        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.57/4.54        = ( minus_minus_rat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2022_add__diff__cancel__left,axiom,
% 8.57/4.54      ! [C: nat,A: nat,B: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.57/4.54        = ( minus_minus_nat @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2023_add__diff__cancel__left,axiom,
% 8.57/4.54      ! [C: int,A: int,B: int] :
% 8.57/4.54        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.57/4.54        = ( minus_minus_int @ A @ B ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2024_diff__add__cancel,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2025_diff__add__cancel,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2026_diff__add__cancel,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2027_add__diff__cancel,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2028_add__diff__cancel,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2029_add__diff__cancel,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.57/4.54        = A ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2030_minus__diff__eq,axiom,
% 8.57/4.54      ! [A: int,B: int] :
% 8.57/4.54        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 8.57/4.54        = ( minus_minus_int @ B @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2031_minus__diff__eq,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.57/4.54        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2032_minus__diff__eq,axiom,
% 8.57/4.54      ! [A: rat,B: rat] :
% 8.57/4.54        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 8.57/4.54        = ( minus_minus_rat @ B @ A ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2033_one__eq__mult__iff,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ( suc @ zero_zero_nat )
% 8.57/4.54          = ( times_times_nat @ M @ N ) )
% 8.57/4.54        = ( ( M
% 8.57/4.54            = ( suc @ zero_zero_nat ) )
% 8.57/4.54          & ( N
% 8.57/4.54            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2034_mult__eq__1__iff,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ( times_times_nat @ M @ N )
% 8.57/4.54          = ( suc @ zero_zero_nat ) )
% 8.57/4.54        = ( ( M
% 8.57/4.54            = ( suc @ zero_zero_nat ) )
% 8.57/4.54          & ( N
% 8.57/4.54            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2035_zero__less__diff,axiom,
% 8.57/4.54      ! [N: nat,M: nat] :
% 8.57/4.54        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 8.57/4.54        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2036_nat__0__less__mult__iff,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 8.57/4.54        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.54          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2037_mult__less__cancel2,axiom,
% 8.57/4.54      ! [M: nat,K: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 8.57/4.54        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.54          & ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2038_of__nat__mult,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 8.57/4.54        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2039_of__nat__mult,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 8.57/4.54        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2040_of__nat__mult,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N ) )
% 8.57/4.54        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2041_of__nat__mult,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 8.57/4.54        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2042_of__nat__mult,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( semiri3763490453095760265atural @ ( times_times_nat @ M @ N ) )
% 8.57/4.54        = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2043_diff__is__0__eq,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ( minus_minus_nat @ M @ N )
% 8.57/4.54          = zero_zero_nat )
% 8.57/4.54        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2044_diff__is__0__eq_H,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.54       => ( ( minus_minus_nat @ M @ N )
% 8.57/4.54          = zero_zero_nat ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2045_mult__Suc__right,axiom,
% 8.57/4.54      ! [M: nat,N: nat] :
% 8.57/4.54        ( ( times_times_nat @ M @ ( suc @ N ) )
% 8.57/4.54        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2046_Nat_Oadd__diff__assoc,axiom,
% 8.57/4.54      ! [K: nat,J: nat,I: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ K @ J )
% 8.57/4.54       => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 8.57/4.54          = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2047_Nat_Oadd__diff__assoc2,axiom,
% 8.57/4.54      ! [K: nat,J: nat,I: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ K @ J )
% 8.57/4.54       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 8.57/4.54          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2048_Nat_Odiff__diff__right,axiom,
% 8.57/4.54      ! [K: nat,J: nat,I: nat] :
% 8.57/4.54        ( ( ord_less_eq_nat @ K @ J )
% 8.57/4.54       => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 8.57/4.54          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2049_of__int__mult,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ring_18347121197199848620nteger @ ( times_times_int @ W2 @ Z2 ) )
% 8.57/4.54        = ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2050_of__int__mult,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ring_1_of_int_rat @ ( times_times_int @ W2 @ Z2 ) )
% 8.57/4.54        = ( times_times_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2051_of__int__mult,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ring_1_of_int_int @ ( times_times_int @ W2 @ Z2 ) )
% 8.57/4.54        = ( times_times_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2052_diff__Suc__1,axiom,
% 8.57/4.54      ! [N: nat] :
% 8.57/4.54        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 8.57/4.54        = N ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2053_of__int__diff,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ring_18347121197199848620nteger @ ( minus_minus_int @ W2 @ Z2 ) )
% 8.57/4.54        = ( minus_8373710615458151222nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2054_of__int__diff,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W2 @ Z2 ) )
% 8.57/4.54        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2055_of__int__diff,axiom,
% 8.57/4.54      ! [W2: int,Z2: int] :
% 8.57/4.54        ( ( ring_1_of_int_int @ ( minus_minus_int @ W2 @ Z2 ) )
% 8.57/4.54        = ( minus_minus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2056_triangle__0,axiom,
% 8.57/4.54      ( ( nat_triangle @ zero_zero_nat )
% 8.57/4.54      = zero_zero_nat ) ).
% 8.57/4.54  
% 8.57/4.54  thf(fact_2057_diff__ge__0__iff__ge,axiom,
% 8.57/4.54      ! [A: code_integer,B: code_integer] :
% 8.57/4.54        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.57/4.54        = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2058_diff__ge__0__iff__ge,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 8.57/4.55        = ( ord_less_eq_rat @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2059_diff__ge__0__iff__ge,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 8.57/4.55        = ( ord_less_eq_int @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2060_zero__comp__diff__simps_I1_J,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.57/4.55        = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2061_zero__comp__diff__simps_I1_J,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 8.57/4.55        = ( ord_less_eq_rat @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2062_zero__comp__diff__simps_I1_J,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 8.57/4.55        = ( ord_less_eq_int @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2063_diff__gt__0__iff__gt,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.57/4.55        = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2064_diff__gt__0__iff__gt,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 8.57/4.55        = ( ord_less_rat @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2065_diff__gt__0__iff__gt,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 8.57/4.55        = ( ord_less_int @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2066_zero__comp__diff__simps_I2_J,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.57/4.55        = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2067_zero__comp__diff__simps_I2_J,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 8.57/4.55        = ( ord_less_rat @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2068_zero__comp__diff__simps_I2_J,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 8.57/4.55        = ( ord_less_int @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2069_le__add__diff__inverse,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.57/4.55       => ( ( plus_p5714425477246183910nteger @ B @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2070_le__add__diff__inverse,axiom,
% 8.57/4.55      ! [B: rat,A: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.55       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2071_le__add__diff__inverse,axiom,
% 8.57/4.55      ! [B: nat,A: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ B @ A )
% 8.57/4.55       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2072_le__add__diff__inverse,axiom,
% 8.57/4.55      ! [B: int,A: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ B @ A )
% 8.57/4.55       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2073_le__add__diff__inverse2,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.57/4.55       => ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2074_le__add__diff__inverse2,axiom,
% 8.57/4.55      ! [B: rat,A: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.55       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2075_le__add__diff__inverse2,axiom,
% 8.57/4.55      ! [B: nat,A: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ B @ A )
% 8.57/4.55       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2076_le__add__diff__inverse2,axiom,
% 8.57/4.55      ! [B: int,A: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ B @ A )
% 8.57/4.55       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2077_mult__cancel__right2,axiom,
% 8.57/4.55      ! [A: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ( times_3573771949741848930nteger @ A @ C )
% 8.57/4.55          = C )
% 8.57/4.55        = ( ( C = zero_z3403309356797280102nteger )
% 8.57/4.55          | ( A = one_one_Code_integer ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2078_mult__cancel__right2,axiom,
% 8.57/4.55      ! [A: rat,C: rat] :
% 8.57/4.55        ( ( ( times_times_rat @ A @ C )
% 8.57/4.55          = C )
% 8.57/4.55        = ( ( C = zero_zero_rat )
% 8.57/4.55          | ( A = one_one_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2079_mult__cancel__right2,axiom,
% 8.57/4.55      ! [A: int,C: int] :
% 8.57/4.55        ( ( ( times_times_int @ A @ C )
% 8.57/4.55          = C )
% 8.57/4.55        = ( ( C = zero_zero_int )
% 8.57/4.55          | ( A = one_one_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2080_mult__cancel__right1,axiom,
% 8.57/4.55      ! [C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( C
% 8.57/4.55          = ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.55        = ( ( C = zero_z3403309356797280102nteger )
% 8.57/4.55          | ( B = one_one_Code_integer ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2081_mult__cancel__right1,axiom,
% 8.57/4.55      ! [C: rat,B: rat] :
% 8.57/4.55        ( ( C
% 8.57/4.55          = ( times_times_rat @ B @ C ) )
% 8.57/4.55        = ( ( C = zero_zero_rat )
% 8.57/4.55          | ( B = one_one_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2082_mult__cancel__right1,axiom,
% 8.57/4.55      ! [C: int,B: int] :
% 8.57/4.55        ( ( C
% 8.57/4.55          = ( times_times_int @ B @ C ) )
% 8.57/4.55        = ( ( C = zero_zero_int )
% 8.57/4.55          | ( B = one_one_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2083_mult__cancel__left2,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer] :
% 8.57/4.55        ( ( ( times_3573771949741848930nteger @ C @ A )
% 8.57/4.55          = C )
% 8.57/4.55        = ( ( C = zero_z3403309356797280102nteger )
% 8.57/4.55          | ( A = one_one_Code_integer ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2084_mult__cancel__left2,axiom,
% 8.57/4.55      ! [C: rat,A: rat] :
% 8.57/4.55        ( ( ( times_times_rat @ C @ A )
% 8.57/4.55          = C )
% 8.57/4.55        = ( ( C = zero_zero_rat )
% 8.57/4.55          | ( A = one_one_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2085_mult__cancel__left2,axiom,
% 8.57/4.55      ! [C: int,A: int] :
% 8.57/4.55        ( ( ( times_times_int @ C @ A )
% 8.57/4.55          = C )
% 8.57/4.55        = ( ( C = zero_zero_int )
% 8.57/4.55          | ( A = one_one_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2086_mult__cancel__left1,axiom,
% 8.57/4.55      ! [C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( C
% 8.57/4.55          = ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.55        = ( ( C = zero_z3403309356797280102nteger )
% 8.57/4.55          | ( B = one_one_Code_integer ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2087_mult__cancel__left1,axiom,
% 8.57/4.55      ! [C: rat,B: rat] :
% 8.57/4.55        ( ( C
% 8.57/4.55          = ( times_times_rat @ C @ B ) )
% 8.57/4.55        = ( ( C = zero_zero_rat )
% 8.57/4.55          | ( B = one_one_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2088_mult__cancel__left1,axiom,
% 8.57/4.55      ! [C: int,B: int] :
% 8.57/4.55        ( ( C
% 8.57/4.55          = ( times_times_int @ C @ B ) )
% 8.57/4.55        = ( ( C = zero_zero_int )
% 8.57/4.55          | ( B = one_one_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2089_diff__add__zero,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( minus_7197305767214868737atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 8.57/4.55        = zero_z2226904508553997617atural ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2090_diff__add__zero,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.57/4.55        = zero_zero_nat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2091_diff__numeral__special_I9_J,axiom,
% 8.57/4.55      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 8.57/4.55      = zero_z3403309356797280102nteger ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2092_diff__numeral__special_I9_J,axiom,
% 8.57/4.55      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 8.57/4.55      = zero_zero_rat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2093_diff__numeral__special_I9_J,axiom,
% 8.57/4.55      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 8.57/4.55      = zero_zero_int ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2094_diff__0,axiom,
% 8.57/4.55      ! [A: int] :
% 8.57/4.55        ( ( minus_minus_int @ zero_zero_int @ A )
% 8.57/4.55        = ( uminus_uminus_int @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2095_diff__0,axiom,
% 8.57/4.55      ! [A: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55        = ( uminus1351360451143612070nteger @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2096_diff__0,axiom,
% 8.57/4.55      ! [A: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 8.57/4.55        = ( uminus_uminus_rat @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2097_verit__minus__simplify_I3_J,axiom,
% 8.57/4.55      ! [B: int] :
% 8.57/4.55        ( ( minus_minus_int @ zero_zero_int @ B )
% 8.57/4.55        = ( uminus_uminus_int @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2098_verit__minus__simplify_I3_J,axiom,
% 8.57/4.55      ! [B: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.55        = ( uminus1351360451143612070nteger @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2099_verit__minus__simplify_I3_J,axiom,
% 8.57/4.55      ! [B: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 8.57/4.55        = ( uminus_uminus_rat @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2100_mult__minus1__right,axiom,
% 8.57/4.55      ! [Z2: int] :
% 8.57/4.55        ( ( times_times_int @ Z2 @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.55        = ( uminus_uminus_int @ Z2 ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2101_mult__minus1__right,axiom,
% 8.57/4.55      ! [Z2: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ Z2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.57/4.55        = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2102_mult__minus1__right,axiom,
% 8.57/4.55      ! [Z2: rat] :
% 8.57/4.55        ( ( times_times_rat @ Z2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.57/4.55        = ( uminus_uminus_rat @ Z2 ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2103_mult__minus1,axiom,
% 8.57/4.55      ! [Z2: int] :
% 8.57/4.55        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z2 )
% 8.57/4.55        = ( uminus_uminus_int @ Z2 ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2104_mult__minus1,axiom,
% 8.57/4.55      ! [Z2: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z2 )
% 8.57/4.55        = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2105_mult__minus1,axiom,
% 8.57/4.55      ! [Z2: rat] :
% 8.57/4.55        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z2 )
% 8.57/4.55        = ( uminus_uminus_rat @ Z2 ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2106_uminus__add__conv__diff,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 8.57/4.55        = ( minus_minus_int @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2107_uminus__add__conv__diff,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.57/4.55        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2108_uminus__add__conv__diff,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.57/4.55        = ( minus_minus_rat @ B @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2109_diff__minus__eq__add,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 8.57/4.55        = ( plus_plus_int @ A @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2110_diff__minus__eq__add,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.57/4.55        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2111_diff__minus__eq__add,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.57/4.55        = ( plus_plus_rat @ A @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2112_Suc__pred,axiom,
% 8.57/4.55      ! [N: nat] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.55       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 8.57/4.55          = N ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2113_length__0__conv,axiom,
% 8.57/4.55      ! [Xs: list_char] :
% 8.57/4.55        ( ( ( size_size_list_char @ Xs )
% 8.57/4.55          = zero_zero_nat )
% 8.57/4.55        = ( Xs = nil_char ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2114_length__0__conv,axiom,
% 8.57/4.55      ! [Xs: list_nat] :
% 8.57/4.55        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.55          = zero_zero_nat )
% 8.57/4.55        = ( Xs = nil_nat ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2115_length__0__conv,axiom,
% 8.57/4.55      ! [Xs: list_int] :
% 8.57/4.55        ( ( ( size_size_list_int @ Xs )
% 8.57/4.55          = zero_zero_nat )
% 8.57/4.55        = ( Xs = nil_int ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2116_length__0__conv,axiom,
% 8.57/4.55      ! [Xs: list_o] :
% 8.57/4.55        ( ( ( size_size_list_o @ Xs )
% 8.57/4.55          = zero_zero_nat )
% 8.57/4.55        = ( Xs = nil_o ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2117_one__le__mult__iff,axiom,
% 8.57/4.55      ! [M: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 8.57/4.55        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.57/4.55          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2118_mult__le__cancel2,axiom,
% 8.57/4.55      ! [M: nat,K: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 8.57/4.55        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.55         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2119_diff__Suc__diff__eq1,axiom,
% 8.57/4.55      ! [K: nat,J: nat,I: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ K @ J )
% 8.57/4.55       => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 8.57/4.55          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2120_diff__Suc__diff__eq2,axiom,
% 8.57/4.55      ! [K: nat,J: nat,I: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ K @ J )
% 8.57/4.55       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 8.57/4.55          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2121_Suc__diff,axiom,
% 8.57/4.55      ! [M: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.55       => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 8.57/4.55         => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 8.57/4.55            = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2122_zle__diff1__eq,axiom,
% 8.57/4.55      ! [W2: int,Z2: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z2 @ one_one_int ) )
% 8.57/4.55        = ( ord_less_int @ W2 @ Z2 ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2123_floor__diff__of__int,axiom,
% 8.57/4.55      ! [X2: rat,Z2: int] :
% 8.57/4.55        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) )
% 8.57/4.55        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z2 ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2124_ceiling__diff__of__int,axiom,
% 8.57/4.55      ! [X2: rat,Z2: int] :
% 8.57/4.55        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) )
% 8.57/4.55        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z2 ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2125_diff__numeral__special_I12_J,axiom,
% 8.57/4.55      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.55      = zero_zero_int ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2126_diff__numeral__special_I12_J,axiom,
% 8.57/4.55      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.57/4.55      = zero_z3403309356797280102nteger ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2127_diff__numeral__special_I12_J,axiom,
% 8.57/4.55      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.57/4.55      = zero_zero_rat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2128_length__greater__0__conv,axiom,
% 8.57/4.55      ! [Xs: list_char] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_char @ Xs ) )
% 8.57/4.55        = ( Xs != nil_char ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2129_length__greater__0__conv,axiom,
% 8.57/4.55      ! [Xs: list_nat] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) )
% 8.57/4.55        = ( Xs != nil_nat ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2130_length__greater__0__conv,axiom,
% 8.57/4.55      ! [Xs: list_int] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) )
% 8.57/4.55        = ( Xs != nil_int ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2131_length__greater__0__conv,axiom,
% 8.57/4.55      ! [Xs: list_o] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) )
% 8.57/4.55        = ( Xs != nil_o ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2132_Suc__diff__1,axiom,
% 8.57/4.55      ! [N: nat] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.55       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.57/4.55          = N ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2133_power__int__minus__one__mult__self,axiom,
% 8.57/4.55      ! [M: int] :
% 8.57/4.55        ( ( times_times_rat @ ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) )
% 8.57/4.55        = one_one_rat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2134_power__int__minus__one__mult__self_H,axiom,
% 8.57/4.55      ! [M: int,B: rat] :
% 8.57/4.55        ( ( times_times_rat @ ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( times_times_rat @ ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ B ) )
% 8.57/4.55        = B ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2135_floor__diff__one,axiom,
% 8.57/4.55      ! [X2: rat] :
% 8.57/4.55        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 8.57/4.55        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2136_ceiling__diff__one,axiom,
% 8.57/4.55      ! [X2: rat] :
% 8.57/4.55        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 8.57/4.55        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2137_int__ops_I7_J,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 8.57/4.55        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2138_ordering__top_Oextremum__uniqueI,axiom,
% 8.57/4.55      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 8.57/4.55        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 8.57/4.55       => ( ( Less_eq @ Top @ A )
% 8.57/4.55         => ( A = Top ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2139_ordering__top_Onot__eq__extremum,axiom,
% 8.57/4.55      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 8.57/4.55        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 8.57/4.55       => ( ( A != Top )
% 8.57/4.55          = ( Less @ A @ Top ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2140_ordering__top_Oextremum__unique,axiom,
% 8.57/4.55      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 8.57/4.55        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 8.57/4.55       => ( ( Less_eq @ Top @ A )
% 8.57/4.55          = ( A = Top ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2141_ordering__top_Oextremum__strict,axiom,
% 8.57/4.55      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 8.57/4.55        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 8.57/4.55       => ~ ( Less @ Top @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2142_ordering__top_Oextremum,axiom,
% 8.57/4.55      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 8.57/4.55        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 8.57/4.55       => ( Less_eq @ A @ Top ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2143_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 8.57/4.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B )
% 8.57/4.55        = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2144_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 8.57/4.55      ! [A: rat,C: rat,B: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 8.57/4.55        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2145_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 8.57/4.55      ! [A: nat,C: nat,B: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 8.57/4.55        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2146_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 8.57/4.55      ! [A: int,C: int,B: int] :
% 8.57/4.55        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 8.57/4.55        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2147_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ B @ ( times_3573771949741848930nteger @ A @ C ) )
% 8.57/4.55        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2148_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 8.57/4.55      ! [B: rat,A: rat,C: rat] :
% 8.57/4.55        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 8.57/4.55        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2149_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 8.57/4.55      ! [B: nat,A: nat,C: nat] :
% 8.57/4.55        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 8.57/4.55        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2150_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 8.57/4.55      ! [B: int,A: int,C: int] :
% 8.57/4.55        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 8.57/4.55        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2151_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 8.57/4.55      ( times_3573771949741848930nteger
% 8.57/4.55      = ( ^ [A2: code_integer,B2: code_integer] : ( times_3573771949741848930nteger @ B2 @ A2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2152_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 8.57/4.55      ( times_times_rat
% 8.57/4.55      = ( ^ [A2: rat,B2: rat] : ( times_times_rat @ B2 @ A2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2153_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 8.57/4.55      ( times_times_nat
% 8.57/4.55      = ( ^ [A2: nat,B2: nat] : ( times_times_nat @ B2 @ A2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2154_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 8.57/4.55      ( times_times_int
% 8.57/4.55      = ( ^ [A2: int,B2: int] : ( times_times_int @ B2 @ A2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2155_mult_Oassoc,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 8.57/4.55        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2156_mult_Oassoc,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 8.57/4.55        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2157_mult_Oassoc,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.57/4.55        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2158_mult_Oassoc,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 8.57/4.55        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2159_diff__eq__diff__eq,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ( minus_8373710615458151222nteger @ A @ B )
% 8.57/4.55          = ( minus_8373710615458151222nteger @ C @ D ) )
% 8.57/4.55       => ( ( A = B )
% 8.57/4.55          = ( C = D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2160_diff__eq__diff__eq,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ( minus_minus_rat @ A @ B )
% 8.57/4.55          = ( minus_minus_rat @ C @ D ) )
% 8.57/4.55       => ( ( A = B )
% 8.57/4.55          = ( C = D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2161_diff__eq__diff__eq,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ( minus_minus_int @ A @ B )
% 8.57/4.55          = ( minus_minus_int @ C @ D ) )
% 8.57/4.55       => ( ( A = B )
% 8.57/4.55          = ( C = D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2162_inf__period_I1_J,axiom,
% 8.57/4.55      ! [P: code_integer > $o,D3: code_integer,Q: code_integer > $o] :
% 8.57/4.55        ( ! [X3: code_integer,K3: code_integer] :
% 8.57/4.55            ( ( P @ X3 )
% 8.57/4.55            = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) )
% 8.57/4.55       => ( ! [X3: code_integer,K3: code_integer] :
% 8.57/4.55              ( ( Q @ X3 )
% 8.57/4.55              = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) )
% 8.57/4.55         => ! [X4: code_integer,K4: code_integer] :
% 8.57/4.55              ( ( ( P @ X4 )
% 8.57/4.55                & ( Q @ X4 ) )
% 8.57/4.55              = ( ( P @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) )
% 8.57/4.55                & ( Q @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2163_inf__period_I1_J,axiom,
% 8.57/4.55      ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 8.57/4.55        ( ! [X3: rat,K3: rat] :
% 8.57/4.55            ( ( P @ X3 )
% 8.57/4.55            = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D3 ) ) ) )
% 8.57/4.55       => ( ! [X3: rat,K3: rat] :
% 8.57/4.55              ( ( Q @ X3 )
% 8.57/4.55              = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D3 ) ) ) )
% 8.57/4.55         => ! [X4: rat,K4: rat] :
% 8.57/4.55              ( ( ( P @ X4 )
% 8.57/4.55                & ( Q @ X4 ) )
% 8.57/4.55              = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D3 ) ) )
% 8.57/4.55                & ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2164_inf__period_I1_J,axiom,
% 8.57/4.55      ! [P: int > $o,D3: int,Q: int > $o] :
% 8.57/4.55        ( ! [X3: int,K3: int] :
% 8.57/4.55            ( ( P @ X3 )
% 8.57/4.55            = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 8.57/4.55       => ( ! [X3: int,K3: int] :
% 8.57/4.55              ( ( Q @ X3 )
% 8.57/4.55              = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 8.57/4.55         => ! [X4: int,K4: int] :
% 8.57/4.55              ( ( ( P @ X4 )
% 8.57/4.55                & ( Q @ X4 ) )
% 8.57/4.55              = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D3 ) ) )
% 8.57/4.55                & ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2165_inf__period_I2_J,axiom,
% 8.57/4.55      ! [P: code_integer > $o,D3: code_integer,Q: code_integer > $o] :
% 8.57/4.55        ( ! [X3: code_integer,K3: code_integer] :
% 8.57/4.55            ( ( P @ X3 )
% 8.57/4.55            = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) )
% 8.57/4.55       => ( ! [X3: code_integer,K3: code_integer] :
% 8.57/4.55              ( ( Q @ X3 )
% 8.57/4.55              = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) )
% 8.57/4.55         => ! [X4: code_integer,K4: code_integer] :
% 8.57/4.55              ( ( ( P @ X4 )
% 8.57/4.55                | ( Q @ X4 ) )
% 8.57/4.55              = ( ( P @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) )
% 8.57/4.55                | ( Q @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2166_inf__period_I2_J,axiom,
% 8.57/4.55      ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 8.57/4.55        ( ! [X3: rat,K3: rat] :
% 8.57/4.55            ( ( P @ X3 )
% 8.57/4.55            = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D3 ) ) ) )
% 8.57/4.55       => ( ! [X3: rat,K3: rat] :
% 8.57/4.55              ( ( Q @ X3 )
% 8.57/4.55              = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D3 ) ) ) )
% 8.57/4.55         => ! [X4: rat,K4: rat] :
% 8.57/4.55              ( ( ( P @ X4 )
% 8.57/4.55                | ( Q @ X4 ) )
% 8.57/4.55              = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D3 ) ) )
% 8.57/4.55                | ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2167_inf__period_I2_J,axiom,
% 8.57/4.55      ! [P: int > $o,D3: int,Q: int > $o] :
% 8.57/4.55        ( ! [X3: int,K3: int] :
% 8.57/4.55            ( ( P @ X3 )
% 8.57/4.55            = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 8.57/4.55       => ( ! [X3: int,K3: int] :
% 8.57/4.55              ( ( Q @ X3 )
% 8.57/4.55              = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 8.57/4.55         => ! [X4: int,K4: int] :
% 8.57/4.55              ( ( ( P @ X4 )
% 8.57/4.55                | ( Q @ X4 ) )
% 8.57/4.55              = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D3 ) ) )
% 8.57/4.55                | ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2168_square__diff__square__factored,axiom,
% 8.57/4.55      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 8.57/4.55        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X2 @ Y ) @ ( minus_8373710615458151222nteger @ X2 @ Y ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2169_square__diff__square__factored,axiom,
% 8.57/4.55      ! [X2: rat,Y: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) )
% 8.57/4.55        = ( times_times_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( minus_minus_rat @ X2 @ Y ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2170_square__diff__square__factored,axiom,
% 8.57/4.55      ! [X2: int,Y: int] :
% 8.57/4.55        ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) )
% 8.57/4.55        = ( times_times_int @ ( plus_plus_int @ X2 @ Y ) @ ( minus_minus_int @ X2 @ Y ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2171_eq__add__iff2,axiom,
% 8.57/4.55      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 8.57/4.55          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 8.57/4.55        = ( C
% 8.57/4.55          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2172_eq__add__iff2,axiom,
% 8.57/4.55      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.57/4.55        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 8.57/4.55          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.57/4.55        = ( C
% 8.57/4.55          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2173_eq__add__iff2,axiom,
% 8.57/4.55      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.57/4.55        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 8.57/4.55          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.57/4.55        = ( C
% 8.57/4.55          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2174_eq__add__iff1,axiom,
% 8.57/4.55      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 8.57/4.55          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 8.57/4.55        = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C )
% 8.57/4.55          = D ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2175_eq__add__iff1,axiom,
% 8.57/4.55      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.57/4.55        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 8.57/4.55          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.57/4.55        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 8.57/4.55          = D ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2176_eq__add__iff1,axiom,
% 8.57/4.55      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.57/4.55        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 8.57/4.55          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.57/4.55        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 8.57/4.55          = D ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2177_le__add__iff1,axiom,
% 8.57/4.55      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2178_le__add__iff1,axiom,
% 8.57/4.55      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2179_le__add__iff1,axiom,
% 8.57/4.55      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2180_le__add__iff2,axiom,
% 8.57/4.55      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2181_le__add__iff2,axiom,
% 8.57/4.55      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2182_le__add__iff2,axiom,
% 8.57/4.55      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2183_less__add__iff2,axiom,
% 8.57/4.55      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2184_less__add__iff2,axiom,
% 8.57/4.55      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2185_less__add__iff2,axiom,
% 8.57/4.55      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.57/4.55        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2186_less__add__iff1,axiom,
% 8.57/4.55      ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2187_less__add__iff1,axiom,
% 8.57/4.55      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2188_less__add__iff1,axiom,
% 8.57/4.55      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.57/4.55        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.57/4.55        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2189_square__diff__one__factored,axiom,
% 8.57/4.55      ! [X2: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ one_one_Code_integer )
% 8.57/4.55        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X2 @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X2 @ one_one_Code_integer ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2190_square__diff__one__factored,axiom,
% 8.57/4.55      ! [X2: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ one_one_rat )
% 8.57/4.55        = ( times_times_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2191_square__diff__one__factored,axiom,
% 8.57/4.55      ! [X2: int] :
% 8.57/4.55        ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ one_one_int )
% 8.57/4.55        = ( times_times_int @ ( plus_plus_int @ X2 @ one_one_int ) @ ( minus_minus_int @ X2 @ one_one_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2192_of__nat__diff,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.55       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.55          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2193_of__nat__diff,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.55       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.55          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2194_of__nat__diff,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.55       => ( ( semiri4939895301339042750nteger @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.55          = ( minus_8373710615458151222nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2195_of__nat__diff,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.55       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.55          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2196_of__nat__diff,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.55       => ( ( semiri3763490453095760265atural @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.55          = ( minus_7197305767214868737atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2197_minusinfinity,axiom,
% 8.57/4.55      ! [D: int,P1: int > $o,P: int > $o] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ D )
% 8.57/4.55       => ( ! [X3: int,K3: int] :
% 8.57/4.55              ( ( P1 @ X3 )
% 8.57/4.55              = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D ) ) ) )
% 8.57/4.55         => ( ? [Z5: int] :
% 8.57/4.55              ! [X3: int] :
% 8.57/4.55                ( ( ord_less_int @ X3 @ Z5 )
% 8.57/4.55               => ( ( P @ X3 )
% 8.57/4.55                  = ( P1 @ X3 ) ) )
% 8.57/4.55           => ( ? [X_1: int] : ( P1 @ X_1 )
% 8.57/4.55             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2198_plusinfinity,axiom,
% 8.57/4.55      ! [D: int,P2: int > $o,P: int > $o] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ D )
% 8.57/4.55       => ( ! [X3: int,K3: int] :
% 8.57/4.55              ( ( P2 @ X3 )
% 8.57/4.55              = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D ) ) ) )
% 8.57/4.55         => ( ? [Z5: int] :
% 8.57/4.55              ! [X3: int] :
% 8.57/4.55                ( ( ord_less_int @ Z5 @ X3 )
% 8.57/4.55               => ( ( P @ X3 )
% 8.57/4.55                  = ( P2 @ X3 ) ) )
% 8.57/4.55           => ( ? [X_1: int] : ( P2 @ X_1 )
% 8.57/4.55             => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2199_int__minus,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 8.57/4.55        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2200_diff__eq__diff__less__eq,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ( minus_8373710615458151222nteger @ A @ B )
% 8.57/4.55          = ( minus_8373710615458151222nteger @ C @ D ) )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.55          = ( ord_le3102999989581377725nteger @ C @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2201_diff__eq__diff__less__eq,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ( minus_minus_rat @ A @ B )
% 8.57/4.55          = ( minus_minus_rat @ C @ D ) )
% 8.57/4.55       => ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.55          = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2202_diff__eq__diff__less__eq,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ( minus_minus_int @ A @ B )
% 8.57/4.55          = ( minus_minus_int @ C @ D ) )
% 8.57/4.55       => ( ( ord_less_eq_int @ A @ B )
% 8.57/4.55          = ( ord_less_eq_int @ C @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2203_diff__right__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.55       => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2204_diff__right__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.55       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2205_diff__right__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.55       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2206_diff__left__mono,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.57/4.55       => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2207_diff__left__mono,axiom,
% 8.57/4.55      ! [B: rat,A: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.55       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2208_diff__left__mono,axiom,
% 8.57/4.55      ! [B: int,A: int,C: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ B @ A )
% 8.57/4.55       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2209_diff__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,D: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ D @ C )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2210_diff__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,D: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_rat @ D @ C )
% 8.57/4.55         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2211_diff__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,D: int,C: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_int @ D @ C )
% 8.57/4.55         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2212_eq__iff__diff__eq__0,axiom,
% 8.57/4.55      ( ( ^ [Y3: code_integer,Z: code_integer] : ( Y3 = Z ) )
% 8.57/4.55      = ( ^ [A2: code_integer,B2: code_integer] :
% 8.57/4.55            ( ( minus_8373710615458151222nteger @ A2 @ B2 )
% 8.57/4.55            = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2213_eq__iff__diff__eq__0,axiom,
% 8.57/4.55      ( ( ^ [Y3: rat,Z: rat] : ( Y3 = Z ) )
% 8.57/4.55      = ( ^ [A2: rat,B2: rat] :
% 8.57/4.55            ( ( minus_minus_rat @ A2 @ B2 )
% 8.57/4.55            = zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2214_eq__iff__diff__eq__0,axiom,
% 8.57/4.55      ( ( ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.57/4.55      = ( ^ [A2: int,B2: int] :
% 8.57/4.55            ( ( minus_minus_int @ A2 @ B2 )
% 8.57/4.55            = zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2215_diff__strict__right__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55       => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2216_diff__strict__right__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ B )
% 8.57/4.55       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2217_diff__strict__right__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ B )
% 8.57/4.55       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2218_diff__strict__left__mono,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.57/4.55       => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2219_diff__strict__left__mono,axiom,
% 8.57/4.55      ! [B: rat,A: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_rat @ B @ A )
% 8.57/4.55       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2220_diff__strict__left__mono,axiom,
% 8.57/4.55      ! [B: int,A: int,C: int] :
% 8.57/4.55        ( ( ord_less_int @ B @ A )
% 8.57/4.55       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2221_diff__eq__diff__less,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ( minus_8373710615458151222nteger @ A @ B )
% 8.57/4.55          = ( minus_8373710615458151222nteger @ C @ D ) )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55          = ( ord_le6747313008572928689nteger @ C @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2222_diff__eq__diff__less,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ( minus_minus_rat @ A @ B )
% 8.57/4.55          = ( minus_minus_rat @ C @ D ) )
% 8.57/4.55       => ( ( ord_less_rat @ A @ B )
% 8.57/4.55          = ( ord_less_rat @ C @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2223_diff__eq__diff__less,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ( minus_minus_int @ A @ B )
% 8.57/4.55          = ( minus_minus_int @ C @ D ) )
% 8.57/4.55       => ( ( ord_less_int @ A @ B )
% 8.57/4.55          = ( ord_less_int @ C @ D ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2224_diff__strict__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,D: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ D @ C )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2225_diff__strict__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,D: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_rat @ D @ C )
% 8.57/4.55         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2226_diff__strict__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,D: int,C: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_int @ D @ C )
% 8.57/4.55         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2227_diff__diff__eq,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 8.57/4.55        = ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2228_diff__diff__eq,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.57/4.55        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2229_diff__diff__eq,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 8.57/4.55        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2230_diff__diff__eq,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.57/4.55        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2231_add__implies__diff,axiom,
% 8.57/4.55      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.57/4.55        ( ( ( plus_p5714425477246183910nteger @ C @ B )
% 8.57/4.55          = A )
% 8.57/4.55       => ( C
% 8.57/4.55          = ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2232_add__implies__diff,axiom,
% 8.57/4.55      ! [C: rat,B: rat,A: rat] :
% 8.57/4.55        ( ( ( plus_plus_rat @ C @ B )
% 8.57/4.55          = A )
% 8.57/4.55       => ( C
% 8.57/4.55          = ( minus_minus_rat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2233_add__implies__diff,axiom,
% 8.57/4.55      ! [C: nat,B: nat,A: nat] :
% 8.57/4.55        ( ( ( plus_plus_nat @ C @ B )
% 8.57/4.55          = A )
% 8.57/4.55       => ( C
% 8.57/4.55          = ( minus_minus_nat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2234_add__implies__diff,axiom,
% 8.57/4.55      ! [C: int,B: int,A: int] :
% 8.57/4.55        ( ( ( plus_plus_int @ C @ B )
% 8.57/4.55          = A )
% 8.57/4.55       => ( C
% 8.57/4.55          = ( minus_minus_int @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2235_diff__add__eq__diff__diff__swap,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.55        = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2236_diff__add__eq__diff__diff__swap,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.55        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2237_diff__add__eq__diff__diff__swap,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.57/4.55        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2238_diff__add__eq,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 8.57/4.55        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2239_diff__add__eq,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.57/4.55        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2240_diff__add__eq,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.57/4.55        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2241_diff__diff__eq2,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 8.57/4.55        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2242_diff__diff__eq2,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 8.57/4.55        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2243_diff__diff__eq2,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 8.57/4.55        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2244_add__diff__eq,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( plus_p5714425477246183910nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 8.57/4.55        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2245_add__diff__eq,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 8.57/4.55        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2246_add__diff__eq,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 8.57/4.55        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2247_eq__diff__eq,axiom,
% 8.57/4.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( A
% 8.57/4.55          = ( minus_8373710615458151222nteger @ C @ B ) )
% 8.57/4.55        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.57/4.55          = C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2248_eq__diff__eq,axiom,
% 8.57/4.55      ! [A: rat,C: rat,B: rat] :
% 8.57/4.55        ( ( A
% 8.57/4.55          = ( minus_minus_rat @ C @ B ) )
% 8.57/4.55        = ( ( plus_plus_rat @ A @ B )
% 8.57/4.55          = C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2249_eq__diff__eq,axiom,
% 8.57/4.55      ! [A: int,C: int,B: int] :
% 8.57/4.55        ( ( A
% 8.57/4.55          = ( minus_minus_int @ C @ B ) )
% 8.57/4.55        = ( ( plus_plus_int @ A @ B )
% 8.57/4.55          = C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2250_diff__eq__eq,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ( minus_8373710615458151222nteger @ A @ B )
% 8.57/4.55          = C )
% 8.57/4.55        = ( A
% 8.57/4.55          = ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2251_diff__eq__eq,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ( minus_minus_rat @ A @ B )
% 8.57/4.55          = C )
% 8.57/4.55        = ( A
% 8.57/4.55          = ( plus_plus_rat @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2252_diff__eq__eq,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ( minus_minus_int @ A @ B )
% 8.57/4.55          = C )
% 8.57/4.55        = ( A
% 8.57/4.55          = ( plus_plus_int @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2253_group__cancel_Osub1,axiom,
% 8.57/4.55      ! [A4: code_integer,K: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( A4
% 8.57/4.55          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 8.57/4.55       => ( ( minus_8373710615458151222nteger @ A4 @ B )
% 8.57/4.55          = ( plus_p5714425477246183910nteger @ K @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2254_group__cancel_Osub1,axiom,
% 8.57/4.55      ! [A4: rat,K: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( A4
% 8.57/4.55          = ( plus_plus_rat @ K @ A ) )
% 8.57/4.55       => ( ( minus_minus_rat @ A4 @ B )
% 8.57/4.55          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2255_group__cancel_Osub1,axiom,
% 8.57/4.55      ! [A4: int,K: int,A: int,B: int] :
% 8.57/4.55        ( ( A4
% 8.57/4.55          = ( plus_plus_int @ K @ A ) )
% 8.57/4.55       => ( ( minus_minus_int @ A4 @ B )
% 8.57/4.55          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2256_minus__diff__commute,axiom,
% 8.57/4.55      ! [B: int,A: int] :
% 8.57/4.55        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 8.57/4.55        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2257_minus__diff__commute,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer] :
% 8.57/4.55        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 8.57/4.55        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2258_minus__diff__commute,axiom,
% 8.57/4.55      ! [B: rat,A: rat] :
% 8.57/4.55        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 8.57/4.55        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2259_mult__not__zero,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ( times_2397367101498566445atural @ A @ B )
% 8.57/4.55         != zero_z2226904508553997617atural )
% 8.57/4.55       => ( ( A != zero_z2226904508553997617atural )
% 8.57/4.55          & ( B != zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2260_mult__not__zero,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ( times_3573771949741848930nteger @ A @ B )
% 8.57/4.55         != zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( A != zero_z3403309356797280102nteger )
% 8.57/4.55          & ( B != zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2261_mult__not__zero,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ( times_times_rat @ A @ B )
% 8.57/4.55         != zero_zero_rat )
% 8.57/4.55       => ( ( A != zero_zero_rat )
% 8.57/4.55          & ( B != zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2262_mult__not__zero,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ( times_times_nat @ A @ B )
% 8.57/4.55         != zero_zero_nat )
% 8.57/4.55       => ( ( A != zero_zero_nat )
% 8.57/4.55          & ( B != zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2263_mult__not__zero,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ( times_times_int @ A @ B )
% 8.57/4.55         != zero_zero_int )
% 8.57/4.55       => ( ( A != zero_zero_int )
% 8.57/4.55          & ( B != zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2264_divisors__zero,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ( times_2397367101498566445atural @ A @ B )
% 8.57/4.55          = zero_z2226904508553997617atural )
% 8.57/4.55       => ( ( A = zero_z2226904508553997617atural )
% 8.57/4.55          | ( B = zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2265_divisors__zero,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ( times_3573771949741848930nteger @ A @ B )
% 8.57/4.55          = zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( A = zero_z3403309356797280102nteger )
% 8.57/4.55          | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2266_divisors__zero,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ( times_times_rat @ A @ B )
% 8.57/4.55          = zero_zero_rat )
% 8.57/4.55       => ( ( A = zero_zero_rat )
% 8.57/4.55          | ( B = zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2267_divisors__zero,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ( times_times_nat @ A @ B )
% 8.57/4.55          = zero_zero_nat )
% 8.57/4.55       => ( ( A = zero_zero_nat )
% 8.57/4.55          | ( B = zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2268_divisors__zero,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ( times_times_int @ A @ B )
% 8.57/4.55          = zero_zero_int )
% 8.57/4.55       => ( ( A = zero_zero_int )
% 8.57/4.55          | ( B = zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2269_no__zero__divisors,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( A != zero_z2226904508553997617atural )
% 8.57/4.55       => ( ( B != zero_z2226904508553997617atural )
% 8.57/4.55         => ( ( times_2397367101498566445atural @ A @ B )
% 8.57/4.55           != zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2270_no__zero__divisors,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( A != zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( B != zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ( times_3573771949741848930nteger @ A @ B )
% 8.57/4.55           != zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2271_no__zero__divisors,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( A != zero_zero_rat )
% 8.57/4.55       => ( ( B != zero_zero_rat )
% 8.57/4.55         => ( ( times_times_rat @ A @ B )
% 8.57/4.55           != zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2272_no__zero__divisors,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( A != zero_zero_nat )
% 8.57/4.55       => ( ( B != zero_zero_nat )
% 8.57/4.55         => ( ( times_times_nat @ A @ B )
% 8.57/4.55           != zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2273_no__zero__divisors,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( A != zero_zero_int )
% 8.57/4.55       => ( ( B != zero_zero_int )
% 8.57/4.55         => ( ( times_times_int @ A @ B )
% 8.57/4.55           != zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2274_mult__left__cancel,axiom,
% 8.57/4.55      ! [C: code_natural,A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( C != zero_z2226904508553997617atural )
% 8.57/4.55       => ( ( ( times_2397367101498566445atural @ C @ A )
% 8.57/4.55            = ( times_2397367101498566445atural @ C @ B ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2275_mult__left__cancel,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( C != zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( ( times_3573771949741848930nteger @ C @ A )
% 8.57/4.55            = ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2276_mult__left__cancel,axiom,
% 8.57/4.55      ! [C: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( C != zero_zero_rat )
% 8.57/4.55       => ( ( ( times_times_rat @ C @ A )
% 8.57/4.55            = ( times_times_rat @ C @ B ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2277_mult__left__cancel,axiom,
% 8.57/4.55      ! [C: nat,A: nat,B: nat] :
% 8.57/4.55        ( ( C != zero_zero_nat )
% 8.57/4.55       => ( ( ( times_times_nat @ C @ A )
% 8.57/4.55            = ( times_times_nat @ C @ B ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2278_mult__left__cancel,axiom,
% 8.57/4.55      ! [C: int,A: int,B: int] :
% 8.57/4.55        ( ( C != zero_zero_int )
% 8.57/4.55       => ( ( ( times_times_int @ C @ A )
% 8.57/4.55            = ( times_times_int @ C @ B ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2279_mult__right__cancel,axiom,
% 8.57/4.55      ! [C: code_natural,A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( C != zero_z2226904508553997617atural )
% 8.57/4.55       => ( ( ( times_2397367101498566445atural @ A @ C )
% 8.57/4.55            = ( times_2397367101498566445atural @ B @ C ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2280_mult__right__cancel,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( C != zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( ( times_3573771949741848930nteger @ A @ C )
% 8.57/4.55            = ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2281_mult__right__cancel,axiom,
% 8.57/4.55      ! [C: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( C != zero_zero_rat )
% 8.57/4.55       => ( ( ( times_times_rat @ A @ C )
% 8.57/4.55            = ( times_times_rat @ B @ C ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2282_mult__right__cancel,axiom,
% 8.57/4.55      ! [C: nat,A: nat,B: nat] :
% 8.57/4.55        ( ( C != zero_zero_nat )
% 8.57/4.55       => ( ( ( times_times_nat @ A @ C )
% 8.57/4.55            = ( times_times_nat @ B @ C ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2283_mult__right__cancel,axiom,
% 8.57/4.55      ! [C: int,A: int,B: int] :
% 8.57/4.55        ( ( C != zero_zero_int )
% 8.57/4.55       => ( ( ( times_times_int @ A @ C )
% 8.57/4.55            = ( times_times_int @ B @ C ) )
% 8.57/4.55          = ( A = B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2284_crossproduct__eq,axiom,
% 8.57/4.55      ! [W2: code_integer,Y: code_integer,X2: code_integer,Z2: code_integer] :
% 8.57/4.55        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W2 @ Y ) @ ( times_3573771949741848930nteger @ X2 @ Z2 ) )
% 8.57/4.55          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W2 @ Z2 ) @ ( times_3573771949741848930nteger @ X2 @ Y ) ) )
% 8.57/4.55        = ( ( W2 = X2 )
% 8.57/4.55          | ( Y = Z2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2285_crossproduct__eq,axiom,
% 8.57/4.55      ! [W2: rat,Y: rat,X2: rat,Z2: rat] :
% 8.57/4.55        ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y ) @ ( times_times_rat @ X2 @ Z2 ) )
% 8.57/4.55          = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z2 ) @ ( times_times_rat @ X2 @ Y ) ) )
% 8.57/4.55        = ( ( W2 = X2 )
% 8.57/4.55          | ( Y = Z2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2286_crossproduct__eq,axiom,
% 8.57/4.55      ! [W2: nat,Y: nat,X2: nat,Z2: nat] :
% 8.57/4.55        ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X2 @ Z2 ) )
% 8.57/4.55          = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z2 ) @ ( times_times_nat @ X2 @ Y ) ) )
% 8.57/4.55        = ( ( W2 = X2 )
% 8.57/4.55          | ( Y = Z2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2287_crossproduct__eq,axiom,
% 8.57/4.55      ! [W2: int,Y: int,X2: int,Z2: int] :
% 8.57/4.55        ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X2 @ Z2 ) )
% 8.57/4.55          = ( plus_plus_int @ ( times_times_int @ W2 @ Z2 ) @ ( times_times_int @ X2 @ Y ) ) )
% 8.57/4.55        = ( ( W2 = X2 )
% 8.57/4.55          | ( Y = Z2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2288_crossproduct__noteq,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ( A != B )
% 8.57/4.55          & ( C != D ) )
% 8.57/4.55        = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) )
% 8.57/4.55         != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ D ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2289_crossproduct__noteq,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ( A != B )
% 8.57/4.55          & ( C != D ) )
% 8.57/4.55        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 8.57/4.55         != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2290_crossproduct__noteq,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.55        ( ( ( A != B )
% 8.57/4.55          & ( C != D ) )
% 8.57/4.55        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 8.57/4.55         != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2291_crossproduct__noteq,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ( A != B )
% 8.57/4.55          & ( C != D ) )
% 8.57/4.55        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 8.57/4.55         != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2292_ring__class_Oring__distribs_I2_J,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.55        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2293_ring__class_Oring__distribs_I2_J,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.57/4.55        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2294_ring__class_Oring__distribs_I2_J,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.57/4.55        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2295_ring__class_Oring__distribs_I1_J,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.55        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2296_ring__class_Oring__distribs_I1_J,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.55        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2297_ring__class_Oring__distribs_I1_J,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.57/4.55        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2298_comm__semiring__class_Odistrib,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.55        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2299_comm__semiring__class_Odistrib,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.57/4.55        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2300_comm__semiring__class_Odistrib,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.57/4.55        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2301_comm__semiring__class_Odistrib,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.57/4.55        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2302_distrib__left,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.55        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2303_distrib__left,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.55        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2304_distrib__left,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 8.57/4.55        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2305_distrib__left,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.57/4.55        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2306_distrib__right,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.55        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2307_distrib__right,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.57/4.55        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2308_distrib__right,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.57/4.55        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2309_distrib__right,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.57/4.55        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2310_combine__common__factor,axiom,
% 8.57/4.55      ! [A: code_integer,E: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ C ) )
% 8.57/4.55        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ E ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2311_combine__common__factor,axiom,
% 8.57/4.55      ! [A: rat,E: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 8.57/4.55        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2312_combine__common__factor,axiom,
% 8.57/4.55      ! [A: nat,E: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 8.57/4.55        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2313_combine__common__factor,axiom,
% 8.57/4.55      ! [A: int,E: int,B: int,C: int] :
% 8.57/4.55        ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 8.57/4.55        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2314_mult_Ocomm__neutral,axiom,
% 8.57/4.55      ! [A: code_natural] :
% 8.57/4.55        ( ( times_2397367101498566445atural @ A @ one_one_Code_natural )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2315_mult_Ocomm__neutral,axiom,
% 8.57/4.55      ! [A: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2316_mult_Ocomm__neutral,axiom,
% 8.57/4.55      ! [A: rat] :
% 8.57/4.55        ( ( times_times_rat @ A @ one_one_rat )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2317_mult_Ocomm__neutral,axiom,
% 8.57/4.55      ! [A: nat] :
% 8.57/4.55        ( ( times_times_nat @ A @ one_one_nat )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2318_mult_Ocomm__neutral,axiom,
% 8.57/4.55      ! [A: int] :
% 8.57/4.55        ( ( times_times_int @ A @ one_one_int )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2319_comm__monoid__mult__class_Omult__1,axiom,
% 8.57/4.55      ! [A: code_natural] :
% 8.57/4.55        ( ( times_2397367101498566445atural @ one_one_Code_natural @ A )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2320_comm__monoid__mult__class_Omult__1,axiom,
% 8.57/4.55      ! [A: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2321_comm__monoid__mult__class_Omult__1,axiom,
% 8.57/4.55      ! [A: rat] :
% 8.57/4.55        ( ( times_times_rat @ one_one_rat @ A )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2322_comm__monoid__mult__class_Omult__1,axiom,
% 8.57/4.55      ! [A: nat] :
% 8.57/4.55        ( ( times_times_nat @ one_one_nat @ A )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2323_comm__monoid__mult__class_Omult__1,axiom,
% 8.57/4.55      ! [A: int] :
% 8.57/4.55        ( ( times_times_int @ one_one_int @ A )
% 8.57/4.55        = A ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2324_diffs0__imp__equal,axiom,
% 8.57/4.55      ! [M: nat,N: nat] :
% 8.57/4.55        ( ( ( minus_minus_nat @ M @ N )
% 8.57/4.55          = zero_zero_nat )
% 8.57/4.55       => ( ( ( minus_minus_nat @ N @ M )
% 8.57/4.55            = zero_zero_nat )
% 8.57/4.55         => ( M = N ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2325_minus__nat_Odiff__0,axiom,
% 8.57/4.55      ! [M: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 8.57/4.55        = M ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2326_minus__int__code_I1_J,axiom,
% 8.57/4.55      ! [K: int] :
% 8.57/4.55        ( ( minus_minus_int @ K @ zero_zero_int )
% 8.57/4.55        = K ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2327_zero__induct__lemma,axiom,
% 8.57/4.55      ! [P: nat > $o,K: nat,I: nat] :
% 8.57/4.55        ( ( P @ K )
% 8.57/4.55       => ( ! [N2: nat] :
% 8.57/4.55              ( ( P @ ( suc @ N2 ) )
% 8.57/4.55             => ( P @ N2 ) )
% 8.57/4.55         => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2328_diff__less__mono2,axiom,
% 8.57/4.55      ! [M: nat,N: nat,L: nat] :
% 8.57/4.55        ( ( ord_less_nat @ M @ N )
% 8.57/4.55       => ( ( ord_less_nat @ M @ L )
% 8.57/4.55         => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2329_less__imp__diff__less,axiom,
% 8.57/4.55      ! [J: nat,K: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_nat @ J @ K )
% 8.57/4.55       => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2330_diff__le__mono2,axiom,
% 8.57/4.55      ! [M: nat,N: nat,L: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.55       => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2331_le__diff__iff_H,axiom,
% 8.57/4.55      ! [A: nat,C: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ C )
% 8.57/4.55       => ( ( ord_less_eq_nat @ B @ C )
% 8.57/4.55         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 8.57/4.55            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2332_diff__le__self,axiom,
% 8.57/4.55      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2333_diff__le__mono,axiom,
% 8.57/4.55      ! [M: nat,N: nat,L: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.55       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2334_Nat_Odiff__diff__eq,axiom,
% 8.57/4.55      ! [K: nat,M: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ K @ M )
% 8.57/4.55       => ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.55         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 8.57/4.55            = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2335_le__diff__iff,axiom,
% 8.57/4.55      ! [K: nat,M: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ K @ M )
% 8.57/4.55       => ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.55         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 8.57/4.55            = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2336_eq__diff__iff,axiom,
% 8.57/4.55      ! [K: nat,M: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ K @ M )
% 8.57/4.55       => ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.55         => ( ( ( minus_minus_nat @ M @ K )
% 8.57/4.55              = ( minus_minus_nat @ N @ K ) )
% 8.57/4.55            = ( M = N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2337_diff__add__inverse2,axiom,
% 8.57/4.55      ! [M: nat,N: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 8.57/4.55        = M ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2338_diff__add__inverse,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 8.57/4.55        = M ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2339_diff__cancel2,axiom,
% 8.57/4.55      ! [M: nat,K: nat,N: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 8.57/4.55        = ( minus_minus_nat @ M @ N ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2340_Nat_Odiff__cancel,axiom,
% 8.57/4.55      ! [K: nat,M: nat,N: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 8.57/4.55        = ( minus_minus_nat @ M @ N ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2341_mult__0,axiom,
% 8.57/4.55      ! [N: nat] :
% 8.57/4.55        ( ( times_times_nat @ zero_zero_nat @ N )
% 8.57/4.55        = zero_zero_nat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2342_Suc__mult__cancel1,axiom,
% 8.57/4.55      ! [K: nat,M: nat,N: nat] :
% 8.57/4.55        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 8.57/4.55          = ( times_times_nat @ ( suc @ K ) @ N ) )
% 8.57/4.55        = ( M = N ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2343_mult__of__nat__commute,axiom,
% 8.57/4.55      ! [X2: nat,Y: int] :
% 8.57/4.55        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X2 ) @ Y )
% 8.57/4.55        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2344_mult__of__nat__commute,axiom,
% 8.57/4.55      ! [X2: nat,Y: nat] :
% 8.57/4.55        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ Y )
% 8.57/4.55        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2345_mult__of__nat__commute,axiom,
% 8.57/4.55      ! [X2: nat,Y: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X2 ) @ Y )
% 8.57/4.55        = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2346_mult__of__nat__commute,axiom,
% 8.57/4.55      ! [X2: nat,Y: rat] :
% 8.57/4.55        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X2 ) @ Y )
% 8.57/4.55        = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2347_mult__of__nat__commute,axiom,
% 8.57/4.55      ! [X2: nat,Y: code_natural] :
% 8.57/4.55        ( ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ X2 ) @ Y )
% 8.57/4.55        = ( times_2397367101498566445atural @ Y @ ( semiri3763490453095760265atural @ X2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2348_times__int__code_I2_J,axiom,
% 8.57/4.55      ! [L: int] :
% 8.57/4.55        ( ( times_times_int @ zero_zero_int @ L )
% 8.57/4.55        = zero_zero_int ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2349_times__int__code_I1_J,axiom,
% 8.57/4.55      ! [K: int] :
% 8.57/4.55        ( ( times_times_int @ K @ zero_zero_int )
% 8.57/4.55        = zero_zero_int ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2350_mult__le__mono2,axiom,
% 8.57/4.55      ! [I: nat,J: nat,K: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.55       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2351_mult__le__mono1,axiom,
% 8.57/4.55      ! [I: nat,J: nat,K: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.55       => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2352_mult__le__mono,axiom,
% 8.57/4.55      ! [I: nat,J: nat,K: nat,L: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.55       => ( ( ord_less_eq_nat @ K @ L )
% 8.57/4.55         => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2353_le__square,axiom,
% 8.57/4.55      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2354_le__cube,axiom,
% 8.57/4.55      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2355_int__diff__cases,axiom,
% 8.57/4.55      ! [Z2: int] :
% 8.57/4.55        ~ ! [M4: nat,N2: nat] :
% 8.57/4.55            ( Z2
% 8.57/4.55           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2356_add__mult__distrib2,axiom,
% 8.57/4.55      ! [K: nat,M: nat,N: nat] :
% 8.57/4.55        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.55        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2357_add__mult__distrib,axiom,
% 8.57/4.55      ! [M: nat,N: nat,K: nat] :
% 8.57/4.55        ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 8.57/4.55        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2358_nat__minus__as__int,axiom,
% 8.57/4.55      ( minus_minus_nat
% 8.57/4.55      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2359_nat__mult__1,axiom,
% 8.57/4.55      ! [N: nat] :
% 8.57/4.55        ( ( times_times_nat @ one_one_nat @ N )
% 8.57/4.55        = N ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2360_nat__mult__1__right,axiom,
% 8.57/4.55      ! [N: nat] :
% 8.57/4.55        ( ( times_times_nat @ N @ one_one_nat )
% 8.57/4.55        = N ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2361_mult__of__int__commute,axiom,
% 8.57/4.55      ! [X2: int,Y: code_integer] :
% 8.57/4.55        ( ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ X2 ) @ Y )
% 8.57/4.55        = ( times_3573771949741848930nteger @ Y @ ( ring_18347121197199848620nteger @ X2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2362_mult__of__int__commute,axiom,
% 8.57/4.55      ! [X2: int,Y: rat] :
% 8.57/4.55        ( ( times_times_rat @ ( ring_1_of_int_rat @ X2 ) @ Y )
% 8.57/4.55        = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2363_mult__of__int__commute,axiom,
% 8.57/4.55      ! [X2: int,Y: int] :
% 8.57/4.55        ( ( times_times_int @ ( ring_1_of_int_int @ X2 ) @ Y )
% 8.57/4.55        = ( times_times_int @ Y @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2364_int__distrib_I2_J,axiom,
% 8.57/4.55      ! [W2: int,Z1: int,Z22: int] :
% 8.57/4.55        ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 8.57/4.55        = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2365_int__distrib_I1_J,axiom,
% 8.57/4.55      ! [Z1: int,Z22: int,W2: int] :
% 8.57/4.55        ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 8.57/4.55        = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2366_nat__times__as__int,axiom,
% 8.57/4.55      ( times_times_nat
% 8.57/4.55      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2367_power__int__mult__distrib,axiom,
% 8.57/4.55      ! [X2: rat,Y: rat,M: int] :
% 8.57/4.55        ( ( power_int_rat @ ( times_times_rat @ X2 @ Y ) @ M )
% 8.57/4.55        = ( times_times_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ Y @ M ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2368_power__int__commutes,axiom,
% 8.57/4.55      ! [X2: rat,N: int] :
% 8.57/4.55        ( ( times_times_rat @ ( power_int_rat @ X2 @ N ) @ X2 )
% 8.57/4.55        = ( times_times_rat @ X2 @ ( power_int_rat @ X2 @ N ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2369_int__ops_I6_J,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 8.57/4.55         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 8.57/4.55            = zero_zero_int ) )
% 8.57/4.55        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 8.57/4.55         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 8.57/4.55            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2370_mult__eq__if,axiom,
% 8.57/4.55      ( times_times_nat
% 8.57/4.55      = ( ^ [M2: nat,N3: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N3 @ ( times_times_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2371_decr__mult__lemma,axiom,
% 8.57/4.55      ! [D: int,P: int > $o,K: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ D )
% 8.57/4.55       => ( ! [X3: int] :
% 8.57/4.55              ( ( P @ X3 )
% 8.57/4.55             => ( P @ ( minus_minus_int @ X3 @ D ) ) )
% 8.57/4.55         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.55           => ! [X4: int] :
% 8.57/4.55                ( ( P @ X4 )
% 8.57/4.55               => ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2372_nat__diff__distrib_H,axiom,
% 8.57/4.55      ! [X2: int,Y: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.55       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.55         => ( ( nat2 @ ( minus_minus_int @ X2 @ Y ) )
% 8.57/4.55            = ( minus_minus_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2373_nat__diff__distrib,axiom,
% 8.57/4.55      ! [Z6: int,Z2: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 8.57/4.55       => ( ( ord_less_eq_int @ Z6 @ Z2 )
% 8.57/4.55         => ( ( nat2 @ ( minus_minus_int @ Z2 @ Z6 ) )
% 8.57/4.55            = ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2374_lambda__zero,axiom,
% 8.57/4.55      ( ( ^ [H3: code_natural] : zero_z2226904508553997617atural )
% 8.57/4.55      = ( times_2397367101498566445atural @ zero_z2226904508553997617atural ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2375_lambda__zero,axiom,
% 8.57/4.55      ( ( ^ [H3: code_integer] : zero_z3403309356797280102nteger )
% 8.57/4.55      = ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2376_lambda__zero,axiom,
% 8.57/4.55      ( ( ^ [H3: rat] : zero_zero_rat )
% 8.57/4.55      = ( times_times_rat @ zero_zero_rat ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2377_lambda__zero,axiom,
% 8.57/4.55      ( ( ^ [H3: nat] : zero_zero_nat )
% 8.57/4.55      = ( times_times_nat @ zero_zero_nat ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2378_lambda__zero,axiom,
% 8.57/4.55      ( ( ^ [H3: int] : zero_zero_int )
% 8.57/4.55      = ( times_times_int @ zero_zero_int ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2379_lambda__one,axiom,
% 8.57/4.55      ( ( ^ [X: code_natural] : X )
% 8.57/4.55      = ( times_2397367101498566445atural @ one_one_Code_natural ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2380_lambda__one,axiom,
% 8.57/4.55      ( ( ^ [X: code_integer] : X )
% 8.57/4.55      = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2381_lambda__one,axiom,
% 8.57/4.55      ( ( ^ [X: rat] : X )
% 8.57/4.55      = ( times_times_rat @ one_one_rat ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2382_lambda__one,axiom,
% 8.57/4.55      ( ( ^ [X: nat] : X )
% 8.57/4.55      = ( times_times_nat @ one_one_nat ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2383_lambda__one,axiom,
% 8.57/4.55      ( ( ^ [X: int] : X )
% 8.57/4.55      = ( times_times_int @ one_one_int ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2384_nat__mult__distrib,axiom,
% 8.57/4.55      ! [Z2: int,Z6: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.55       => ( ( nat2 @ ( times_times_int @ Z2 @ Z6 ) )
% 8.57/4.55          = ( times_times_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2385_zdiff__int__split,axiom,
% 8.57/4.55      ! [P: int > $o,X2: nat,Y: nat] :
% 8.57/4.55        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X2 @ Y ) ) )
% 8.57/4.55        = ( ( ( ord_less_eq_nat @ Y @ X2 )
% 8.57/4.55           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 8.57/4.55          & ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.55           => ( P @ zero_zero_int ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2386_le__iff__diff__le__0,axiom,
% 8.57/4.55      ( ord_le3102999989581377725nteger
% 8.57/4.55      = ( ^ [A2: code_integer,B2: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2387_le__iff__diff__le__0,axiom,
% 8.57/4.55      ( ord_less_eq_rat
% 8.57/4.55      = ( ^ [A2: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2388_le__iff__diff__le__0,axiom,
% 8.57/4.55      ( ord_less_eq_int
% 8.57/4.55      = ( ^ [A2: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2389_power__int__minus__mult,axiom,
% 8.57/4.55      ! [X2: rat,N: int] :
% 8.57/4.55        ( ( ( X2 != zero_zero_rat )
% 8.57/4.55          | ( N != zero_zero_int ) )
% 8.57/4.55       => ( ( times_times_rat @ ( power_int_rat @ X2 @ ( minus_minus_int @ N @ one_one_int ) ) @ X2 )
% 8.57/4.55          = ( power_int_rat @ X2 @ N ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2390_less__iff__diff__less__0,axiom,
% 8.57/4.55      ( ord_le6747313008572928689nteger
% 8.57/4.55      = ( ^ [A2: code_integer,B2: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2391_less__iff__diff__less__0,axiom,
% 8.57/4.55      ( ord_less_rat
% 8.57/4.55      = ( ^ [A2: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2392_less__iff__diff__less__0,axiom,
% 8.57/4.55      ( ord_less_int
% 8.57/4.55      = ( ^ [A2: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2393_le__mult__floor,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.55         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2394_diff__le__eq,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 8.57/4.55        = ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2395_diff__le__eq,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.57/4.55        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2396_diff__le__eq,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.57/4.55        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2397_le__diff__eq,axiom,
% 8.57/4.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 8.57/4.55        = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2398_le__diff__eq,axiom,
% 8.57/4.55      ! [A: rat,C: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 8.57/4.55        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2399_le__diff__eq,axiom,
% 8.57/4.55      ! [A: int,C: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 8.57/4.55        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2400_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 8.57/4.55          = B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2401_le__add__diff,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2402_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 8.57/4.55          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2403_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 8.57/4.55          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2404_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 8.57/4.55          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2405_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 8.57/4.55          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2406_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 8.57/4.55          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2407_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 8.57/4.55          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2408_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 8.57/4.55          = B ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2409_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55         => ( ( ( minus_minus_nat @ B @ A )
% 8.57/4.55              = C )
% 8.57/4.55            = ( B
% 8.57/4.55              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2410_add__le__imp__le__diff,axiom,
% 8.57/4.55      ! [I: code_integer,K: code_integer,N: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N )
% 8.57/4.55       => ( ord_le3102999989581377725nteger @ I @ ( minus_8373710615458151222nteger @ N @ K ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2411_add__le__imp__le__diff,axiom,
% 8.57/4.55      ! [I: rat,K: rat,N: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 8.57/4.55       => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2412_add__le__imp__le__diff,axiom,
% 8.57/4.55      ! [I: nat,K: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 8.57/4.55       => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2413_add__le__imp__le__diff,axiom,
% 8.57/4.55      ! [I: int,K: int,N: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 8.57/4.55       => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2414_add__le__add__imp__diff__le,axiom,
% 8.57/4.55      ! [I: code_integer,K: code_integer,N: code_integer,J: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ N @ ( plus_p5714425477246183910nteger @ J @ K ) )
% 8.57/4.55         => ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I @ K ) @ N )
% 8.57/4.55           => ( ( ord_le3102999989581377725nteger @ N @ ( plus_p5714425477246183910nteger @ J @ K ) )
% 8.57/4.55             => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ N @ K ) @ J ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2415_add__le__add__imp__diff__le,axiom,
% 8.57/4.55      ! [I: rat,K: rat,N: rat,J: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 8.57/4.55       => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 8.57/4.55         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 8.57/4.55           => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 8.57/4.55             => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2416_add__le__add__imp__diff__le,axiom,
% 8.57/4.55      ! [I: nat,K: nat,N: nat,J: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 8.57/4.55       => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 8.57/4.55         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 8.57/4.55           => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 8.57/4.55             => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2417_add__le__add__imp__diff__le,axiom,
% 8.57/4.55      ! [I: int,K: int,N: int,J: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 8.57/4.55       => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 8.57/4.55         => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 8.57/4.55           => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 8.57/4.55             => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2418_mult__ceiling__le,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.55         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2419_less__diff__eq,axiom,
% 8.57/4.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 8.57/4.55        = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2420_less__diff__eq,axiom,
% 8.57/4.55      ! [A: rat,C: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 8.57/4.55        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2421_less__diff__eq,axiom,
% 8.57/4.55      ! [A: int,C: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 8.57/4.55        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2422_diff__less__eq,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 8.57/4.55        = ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2423_diff__less__eq,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.57/4.55        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2424_diff__less__eq,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.57/4.55        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2425_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ~ ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55       => ( ( plus_p5714425477246183910nteger @ B @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2426_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ~ ( ord_less_rat @ A @ B )
% 8.57/4.55       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2427_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ~ ( ord_less_nat @ A @ B )
% 8.57/4.55       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2428_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ~ ( ord_less_int @ A @ B )
% 8.57/4.55       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 8.57/4.55          = A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2429_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.57/4.55      ( minus_minus_int
% 8.57/4.55      = ( ^ [A2: int,B2: int] : ( plus_plus_int @ A2 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2430_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.57/4.55      ( minus_8373710615458151222nteger
% 8.57/4.55      = ( ^ [A2: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A2 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2431_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.57/4.55      ( minus_minus_rat
% 8.57/4.55      = ( ^ [A2: rat,B2: rat] : ( plus_plus_rat @ A2 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2432_diff__conv__add__uminus,axiom,
% 8.57/4.55      ( minus_minus_int
% 8.57/4.55      = ( ^ [A2: int,B2: int] : ( plus_plus_int @ A2 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2433_diff__conv__add__uminus,axiom,
% 8.57/4.55      ( minus_8373710615458151222nteger
% 8.57/4.55      = ( ^ [A2: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A2 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2434_diff__conv__add__uminus,axiom,
% 8.57/4.55      ( minus_minus_rat
% 8.57/4.55      = ( ^ [A2: rat,B2: rat] : ( plus_plus_rat @ A2 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2435_group__cancel_Osub2,axiom,
% 8.57/4.55      ! [B4: int,K: int,B: int,A: int] :
% 8.57/4.55        ( ( B4
% 8.57/4.55          = ( plus_plus_int @ K @ B ) )
% 8.57/4.55       => ( ( minus_minus_int @ A @ B4 )
% 8.57/4.55          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2436_group__cancel_Osub2,axiom,
% 8.57/4.55      ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 8.57/4.55        ( ( B4
% 8.57/4.55          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 8.57/4.55       => ( ( minus_8373710615458151222nteger @ A @ B4 )
% 8.57/4.55          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2437_group__cancel_Osub2,axiom,
% 8.57/4.55      ! [B4: rat,K: rat,B: rat,A: rat] :
% 8.57/4.55        ( ( B4
% 8.57/4.55          = ( plus_plus_rat @ K @ B ) )
% 8.57/4.55       => ( ( minus_minus_rat @ A @ B4 )
% 8.57/4.55          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2438_nat__mult__distrib__neg,axiom,
% 8.57/4.55      ! [Z2: int,Z6: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 8.57/4.55       => ( ( nat2 @ ( times_times_int @ Z2 @ Z6 ) )
% 8.57/4.55          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z2 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2439_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2440_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2441_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2442_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.55         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2443_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2444_zero__le__mult__iff,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.57/4.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 8.57/4.55          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2445_zero__le__mult__iff,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.57/4.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 8.57/4.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2446_zero__le__mult__iff,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 8.57/4.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 8.57/4.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.55            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2447_mult__nonneg__nonpos2,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 8.57/4.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ B @ A ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2448_mult__nonneg__nonpos2,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2449_mult__nonneg__nonpos2,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2450_mult__nonneg__nonpos2,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.55       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.57/4.55         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2451_mult__nonneg__nonpos2,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.57/4.55         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2452_mult__nonpos__nonneg,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2453_mult__nonpos__nonneg,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2454_mult__nonpos__nonneg,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2455_mult__nonpos__nonneg,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.57/4.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2456_mult__nonpos__nonneg,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.55         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2457_mult__nonneg__nonpos,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 8.57/4.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2458_mult__nonneg__nonpos,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2459_mult__nonneg__nonpos,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2460_mult__nonneg__nonpos,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.55       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.57/4.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2461_mult__nonneg__nonpos,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.57/4.55         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2462_mult__nonneg__nonneg,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.55         => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2463_mult__nonneg__nonneg,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2464_mult__nonneg__nonneg,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.55         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2465_mult__nonneg__nonneg,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.55         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2466_mult__nonneg__nonneg,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.55         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2467_split__mult__neg__le,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55            & ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural ) )
% 8.57/4.55          | ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.55            & ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B ) ) )
% 8.57/4.55       => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2468_split__mult__neg__le,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 8.57/4.55          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) )
% 8.57/4.55       => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2469_split__mult__neg__le,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 8.57/4.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 8.57/4.55       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2470_split__mult__neg__le,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.55            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 8.57/4.55          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.57/4.55            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 8.57/4.55       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2471_split__mult__neg__le,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 8.57/4.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.55            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 8.57/4.55       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2472_mult__le__0__iff,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 8.57/4.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 8.57/4.55          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2473_mult__le__0__iff,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 8.57/4.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 8.57/4.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2474_mult__le__0__iff,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 8.57/4.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 8.57/4.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.55            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2475_mult__right__mono,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2476_mult__right__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2477_mult__right__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2478_mult__right__mono,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.55         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2479_mult__right__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2480_mult__right__mono__neg,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2481_mult__right__mono__neg,axiom,
% 8.57/4.55      ! [B: rat,A: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.55       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2482_mult__right__mono__neg,axiom,
% 8.57/4.55      ! [B: int,A: int,C: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ B @ A )
% 8.57/4.55       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.57/4.55         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2483_mult__left__mono,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2484_mult__left__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2485_mult__left__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2486_mult__left__mono,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.55         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2487_mult__left__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2488_mult__nonpos__nonpos,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2489_mult__nonpos__nonpos,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.55       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2490_mult__nonpos__nonpos,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.55       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.57/4.55         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2491_mult__left__mono__neg,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2492_mult__left__mono__neg,axiom,
% 8.57/4.55      ! [B: rat,A: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.55       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2493_mult__left__mono__neg,axiom,
% 8.57/4.55      ! [B: int,A: int,C: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ B @ A )
% 8.57/4.55       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.57/4.55         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2494_split__mult__pos__le,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 8.57/4.55          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 8.57/4.55       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2495_split__mult__pos__le,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 8.57/4.55          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.55            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 8.57/4.55       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2496_split__mult__pos__le,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 8.57/4.55          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.55            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 8.57/4.55       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2497_zero__le__square,axiom,
% 8.57/4.55      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2498_zero__le__square,axiom,
% 8.57/4.55      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2499_zero__le__square,axiom,
% 8.57/4.55      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2500_mult__mono_H,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ C @ D )
% 8.57/4.55         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55             => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2501_mult__mono_H,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 8.57/4.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55             => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2502_mult__mono_H,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_rat @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2503_mult__mono_H,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_nat @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.55             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2504_mult__mono_H,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_int @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2505_mult__mono,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ C @ D )
% 8.57/4.55         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55             => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2506_mult__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 8.57/4.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55             => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2507_mult__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_rat @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2508_mult__mono,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_nat @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.55             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2509_mult__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_int @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2510_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2511_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2512_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2513_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.57/4.55         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2514_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2515_mult__less__cancel__right__disj,axiom,
% 8.57/4.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55            & ( ord_le6747313008572928689nteger @ A @ B ) )
% 8.57/4.55          | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55            & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2516_mult__less__cancel__right__disj,axiom,
% 8.57/4.55      ! [A: rat,C: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.57/4.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55            & ( ord_less_rat @ A @ B ) )
% 8.57/4.55          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.55            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2517_mult__less__cancel__right__disj,axiom,
% 8.57/4.55      ! [A: int,C: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.57/4.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55            & ( ord_less_int @ A @ B ) )
% 8.57/4.55          | ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.55            & ( ord_less_int @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2518_mult__strict__right__mono,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2519_mult__strict__right__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2520_mult__strict__right__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2521_mult__strict__right__mono,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.57/4.55         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2522_mult__strict__right__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2523_mult__strict__right__mono__neg,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2524_mult__strict__right__mono__neg,axiom,
% 8.57/4.55      ! [B: rat,A: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_rat @ B @ A )
% 8.57/4.55       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2525_mult__strict__right__mono__neg,axiom,
% 8.57/4.55      ! [B: int,A: int,C: int] :
% 8.57/4.55        ( ( ord_less_int @ B @ A )
% 8.57/4.55       => ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.55         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2526_mult__less__cancel__left__disj,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55            & ( ord_le6747313008572928689nteger @ A @ B ) )
% 8.57/4.55          | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55            & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2527_mult__less__cancel__left__disj,axiom,
% 8.57/4.55      ! [C: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55            & ( ord_less_rat @ A @ B ) )
% 8.57/4.55          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.55            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2528_mult__less__cancel__left__disj,axiom,
% 8.57/4.55      ! [C: int,A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55            & ( ord_less_int @ A @ B ) )
% 8.57/4.55          | ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.55            & ( ord_less_int @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2529_mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2530_mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2531_mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2532_mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.57/4.55         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2533_mult__strict__left__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2534_mult__strict__left__mono__neg,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2535_mult__strict__left__mono__neg,axiom,
% 8.57/4.55      ! [B: rat,A: rat,C: rat] :
% 8.57/4.55        ( ( ord_less_rat @ B @ A )
% 8.57/4.55       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2536_mult__strict__left__mono__neg,axiom,
% 8.57/4.55      ! [B: int,A: int,C: int] :
% 8.57/4.55        ( ( ord_less_int @ B @ A )
% 8.57/4.55       => ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.55         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2537_mult__less__cancel__left__pos,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.55          = ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2538_mult__less__cancel__left__pos,axiom,
% 8.57/4.55      ! [C: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.55          = ( ord_less_rat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2539_mult__less__cancel__left__pos,axiom,
% 8.57/4.55      ! [C: int,A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.55          = ( ord_less_int @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2540_mult__less__cancel__left__neg,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.55          = ( ord_le6747313008572928689nteger @ B @ A ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2541_mult__less__cancel__left__neg,axiom,
% 8.57/4.55      ! [C: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.55       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.55          = ( ord_less_rat @ B @ A ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2542_mult__less__cancel__left__neg,axiom,
% 8.57/4.55      ! [C: int,A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.55       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.55          = ( ord_less_int @ B @ A ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2543_zero__less__mult__pos2,axiom,
% 8.57/4.55      ! [B: code_natural,A: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ B @ A ) )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2544_zero__less__mult__pos2,axiom,
% 8.57/4.55      ! [B: code_integer,A: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B @ A ) )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2545_zero__less__mult__pos2,axiom,
% 8.57/4.55      ! [B: rat,A: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 8.57/4.55       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.55         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2546_zero__less__mult__pos2,axiom,
% 8.57/4.55      ! [B: nat,A: nat] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.55         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2547_zero__less__mult__pos2,axiom,
% 8.57/4.55      ! [B: int,A: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.55         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2548_zero__less__mult__pos,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ A @ B ) )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2549_zero__less__mult__pos,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2550_zero__less__mult__pos,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.57/4.55       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.55         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2551_zero__less__mult__pos,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.55         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2552_zero__less__mult__pos,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.55         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2553_zero__less__mult__iff,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.57/4.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55            & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) )
% 8.57/4.55          | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55            & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2554_zero__less__mult__iff,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.57/4.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.55            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 8.57/4.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.55            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2555_zero__less__mult__iff,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 8.57/4.55        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.55            & ( ord_less_int @ zero_zero_int @ B ) )
% 8.57/4.55          | ( ( ord_less_int @ A @ zero_zero_int )
% 8.57/4.55            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2556_mult__pos__neg2,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ B @ A ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2557_mult__pos__neg2,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2558_mult__pos__neg2,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2559_mult__pos__neg2,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.55       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.57/4.55         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2560_mult__pos__neg2,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.55         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2561_mult__pos__pos,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2562_mult__pos__pos,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2563_mult__pos__pos,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.57/4.55         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2564_mult__pos__pos,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.55         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2565_mult__pos__pos,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.55         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2566_mult__pos__neg,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2567_mult__pos__neg,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2568_mult__pos__neg,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2569_mult__pos__neg,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.55       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.57/4.55         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2570_mult__pos__neg,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.55         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2571_mult__neg__pos,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2572_mult__neg__pos,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2573_mult__neg__pos,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.57/4.55         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2574_mult__neg__pos,axiom,
% 8.57/4.55      ! [A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ zero_zero_nat )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.55         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2575_mult__neg__pos,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ zero_zero_int )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.55         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2576_mult__less__0__iff,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 8.57/4.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55            & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) )
% 8.57/4.55          | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55            & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2577_mult__less__0__iff,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 8.57/4.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.55            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 8.57/4.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.55            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2578_mult__less__0__iff,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 8.57/4.55        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.55            & ( ord_less_int @ B @ zero_zero_int ) )
% 8.57/4.55          | ( ( ord_less_int @ A @ zero_zero_int )
% 8.57/4.55            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2579_not__square__less__zero,axiom,
% 8.57/4.55      ! [A: code_integer] :
% 8.57/4.55        ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ A ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2580_not__square__less__zero,axiom,
% 8.57/4.55      ! [A: rat] :
% 8.57/4.55        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2581_not__square__less__zero,axiom,
% 8.57/4.55      ! [A: int] :
% 8.57/4.55        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2582_mult__neg__neg,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2583_mult__neg__neg,axiom,
% 8.57/4.55      ! [A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.57/4.55         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2584_mult__neg__neg,axiom,
% 8.57/4.55      ! [A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ zero_zero_int )
% 8.57/4.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.55         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2585_add__scale__eq__noteq,axiom,
% 8.57/4.55      ! [R: code_integer,A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( R != zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( ( A = B )
% 8.57/4.55            & ( C != D ) )
% 8.57/4.55         => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R @ C ) )
% 8.57/4.55           != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R @ D ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2586_add__scale__eq__noteq,axiom,
% 8.57/4.55      ! [R: rat,A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( R != zero_zero_rat )
% 8.57/4.55       => ( ( ( A = B )
% 8.57/4.55            & ( C != D ) )
% 8.57/4.55         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 8.57/4.55           != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2587_add__scale__eq__noteq,axiom,
% 8.57/4.55      ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.55        ( ( R != zero_zero_nat )
% 8.57/4.55       => ( ( ( A = B )
% 8.57/4.55            & ( C != D ) )
% 8.57/4.55         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 8.57/4.55           != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2588_add__scale__eq__noteq,axiom,
% 8.57/4.55      ! [R: int,A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( R != zero_zero_int )
% 8.57/4.55       => ( ( ( A = B )
% 8.57/4.55            & ( C != D ) )
% 8.57/4.55         => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 8.57/4.55           != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2589_less__1__mult,axiom,
% 8.57/4.55      ! [M: code_natural,N: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ M )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ N )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ M @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2590_less__1__mult,axiom,
% 8.57/4.55      ! [M: code_integer,N: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2591_less__1__mult,axiom,
% 8.57/4.55      ! [M: rat,N: rat] :
% 8.57/4.55        ( ( ord_less_rat @ one_one_rat @ M )
% 8.57/4.55       => ( ( ord_less_rat @ one_one_rat @ N )
% 8.57/4.55         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2592_less__1__mult,axiom,
% 8.57/4.55      ! [M: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_nat @ one_one_nat @ M )
% 8.57/4.55       => ( ( ord_less_nat @ one_one_nat @ N )
% 8.57/4.55         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2593_less__1__mult,axiom,
% 8.57/4.55      ! [M: int,N: int] :
% 8.57/4.55        ( ( ord_less_int @ one_one_int @ M )
% 8.57/4.55       => ( ( ord_less_int @ one_one_int @ N )
% 8.57/4.55         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2594_Suc__to__right,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( ( suc @ N )
% 8.57/4.55          = M )
% 8.57/4.55       => ( N
% 8.57/4.55          = ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2595_diff__less,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.55         => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2596_Suc__diff__Suc,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( ord_less_nat @ N @ M )
% 8.57/4.55       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 8.57/4.55          = ( minus_minus_nat @ M @ N ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2597_diff__less__Suc,axiom,
% 8.57/4.55      ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2598_square__eq__1__iff,axiom,
% 8.57/4.55      ! [X2: int] :
% 8.57/4.55        ( ( ( times_times_int @ X2 @ X2 )
% 8.57/4.55          = one_one_int )
% 8.57/4.55        = ( ( X2 = one_one_int )
% 8.57/4.55          | ( X2
% 8.57/4.55            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2599_square__eq__1__iff,axiom,
% 8.57/4.55      ! [X2: code_integer] :
% 8.57/4.55        ( ( ( times_3573771949741848930nteger @ X2 @ X2 )
% 8.57/4.55          = one_one_Code_integer )
% 8.57/4.55        = ( ( X2 = one_one_Code_integer )
% 8.57/4.55          | ( X2
% 8.57/4.55            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2600_square__eq__1__iff,axiom,
% 8.57/4.55      ! [X2: rat] :
% 8.57/4.55        ( ( ( times_times_rat @ X2 @ X2 )
% 8.57/4.55          = one_one_rat )
% 8.57/4.55        = ( ( X2 = one_one_rat )
% 8.57/4.55          | ( X2
% 8.57/4.55            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2601_Suc__diff__le,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.55       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 8.57/4.55          = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2602_diff__add__0,axiom,
% 8.57/4.55      ! [N: nat,M: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 8.57/4.55        = zero_zero_nat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2603_less__diff__iff,axiom,
% 8.57/4.55      ! [K: nat,M: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ K @ M )
% 8.57/4.55       => ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.55         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 8.57/4.55            = ( ord_less_nat @ M @ N ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2604_diff__less__mono,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_nat @ C @ A )
% 8.57/4.55         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2605_add__diff__inverse__nat,axiom,
% 8.57/4.55      ! [M: nat,N: nat] :
% 8.57/4.55        ( ~ ( ord_less_nat @ M @ N )
% 8.57/4.55       => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.55          = M ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2606_less__diff__conv,axiom,
% 8.57/4.55      ! [I: nat,J: nat,K: nat] :
% 8.57/4.55        ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 8.57/4.55        = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2607_le__diff__conv,axiom,
% 8.57/4.55      ! [J: nat,K: nat,I: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 8.57/4.55        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2608_Nat_Ole__diff__conv2,axiom,
% 8.57/4.55      ! [K: nat,J: nat,I: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ K @ J )
% 8.57/4.55       => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 8.57/4.55          = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2609_Nat_Odiff__add__assoc,axiom,
% 8.57/4.55      ! [K: nat,J: nat,I: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ K @ J )
% 8.57/4.55       => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 8.57/4.55          = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2610_Nat_Odiff__add__assoc2,axiom,
% 8.57/4.55      ! [K: nat,J: nat,I: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ K @ J )
% 8.57/4.55       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 8.57/4.55          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2611_Nat_Ole__imp__diff__is__add,axiom,
% 8.57/4.55      ! [I: nat,J: nat,K: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.55       => ( ( ( minus_minus_nat @ J @ I )
% 8.57/4.55            = K )
% 8.57/4.55          = ( J
% 8.57/4.55            = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2612_minus__int__code_I2_J,axiom,
% 8.57/4.55      ! [L: int] :
% 8.57/4.55        ( ( minus_minus_int @ zero_zero_int @ L )
% 8.57/4.55        = ( uminus_uminus_int @ L ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2613_mult__less__mono2,axiom,
% 8.57/4.55      ! [I: nat,J: nat,K: nat] :
% 8.57/4.55        ( ( ord_less_nat @ I @ J )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.55         => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2614_mult__less__mono1,axiom,
% 8.57/4.55      ! [I: nat,J: nat,K: nat] :
% 8.57/4.55        ( ( ord_less_nat @ I @ J )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.55         => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2615_int__le__induct,axiom,
% 8.57/4.55      ! [I: int,K: int,P: int > $o] :
% 8.57/4.55        ( ( ord_less_eq_int @ I @ K )
% 8.57/4.55       => ( ( P @ K )
% 8.57/4.55         => ( ! [I3: int] :
% 8.57/4.55                ( ( ord_less_eq_int @ I3 @ K )
% 8.57/4.55               => ( ( P @ I3 )
% 8.57/4.55                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 8.57/4.55           => ( P @ I ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2616_Suc__mult__less__cancel1,axiom,
% 8.57/4.55      ! [K: nat,M: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 8.57/4.55        = ( ord_less_nat @ M @ N ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2617_diff__Suc__eq__diff__pred,axiom,
% 8.57/4.55      ! [M: nat,N: nat] :
% 8.57/4.55        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 8.57/4.55        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2618_diff__nat__eq__if,axiom,
% 8.57/4.55      ! [Z6: int,Z2: int] :
% 8.57/4.55        ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 8.57/4.55         => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) )
% 8.57/4.55            = ( nat2 @ Z2 ) ) )
% 8.57/4.55        & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 8.57/4.55         => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z6 ) )
% 8.57/4.55            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z2 @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z2 @ Z6 ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2619_int__less__induct,axiom,
% 8.57/4.55      ! [I: int,K: int,P: int > $o] :
% 8.57/4.55        ( ( ord_less_int @ I @ K )
% 8.57/4.55       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 8.57/4.55         => ( ! [I3: int] :
% 8.57/4.55                ( ( ord_less_int @ I3 @ K )
% 8.57/4.55               => ( ( P @ I3 )
% 8.57/4.55                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 8.57/4.55           => ( P @ I ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2620_Suc__mult__le__cancel1,axiom,
% 8.57/4.55      ! [K: nat,M: nat,N: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 8.57/4.55        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2621_mult__Suc,axiom,
% 8.57/4.55      ! [M: nat,N: nat] :
% 8.57/4.55        ( ( times_times_nat @ ( suc @ M ) @ N )
% 8.57/4.55        = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2622_mlex__snd__decrI,axiom,
% 8.57/4.55      ! [A: nat,A5: nat,B: nat,B5: nat,N4: nat] :
% 8.57/4.55        ( ( A = A5 )
% 8.57/4.55       => ( ( ord_less_nat @ B @ B5 )
% 8.57/4.55         => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A5 @ N4 ) @ B5 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2623_mlex__fst__decrI,axiom,
% 8.57/4.55      ! [A: nat,A5: nat,B: nat,N4: nat,B5: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ A5 )
% 8.57/4.55       => ( ( ord_less_nat @ B @ N4 )
% 8.57/4.55         => ( ( ord_less_nat @ B5 @ N4 )
% 8.57/4.55           => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A5 @ N4 ) @ B5 ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2624_mlex__bound,axiom,
% 8.57/4.55      ! [A: nat,A4: nat,B: nat,N4: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ A4 )
% 8.57/4.55       => ( ( ord_less_nat @ B @ N4 )
% 8.57/4.55         => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( times_times_nat @ A4 @ N4 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2625_mlex__leI,axiom,
% 8.57/4.55      ! [A: nat,A5: nat,B: nat,B5: nat,N4: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ A5 )
% 8.57/4.55       => ( ( ord_less_eq_nat @ B @ B5 )
% 8.57/4.55         => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A5 @ N4 ) @ B5 ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2626_mult__eq__self__implies__10,axiom,
% 8.57/4.55      ! [M: nat,N: nat] :
% 8.57/4.55        ( ( M
% 8.57/4.55          = ( times_times_nat @ M @ N ) )
% 8.57/4.55       => ( ( N = one_one_nat )
% 8.57/4.55          | ( M = zero_zero_nat ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2627_zmult__zless__mono2,axiom,
% 8.57/4.55      ! [I: int,J: int,K: int] :
% 8.57/4.55        ( ( ord_less_int @ I @ J )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.55         => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2628_zmult__eq__1__iff,axiom,
% 8.57/4.55      ! [M: int,N: int] :
% 8.57/4.55        ( ( ( times_times_int @ M @ N )
% 8.57/4.55          = one_one_int )
% 8.57/4.55        = ( ( ( M = one_one_int )
% 8.57/4.55            & ( N = one_one_int ) )
% 8.57/4.55          | ( ( M
% 8.57/4.55              = ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.55            & ( N
% 8.57/4.55              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2629_pos__zmult__eq__1__iff__lemma,axiom,
% 8.57/4.55      ! [M: int,N: int] :
% 8.57/4.55        ( ( ( times_times_int @ M @ N )
% 8.57/4.55          = one_one_int )
% 8.57/4.55       => ( ( M = one_one_int )
% 8.57/4.55          | ( M
% 8.57/4.55            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2630_list_Osize_I3_J,axiom,
% 8.57/4.55      ( ( size_size_list_char @ nil_char )
% 8.57/4.55      = zero_zero_nat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2631_list_Osize_I3_J,axiom,
% 8.57/4.55      ( ( size_size_list_nat @ nil_nat )
% 8.57/4.55      = zero_zero_nat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2632_list_Osize_I3_J,axiom,
% 8.57/4.55      ( ( size_size_list_int @ nil_int )
% 8.57/4.55      = zero_zero_nat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2633_list_Osize_I3_J,axiom,
% 8.57/4.55      ( ( size_size_list_o @ nil_o )
% 8.57/4.55      = zero_zero_nat ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2634_len__greater__imp__nonempty,axiom,
% 8.57/4.55      ! [X2: nat,L: list_char] :
% 8.57/4.55        ( ( ord_less_nat @ X2 @ ( size_size_list_char @ L ) )
% 8.57/4.55       => ( L != nil_char ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2635_len__greater__imp__nonempty,axiom,
% 8.57/4.55      ! [X2: nat,L: list_nat] :
% 8.57/4.55        ( ( ord_less_nat @ X2 @ ( size_size_list_nat @ L ) )
% 8.57/4.55       => ( L != nil_nat ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2636_len__greater__imp__nonempty,axiom,
% 8.57/4.55      ! [X2: nat,L: list_int] :
% 8.57/4.55        ( ( ord_less_nat @ X2 @ ( size_size_list_int @ L ) )
% 8.57/4.55       => ( L != nil_int ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2637_len__greater__imp__nonempty,axiom,
% 8.57/4.55      ! [X2: nat,L: list_o] :
% 8.57/4.55        ( ( ord_less_nat @ X2 @ ( size_size_list_o @ L ) )
% 8.57/4.55       => ( L != nil_o ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2638_mult__less__le__imp__less,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ C @ D )
% 8.57/4.55         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55           => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55             => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2639_mult__less__le__imp__less,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ C @ D )
% 8.57/4.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55           => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2640_mult__less__le__imp__less,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_rat @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2641_mult__less__le__imp__less,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_nat @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.55           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.57/4.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2642_mult__less__le__imp__less,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_eq_int @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55           => ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2643_mult__le__less__imp__less,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ A @ B )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ C @ D )
% 8.57/4.55         => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55             => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2644_mult__le__less__imp__less,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 8.57/4.55         => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2645_mult__le__less__imp__less,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_rat @ C @ D )
% 8.57/4.55         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2646_mult__le__less__imp__less,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_nat @ C @ D )
% 8.57/4.55         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2647_mult__le__less__imp__less,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_int @ C @ D )
% 8.57/4.55         => ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2648_mult__right__le__imp__le,axiom,
% 8.57/4.55      ! [A: code_natural,C: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55         => ( ord_le1926595141338095240atural @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2649_mult__right__le__imp__le,axiom,
% 8.57/4.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2650_mult__right__le__imp__le,axiom,
% 8.57/4.55      ! [A: rat,C: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.57/4.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2651_mult__right__le__imp__le,axiom,
% 8.57/4.55      ! [A: nat,C: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.57/4.55         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2652_mult__right__le__imp__le,axiom,
% 8.57/4.55      ! [A: int,C: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2653_mult__left__le__imp__le,axiom,
% 8.57/4.55      ! [C: code_natural,A: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55         => ( ord_le1926595141338095240atural @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2654_mult__left__le__imp__le,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2655_mult__left__le__imp__le,axiom,
% 8.57/4.55      ! [C: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.55       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2656_mult__left__le__imp__le,axiom,
% 8.57/4.55      ! [C: nat,A: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.57/4.55       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.57/4.55         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2657_mult__left__le__imp__le,axiom,
% 8.57/4.55      ! [C: int,A: int,B: int] :
% 8.57/4.55        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.55       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2658_mult__le__cancel__left__pos,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.55          = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2659_mult__le__cancel__left__pos,axiom,
% 8.57/4.55      ! [C: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.55          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2660_mult__le__cancel__left__pos,axiom,
% 8.57/4.55      ! [C: int,A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.55       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.55          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2661_mult__le__cancel__left__neg,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.55          = ( ord_le3102999989581377725nteger @ B @ A ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2662_mult__le__cancel__left__neg,axiom,
% 8.57/4.55      ! [C: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.55          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2663_mult__le__cancel__left__neg,axiom,
% 8.57/4.55      ! [C: int,A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.55       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.55          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2664_mult__less__cancel__right,axiom,
% 8.57/4.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55           => ( ord_le6747313008572928689nteger @ A @ B ) )
% 8.57/4.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55           => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2665_mult__less__cancel__right,axiom,
% 8.57/4.55      ! [A: rat,C: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.57/4.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55           => ( ord_less_rat @ A @ B ) )
% 8.57/4.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.55           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2666_mult__less__cancel__right,axiom,
% 8.57/4.55      ! [A: int,C: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.57/4.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55           => ( ord_less_int @ A @ B ) )
% 8.57/4.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.57/4.55           => ( ord_less_int @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2667_mult__strict__mono_H,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ C @ D )
% 8.57/4.55         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55             => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2668_mult__strict__mono_H,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 8.57/4.55         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2669_mult__strict__mono_H,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_rat @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2670_mult__strict__mono_H,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_nat @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2671_mult__strict__mono_H,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ B )
% 8.57/4.55       => ( ( ord_less_int @ C @ D )
% 8.57/4.55         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.55           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2672_mult__right__less__imp__less,axiom,
% 8.57/4.55      ! [A: code_natural,C: code_natural,B: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 8.57/4.55       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55         => ( ord_le5570908160329646204atural @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2673_mult__right__less__imp__less,axiom,
% 8.57/4.55      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.55       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2674_mult__right__less__imp__less,axiom,
% 8.57/4.55      ! [A: rat,C: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.57/4.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2675_mult__right__less__imp__less,axiom,
% 8.57/4.55      ! [A: nat,C: nat,B: nat] :
% 8.57/4.55        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 8.57/4.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.55         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2676_mult__right__less__imp__less,axiom,
% 8.57/4.55      ! [A: int,C: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.57/4.55       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55         => ( ord_less_int @ A @ B ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2677_mult__less__cancel__left,axiom,
% 8.57/4.55      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55           => ( ord_le6747313008572928689nteger @ A @ B ) )
% 8.57/4.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.55           => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2678_mult__less__cancel__left,axiom,
% 8.57/4.55      ! [C: rat,A: rat,B: rat] :
% 8.57/4.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55           => ( ord_less_rat @ A @ B ) )
% 8.57/4.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.55           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2679_mult__less__cancel__left,axiom,
% 8.57/4.55      ! [C: int,A: int,B: int] :
% 8.57/4.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.55           => ( ord_less_int @ A @ B ) )
% 8.57/4.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.57/4.55           => ( ord_less_int @ B @ A ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2680_mult__strict__mono,axiom,
% 8.57/4.55      ! [A: code_natural,B: code_natural,C: code_natural,D: code_natural] :
% 8.57/4.55        ( ( ord_le5570908160329646204atural @ A @ B )
% 8.57/4.55       => ( ( ord_le5570908160329646204atural @ C @ D )
% 8.57/4.55         => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.55           => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.55             => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2681_mult__strict__mono,axiom,
% 8.57/4.55      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.57/4.55        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.55       => ( ( ord_le6747313008572928689nteger @ C @ D )
% 8.57/4.55         => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.55           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.55             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2682_mult__strict__mono,axiom,
% 8.57/4.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.57/4.55        ( ( ord_less_rat @ A @ B )
% 8.57/4.55       => ( ( ord_less_rat @ C @ D )
% 8.57/4.55         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.57/4.55           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.55             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2683_mult__strict__mono,axiom,
% 8.57/4.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.57/4.55        ( ( ord_less_nat @ A @ B )
% 8.57/4.55       => ( ( ord_less_nat @ C @ D )
% 8.57/4.55         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.55           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.55             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.57/4.55  
% 8.57/4.55  thf(fact_2684_mult__strict__mono,axiom,
% 8.57/4.55      ! [A: int,B: int,C: int,D: int] :
% 8.57/4.55        ( ( ord_less_int @ A @ B )
% 8.57/4.56       => ( ( ord_less_int @ C @ D )
% 8.57/4.56         => ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.56           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.56             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2685_mult__left__less__imp__less,axiom,
% 8.57/4.56      ! [C: code_natural,A: code_natural,B: code_natural] :
% 8.57/4.56        ( ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 8.57/4.56       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 8.57/4.56         => ( ord_le5570908160329646204atural @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2686_mult__left__less__imp__less,axiom,
% 8.57/4.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2687_mult__left__less__imp__less,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.56         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2688_mult__left__less__imp__less,axiom,
% 8.57/4.56      ! [C: nat,A: nat,B: nat] :
% 8.57/4.56        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.57/4.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.56         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2689_mult__left__less__imp__less,axiom,
% 8.57/4.56      ! [C: int,A: int,B: int] :
% 8.57/4.56        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.56         => ( ord_less_int @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2690_mult__le__cancel__right,axiom,
% 8.57/4.56      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ A @ B ) )
% 8.57/4.56          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2691_mult__le__cancel__right,axiom,
% 8.57/4.56      ! [A: rat,C: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ A @ B ) )
% 8.57/4.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2692_mult__le__cancel__right,axiom,
% 8.57/4.56      ! [A: int,C: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_eq_int @ A @ B ) )
% 8.57/4.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2693_mult__le__cancel__left,axiom,
% 8.57/4.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.56        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ A @ B ) )
% 8.57/4.56          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2694_mult__le__cancel__left,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ A @ B ) )
% 8.57/4.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2695_mult__le__cancel__left,axiom,
% 8.57/4.56      ! [C: int,A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_eq_int @ A @ B ) )
% 8.57/4.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2696_sum__squares__ge__zero,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2697_sum__squares__ge__zero,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2698_sum__squares__ge__zero,axiom,
% 8.57/4.56      ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2699_mult__left__le,axiom,
% 8.57/4.56      ! [C: code_natural,A: code_natural] :
% 8.57/4.56        ( ( ord_le1926595141338095240atural @ C @ one_one_Code_natural )
% 8.57/4.56       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.56         => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2700_mult__left__le,axiom,
% 8.57/4.56      ! [C: code_integer,A: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2701_mult__left__le,axiom,
% 8.57/4.56      ! [C: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2702_mult__left__le,axiom,
% 8.57/4.56      ! [C: nat,A: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 8.57/4.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.56         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2703_mult__left__le,axiom,
% 8.57/4.56      ! [C: int,A: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ C @ one_one_int )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.56         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2704_mult__le__one,axiom,
% 8.57/4.56      ! [A: code_natural,B: code_natural] :
% 8.57/4.56        ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 8.57/4.56       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.56         => ( ( ord_le1926595141338095240atural @ B @ one_one_Code_natural )
% 8.57/4.56           => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ one_one_Code_natural ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2705_mult__le__one,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.56         => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2706_mult__le__one,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.56         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2707_mult__le__one,axiom,
% 8.57/4.56      ! [A: nat,B: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.57/4.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.56         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 8.57/4.56           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2708_mult__le__one,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ A @ one_one_int )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.56         => ( ( ord_less_eq_int @ B @ one_one_int )
% 8.57/4.56           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2709_mult__right__le__one__le,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 8.57/4.56         => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X2 @ Y ) @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2710_mult__right__le__one__le,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.57/4.56         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Y ) @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2711_mult__right__le__one__le,axiom,
% 8.57/4.56      ! [X2: int,Y: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.56         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 8.57/4.56           => ( ord_less_eq_int @ ( times_times_int @ X2 @ Y ) @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2712_mult__left__le__one__le,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 8.57/4.56         => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X2 ) @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2713_mult__left__le__one__le,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.57/4.56         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X2 ) @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2714_mult__left__le__one__le,axiom,
% 8.57/4.56      ! [X2: int,Y: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.56         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 8.57/4.56           => ( ord_less_eq_int @ ( times_times_int @ Y @ X2 ) @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2715_not__sum__squares__lt__zero,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.56        ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2716_not__sum__squares__lt__zero,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2717_not__sum__squares__lt__zero,axiom,
% 8.57/4.56      ! [X2: int,Y: int] :
% 8.57/4.56        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2718_ex__less__of__nat__mult,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ? [N2: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2719_diff__Suc__less,axiom,
% 8.57/4.56      ! [N: nat,I: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.56       => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2720_nat__diff__split__asm,axiom,
% 8.57/4.56      ! [P: nat > $o,A: nat,B: nat] :
% 8.57/4.56        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 8.57/4.56        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 8.57/4.56                & ~ ( P @ zero_zero_nat ) )
% 8.57/4.56              | ? [D4: nat] :
% 8.57/4.56                  ( ( A
% 8.57/4.56                    = ( plus_plus_nat @ B @ D4 ) )
% 8.57/4.56                  & ~ ( P @ D4 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2721_nat__diff__split,axiom,
% 8.57/4.56      ! [P: nat > $o,A: nat,B: nat] :
% 8.57/4.56        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 8.57/4.56        = ( ( ( ord_less_nat @ A @ B )
% 8.57/4.56           => ( P @ zero_zero_nat ) )
% 8.57/4.56          & ! [D4: nat] :
% 8.57/4.56              ( ( A
% 8.57/4.56                = ( plus_plus_nat @ B @ D4 ) )
% 8.57/4.56             => ( P @ D4 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2722_less__diff__conv2,axiom,
% 8.57/4.56      ! [K: nat,J: nat,I: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ K @ J )
% 8.57/4.56       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 8.57/4.56          = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2723_power__int__minus__one__diff__commute,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_int @ A @ B ) )
% 8.57/4.56        = ( power_int_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_int @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2724_n__less__n__mult__m,axiom,
% 8.57/4.56      ! [N: nat,M: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.56       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.57/4.56         => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2725_n__less__m__mult__n,axiom,
% 8.57/4.56      ! [N: nat,M: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.56       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.57/4.56         => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2726_one__less__mult,axiom,
% 8.57/4.56      ! [N: nat,M: nat] :
% 8.57/4.56        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.56       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.57/4.56         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2727_int__induct,axiom,
% 8.57/4.56      ! [P: int > $o,K: int,I: int] :
% 8.57/4.56        ( ( P @ K )
% 8.57/4.56       => ( ! [I3: int] :
% 8.57/4.56              ( ( ord_less_eq_int @ K @ I3 )
% 8.57/4.56             => ( ( P @ I3 )
% 8.57/4.56               => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 8.57/4.56         => ( ! [I3: int] :
% 8.57/4.56                ( ( ord_less_eq_int @ I3 @ K )
% 8.57/4.56               => ( ( P @ I3 )
% 8.57/4.56                 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 8.57/4.56           => ( P @ I ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2728_pos__zmult__eq__1__iff,axiom,
% 8.57/4.56      ! [M: int,N: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ M )
% 8.57/4.56       => ( ( ( times_times_int @ M @ N )
% 8.57/4.56            = one_one_int )
% 8.57/4.56          = ( ( M = one_one_int )
% 8.57/4.56            & ( N = one_one_int ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2729_frac__def,axiom,
% 8.57/4.56      ( archimedean_frac_rat
% 8.57/4.56      = ( ^ [X: rat] : ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2730_dbl__dec__def,axiom,
% 8.57/4.56      ( neg_nu7757733837767384882nteger
% 8.57/4.56      = ( ^ [X: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X @ X ) @ one_one_Code_integer ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2731_dbl__dec__def,axiom,
% 8.57/4.56      ( neg_nu3179335615603231917ec_rat
% 8.57/4.56      = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2732_dbl__dec__def,axiom,
% 8.57/4.56      ( neg_nu3811975205180677377ec_int
% 8.57/4.56      = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2733_field__le__mult__one__interval,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ! [Z4: rat] :
% 8.57/4.56            ( ( ord_less_rat @ zero_zero_rat @ Z4 )
% 8.57/4.56           => ( ( ord_less_rat @ Z4 @ one_one_rat )
% 8.57/4.56             => ( ord_less_eq_rat @ ( times_times_rat @ Z4 @ X2 ) @ Y ) ) )
% 8.57/4.56       => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2734_mult__less__cancel__right2,axiom,
% 8.57/4.56      ! [A: code_integer,C: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 8.57/4.56        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 8.57/4.56          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2735_mult__less__cancel__right2,axiom,
% 8.57/4.56      ! [A: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 8.57/4.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_rat @ A @ one_one_rat ) )
% 8.57/4.56          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2736_mult__less__cancel__right2,axiom,
% 8.57/4.56      ! [A: int,C: int] :
% 8.57/4.56        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 8.57/4.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_int @ A @ one_one_int ) )
% 8.57/4.56          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2737_mult__less__cancel__right1,axiom,
% 8.57/4.56      ! [C: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 8.57/4.56          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2738_mult__less__cancel__right1,axiom,
% 8.57/4.56      ! [C: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_rat @ one_one_rat @ B ) )
% 8.57/4.56          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2739_mult__less__cancel__right1,axiom,
% 8.57/4.56      ! [C: int,B: int] :
% 8.57/4.56        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_int @ one_one_int @ B ) )
% 8.57/4.56          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2740_mult__less__cancel__left2,axiom,
% 8.57/4.56      ! [C: code_integer,A: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 8.57/4.56        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 8.57/4.56          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2741_mult__less__cancel__left2,axiom,
% 8.57/4.56      ! [C: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 8.57/4.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_rat @ A @ one_one_rat ) )
% 8.57/4.56          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2742_mult__less__cancel__left2,axiom,
% 8.57/4.56      ! [C: int,A: int] :
% 8.57/4.56        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 8.57/4.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_int @ A @ one_one_int ) )
% 8.57/4.56          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2743_mult__less__cancel__left1,axiom,
% 8.57/4.56      ! [C: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.56        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 8.57/4.56          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2744_mult__less__cancel__left1,axiom,
% 8.57/4.56      ! [C: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 8.57/4.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_rat @ one_one_rat @ B ) )
% 8.57/4.56          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2745_mult__less__cancel__left1,axiom,
% 8.57/4.56      ! [C: int,B: int] :
% 8.57/4.56        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 8.57/4.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_int @ one_one_int @ B ) )
% 8.57/4.56          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2746_mult__le__cancel__right2,axiom,
% 8.57/4.56      ! [A: code_integer,C: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 8.57/4.56        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 8.57/4.56          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2747_mult__le__cancel__right2,axiom,
% 8.57/4.56      ! [A: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 8.57/4.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2748_mult__le__cancel__right2,axiom,
% 8.57/4.56      ! [A: int,C: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 8.57/4.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_eq_int @ A @ one_one_int ) )
% 8.57/4.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2749_mult__le__cancel__right1,axiom,
% 8.57/4.56      ! [C: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 8.57/4.56          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2750_mult__le__cancel__right1,axiom,
% 8.57/4.56      ! [C: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 8.57/4.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2751_mult__le__cancel__right1,axiom,
% 8.57/4.56      ! [C: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_eq_int @ one_one_int @ B ) )
% 8.57/4.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2752_mult__le__cancel__left2,axiom,
% 8.57/4.56      ! [C: code_integer,A: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 8.57/4.56        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 8.57/4.56          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2753_mult__le__cancel__left2,axiom,
% 8.57/4.56      ! [C: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 8.57/4.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2754_mult__le__cancel__left2,axiom,
% 8.57/4.56      ! [C: int,A: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 8.57/4.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_eq_int @ A @ one_one_int ) )
% 8.57/4.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2755_mult__le__cancel__left1,axiom,
% 8.57/4.56      ! [C: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.56        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 8.57/4.56          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 8.57/4.56           => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2756_mult__le__cancel__left1,axiom,
% 8.57/4.56      ! [C: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 8.57/4.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2757_mult__le__cancel__left1,axiom,
% 8.57/4.56      ! [C: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 8.57/4.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.57/4.56           => ( ord_less_eq_int @ one_one_int @ B ) )
% 8.57/4.56          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.57/4.56           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2758_convex__bound__le,axiom,
% 8.57/4.56      ! [X2: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ X2 @ A )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 8.57/4.56         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 8.57/4.56           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 8.57/4.56             => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 8.57/4.56                  = one_one_Code_integer )
% 8.57/4.56               => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X2 ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2759_convex__bound__le,axiom,
% 8.57/4.56      ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ X2 @ A )
% 8.57/4.56       => ( ( ord_less_eq_rat @ Y @ A )
% 8.57/4.56         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 8.57/4.56           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 8.57/4.56             => ( ( ( plus_plus_rat @ U @ V )
% 8.57/4.56                  = one_one_rat )
% 8.57/4.56               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2760_convex__bound__le,axiom,
% 8.57/4.56      ! [X2: int,A: int,Y: int,U: int,V: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ X2 @ A )
% 8.57/4.56       => ( ( ord_less_eq_int @ Y @ A )
% 8.57/4.56         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.57/4.56           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 8.57/4.56             => ( ( ( plus_plus_int @ U @ V )
% 8.57/4.56                  = one_one_int )
% 8.57/4.56               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2761_nz__le__conv__less,axiom,
% 8.57/4.56      ! [K: nat,M: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.56       => ( ( ord_less_eq_nat @ K @ M )
% 8.57/4.56         => ( ord_less_nat @ ( minus_minus_nat @ K @ ( suc @ zero_zero_nat ) ) @ M ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2762_Suc__diff__eq__diff__pred,axiom,
% 8.57/4.56      ! [N: nat,M: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.56       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 8.57/4.56          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2763_Suc__pred_H,axiom,
% 8.57/4.56      ! [N: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.56       => ( N
% 8.57/4.56          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2764_frac__add,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 8.57/4.56         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 8.57/4.56            = ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 8.57/4.56        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 8.57/4.56         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 8.57/4.56            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2765_add__eq__if,axiom,
% 8.57/4.56      ( plus_plus_nat
% 8.57/4.56      = ( ^ [M2: nat,N3: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2766_Suc__n__minus__m__eq,axiom,
% 8.57/4.56      ! [M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.56       => ( ( ord_less_nat @ one_one_nat @ M )
% 8.57/4.56         => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 8.57/4.56            = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2767_foldr__length__aux,axiom,
% 8.57/4.56      ! [L: list_nat,A: nat] :
% 8.57/4.56        ( ( foldr_nat_nat
% 8.57/4.56          @ ^ [X: nat] : suc
% 8.57/4.56          @ L
% 8.57/4.56          @ A )
% 8.57/4.56        = ( plus_plus_nat @ A @ ( size_size_list_nat @ L ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2768_foldr__length__aux,axiom,
% 8.57/4.56      ! [L: list_int,A: nat] :
% 8.57/4.56        ( ( foldr_int_nat
% 8.57/4.56          @ ^ [X: int] : suc
% 8.57/4.56          @ L
% 8.57/4.56          @ A )
% 8.57/4.56        = ( plus_plus_nat @ A @ ( size_size_list_int @ L ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2769_foldr__length__aux,axiom,
% 8.57/4.56      ! [L: list_o,A: nat] :
% 8.57/4.56        ( ( foldr_o_nat
% 8.57/4.56          @ ^ [X: $o] : suc
% 8.57/4.56          @ L
% 8.57/4.56          @ A )
% 8.57/4.56        = ( plus_plus_nat @ A @ ( size_size_list_o @ L ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2770_zmult__zless__mono2__lemma,axiom,
% 8.57/4.56      ! [I: int,J: int,K: nat] :
% 8.57/4.56        ( ( ord_less_int @ I @ J )
% 8.57/4.56       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.56         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2771_power__int__add,axiom,
% 8.57/4.56      ! [X2: rat,M: int,N: int] :
% 8.57/4.56        ( ( ( X2 != zero_zero_rat )
% 8.57/4.56          | ( ( plus_plus_int @ M @ N )
% 8.57/4.56           != zero_zero_int ) )
% 8.57/4.56       => ( ( power_int_rat @ X2 @ ( plus_plus_int @ M @ N ) )
% 8.57/4.56          = ( times_times_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ X2 @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2772_unique__quotient__lemma__neg,axiom,
% 8.57/4.56      ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.57/4.56       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 8.57/4.56         => ( ( ord_less_int @ B @ R )
% 8.57/4.56           => ( ( ord_less_int @ B @ R4 )
% 8.57/4.56             => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2773_unique__quotient__lemma,axiom,
% 8.57/4.56      ! [B: int,Q5: int,R4: int,Q2: int,R: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 8.57/4.56         => ( ( ord_less_int @ R4 @ B )
% 8.57/4.56           => ( ( ord_less_int @ R @ B )
% 8.57/4.56             => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2774_zdiv__mono2__neg__lemma,axiom,
% 8.57/4.56      ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 8.57/4.56        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 8.57/4.56          = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 8.57/4.56       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) @ zero_zero_int )
% 8.57/4.56         => ( ( ord_less_int @ R @ B )
% 8.57/4.56           => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 8.57/4.56             => ( ( ord_less_int @ zero_zero_int @ B5 )
% 8.57/4.56               => ( ( ord_less_eq_int @ B5 @ B )
% 8.57/4.56                 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2775_zdiv__mono2__lemma,axiom,
% 8.57/4.56      ! [B: int,Q2: int,R: int,B5: int,Q5: int,R4: int] :
% 8.57/4.56        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 8.57/4.56          = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 8.57/4.56         => ( ( ord_less_int @ R4 @ B5 )
% 8.57/4.56           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 8.57/4.56             => ( ( ord_less_int @ zero_zero_int @ B5 )
% 8.57/4.56               => ( ( ord_less_eq_int @ B5 @ B )
% 8.57/4.56                 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2776_q__pos__lemma,axiom,
% 8.57/4.56      ! [B5: int,Q5: int,R4: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 8.57/4.56       => ( ( ord_less_int @ R4 @ B5 )
% 8.57/4.56         => ( ( ord_less_int @ zero_zero_int @ B5 )
% 8.57/4.56           => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2777_incr__mult__lemma,axiom,
% 8.57/4.56      ! [D: int,P: int > $o,K: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ D )
% 8.57/4.56       => ( ! [X3: int] :
% 8.57/4.56              ( ( P @ X3 )
% 8.57/4.56             => ( P @ ( plus_plus_int @ X3 @ D ) ) )
% 8.57/4.56         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.56           => ! [X4: int] :
% 8.57/4.56                ( ( P @ X4 )
% 8.57/4.56               => ( P @ ( plus_plus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2778_ceiling__diff__floor__le__1,axiom,
% 8.57/4.56      ! [X2: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim3151403230148437115or_rat @ X2 ) ) @ one_one_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2779_convex__bound__lt,axiom,
% 8.57/4.56      ! [X2: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ X2 @ A )
% 8.57/4.56       => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 8.57/4.56         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 8.57/4.56           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 8.57/4.56             => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 8.57/4.56                  = one_one_Code_integer )
% 8.57/4.56               => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X2 ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2780_convex__bound__lt,axiom,
% 8.57/4.56      ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
% 8.57/4.56        ( ( ord_less_rat @ X2 @ A )
% 8.57/4.56       => ( ( ord_less_rat @ Y @ A )
% 8.57/4.56         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 8.57/4.56           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 8.57/4.56             => ( ( ( plus_plus_rat @ U @ V )
% 8.57/4.56                  = one_one_rat )
% 8.57/4.56               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2781_convex__bound__lt,axiom,
% 8.57/4.56      ! [X2: int,A: int,Y: int,U: int,V: int] :
% 8.57/4.56        ( ( ord_less_int @ X2 @ A )
% 8.57/4.56       => ( ( ord_less_int @ Y @ A )
% 8.57/4.56         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.57/4.56           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 8.57/4.56             => ( ( ( plus_plus_int @ U @ V )
% 8.57/4.56                  = one_one_int )
% 8.57/4.56               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2782_ceiling__correct,axiom,
% 8.57/4.56      ! [X2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) @ one_one_rat ) @ X2 )
% 8.57/4.56        & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2783_ceiling__unique,axiom,
% 8.57/4.56      ! [Z2: int,X2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) @ X2 )
% 8.57/4.56       => ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.56         => ( ( archim2889992004027027881ng_rat @ X2 )
% 8.57/4.56            = Z2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2784_ceiling__eq__iff,axiom,
% 8.57/4.56      ! [X2: rat,A: int] :
% 8.57/4.56        ( ( ( archim2889992004027027881ng_rat @ X2 )
% 8.57/4.56          = A )
% 8.57/4.56        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X2 )
% 8.57/4.56          & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2785_ceiling__split,axiom,
% 8.57/4.56      ! [P: int > $o,T: rat] :
% 8.57/4.56        ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 8.57/4.56        = ( ! [I2: int] :
% 8.57/4.56              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) @ T )
% 8.57/4.56                & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I2 ) ) )
% 8.57/4.56             => ( P @ I2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2786_ceiling__less__iff,axiom,
% 8.57/4.56      ! [X2: rat,Z2: int] :
% 8.57/4.56        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z2 )
% 8.57/4.56        = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2787_nat__mult__le__cancel__disj,axiom,
% 8.57/4.56      ! [K: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.56        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.56         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2788_nat__mult__less__cancel__disj,axiom,
% 8.57/4.56      ! [K: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.56        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.56          & ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2789_sum__squares__gt__zero__iff,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 8.57/4.56        = ( ( X2 != zero_z3403309356797280102nteger )
% 8.57/4.56          | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2790_sum__squares__gt__zero__iff,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) )
% 8.57/4.56        = ( ( X2 != zero_zero_rat )
% 8.57/4.56          | ( Y != zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2791_sum__squares__gt__zero__iff,axiom,
% 8.57/4.56      ! [X2: int,Y: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) )
% 8.57/4.56        = ( ( X2 != zero_zero_int )
% 8.57/4.56          | ( Y != zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2792_sum__squares__le__zero__iff,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 8.57/4.56        = ( ( X2 = zero_z3403309356797280102nteger )
% 8.57/4.56          & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2793_sum__squares__le__zero__iff,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 8.57/4.56        = ( ( X2 = zero_zero_rat )
% 8.57/4.56          & ( Y = zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2794_sum__squares__le__zero__iff,axiom,
% 8.57/4.56      ! [X2: int,Y: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 8.57/4.56        = ( ( X2 = zero_zero_int )
% 8.57/4.56          & ( Y = zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2795_mult__le__cancel__iff2,axiom,
% 8.57/4.56      ! [Z2: code_integer,X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z2 )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z2 @ X2 ) @ ( times_3573771949741848930nteger @ Z2 @ Y ) )
% 8.57/4.56          = ( ord_le3102999989581377725nteger @ X2 @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2796_mult__le__cancel__iff2,axiom,
% 8.57/4.56      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X2 ) @ ( times_times_rat @ Z2 @ Y ) )
% 8.57/4.56          = ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2797_mult__le__cancel__iff2,axiom,
% 8.57/4.56      ! [Z2: int,X2: int,Y: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 8.57/4.56       => ( ( ord_less_eq_int @ ( times_times_int @ Z2 @ X2 ) @ ( times_times_int @ Z2 @ Y ) )
% 8.57/4.56          = ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2798_mult__le__cancel__iff1,axiom,
% 8.57/4.56      ! [Z2: code_integer,X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z2 )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X2 @ Z2 ) @ ( times_3573771949741848930nteger @ Y @ Z2 ) )
% 8.57/4.56          = ( ord_le3102999989581377725nteger @ X2 @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2799_mult__le__cancel__iff1,axiom,
% 8.57/4.56      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 8.57/4.56          = ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2800_mult__le__cancel__iff1,axiom,
% 8.57/4.56      ! [Z2: int,X2: int,Y: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 8.57/4.56       => ( ( ord_less_eq_int @ ( times_times_int @ X2 @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 8.57/4.56          = ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2801_nat__less__add__iff2,axiom,
% 8.57/4.56      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.56       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.57/4.56          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2802_int__distrib_I3_J,axiom,
% 8.57/4.56      ! [Z1: int,Z22: int,W2: int] :
% 8.57/4.56        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W2 )
% 8.57/4.56        = ( minus_minus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2803_int__distrib_I4_J,axiom,
% 8.57/4.56      ! [W2: int,Z1: int,Z22: int] :
% 8.57/4.56        ( ( times_times_int @ W2 @ ( minus_minus_int @ Z1 @ Z22 ) )
% 8.57/4.56        = ( minus_minus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2804_diff__mult__distrib2,axiom,
% 8.57/4.56      ! [K: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.56        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2805_diff__mult__distrib,axiom,
% 8.57/4.56      ! [M: nat,N: nat,K: nat] :
% 8.57/4.56        ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 8.57/4.56        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2806_diff__commute,axiom,
% 8.57/4.56      ! [I: nat,J: nat,K: nat] :
% 8.57/4.56        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 8.57/4.56        = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2807_nat__mult__eq__cancel__disj,axiom,
% 8.57/4.56      ! [K: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ( times_times_nat @ K @ M )
% 8.57/4.56          = ( times_times_nat @ K @ N ) )
% 8.57/4.56        = ( ( K = zero_zero_nat )
% 8.57/4.56          | ( M = N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2808_left__add__mult__distrib,axiom,
% 8.57/4.56      ! [I: nat,U: nat,J: nat,K: nat] :
% 8.57/4.56        ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 8.57/4.56        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2809_nat__mult__less__cancel1,axiom,
% 8.57/4.56      ! [K: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.56       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.56          = ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2810_nat__mult__eq__cancel1,axiom,
% 8.57/4.56      ! [K: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.56       => ( ( ( times_times_nat @ K @ M )
% 8.57/4.56            = ( times_times_nat @ K @ N ) )
% 8.57/4.56          = ( M = N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2811_nat__diff__add__eq2,axiom,
% 8.57/4.56      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.56       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.57/4.56          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2812_nat__diff__add__eq1,axiom,
% 8.57/4.56      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ J @ I )
% 8.57/4.56       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.57/4.56          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2813_nat__le__add__iff2,axiom,
% 8.57/4.56      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.56       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.57/4.56          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2814_nat__le__add__iff1,axiom,
% 8.57/4.56      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ J @ I )
% 8.57/4.56       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.57/4.56          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2815_nat__eq__add__iff2,axiom,
% 8.57/4.56      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ I @ J )
% 8.57/4.56       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 8.57/4.56            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.57/4.56          = ( M
% 8.57/4.56            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2816_nat__eq__add__iff1,axiom,
% 8.57/4.56      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ J @ I )
% 8.57/4.56       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 8.57/4.56            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.57/4.56          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 8.57/4.56            = N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2817_mult__less__iff1,axiom,
% 8.57/4.56      ! [Z2: code_integer,X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z2 )
% 8.57/4.56       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X2 @ Z2 ) @ ( times_3573771949741848930nteger @ Y @ Z2 ) )
% 8.57/4.56          = ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2818_mult__less__iff1,axiom,
% 8.57/4.56      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 8.57/4.56       => ( ( ord_less_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 8.57/4.56          = ( ord_less_rat @ X2 @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2819_mult__less__iff1,axiom,
% 8.57/4.56      ! [Z2: int,X2: int,Y: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ Z2 )
% 8.57/4.56       => ( ( ord_less_int @ ( times_times_int @ X2 @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 8.57/4.56          = ( ord_less_int @ X2 @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2820_sum__squares__eq__zero__iff,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X2 @ X2 ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 8.57/4.56          = zero_z3403309356797280102nteger )
% 8.57/4.56        = ( ( X2 = zero_z3403309356797280102nteger )
% 8.57/4.56          & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2821_sum__squares__eq__zero__iff,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) )
% 8.57/4.56          = zero_zero_rat )
% 8.57/4.56        = ( ( X2 = zero_zero_rat )
% 8.57/4.56          & ( Y = zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2822_sum__squares__eq__zero__iff,axiom,
% 8.57/4.56      ! [X2: int,Y: int] :
% 8.57/4.56        ( ( ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) )
% 8.57/4.56          = zero_zero_int )
% 8.57/4.56        = ( ( X2 = zero_zero_int )
% 8.57/4.56          & ( Y = zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2823_nat__mult__le__cancel1,axiom,
% 8.57/4.56      ! [K: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.56       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.56          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2824_nat__less__add__iff1,axiom,
% 8.57/4.56      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ J @ I )
% 8.57/4.56       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.57/4.56          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2825_nat0__intermed__int__val,axiom,
% 8.57/4.56      ! [N: nat,F: nat > int,K: int] :
% 8.57/4.56        ( ! [I3: nat] :
% 8.57/4.56            ( ( ord_less_nat @ I3 @ N )
% 8.57/4.56           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 8.57/4.56       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 8.57/4.56         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 8.57/4.56           => ? [I3: nat] :
% 8.57/4.56                ( ( ord_less_eq_nat @ I3 @ N )
% 8.57/4.56                & ( ( F @ I3 )
% 8.57/4.56                  = K ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2826_slice__len,axiom,
% 8.57/4.56      ! [From: nat,To: nat,Xs: list_nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ From @ To )
% 8.57/4.56       => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 8.57/4.56         => ( ( size_size_list_nat @ ( slice_nat @ From @ To @ Xs ) )
% 8.57/4.56            = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2827_slice__len,axiom,
% 8.57/4.56      ! [From: nat,To: nat,Xs: list_int] :
% 8.57/4.56        ( ( ord_less_eq_nat @ From @ To )
% 8.57/4.56       => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 8.57/4.56         => ( ( size_size_list_int @ ( slice_int @ From @ To @ Xs ) )
% 8.57/4.56            = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2828_slice__len,axiom,
% 8.57/4.56      ! [From: nat,To: nat,Xs: list_o] :
% 8.57/4.56        ( ( ord_less_eq_nat @ From @ To )
% 8.57/4.56       => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 8.57/4.56         => ( ( size_size_list_o @ ( slice_o @ From @ To @ Xs ) )
% 8.57/4.56            = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2829_ceiling__divide__lower,axiom,
% 8.57/4.56      ! [Q2: rat,P3: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 8.57/4.56       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P3 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) @ P3 ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2830_floor__divide__upper,axiom,
% 8.57/4.56      ! [Q2: rat,P3: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 8.57/4.56       => ( ord_less_rat @ P3 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P3 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2831_nat__ivt__aux,axiom,
% 8.57/4.56      ! [N: nat,F: nat > int,K: int] :
% 8.57/4.56        ( ! [I3: nat] :
% 8.57/4.56            ( ( ord_less_nat @ I3 @ N )
% 8.57/4.56           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 8.57/4.56       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 8.57/4.56         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 8.57/4.56           => ? [I3: nat] :
% 8.57/4.56                ( ( ord_less_eq_nat @ I3 @ N )
% 8.57/4.56                & ( ( F @ I3 )
% 8.57/4.56                  = K ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2832_mult__ceiling__le__Ints,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56         => ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_18347121197199848620nteger @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2833_mult__ceiling__le__Ints,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2834_mult__ceiling__le__Ints,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2835_le__mult__floor__Ints,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56         => ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_18347121197199848620nteger @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2836_le__mult__floor__Ints,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56         => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2837_le__mult__floor__Ints,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56         => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2838_frac__unique__iff,axiom,
% 8.57/4.56      ! [X2: rat,A: rat] :
% 8.57/4.56        ( ( ( archimedean_frac_rat @ X2 )
% 8.57/4.56          = A )
% 8.57/4.56        = ( ( member_rat @ ( minus_minus_rat @ X2 @ A ) @ ring_1_Ints_rat )
% 8.57/4.56          & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56          & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2839_abs__idempotent,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 8.57/4.56        = ( abs_abs_int @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2840_abs__idempotent,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 8.57/4.56        = ( abs_abs_Code_integer @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2841_abs__idempotent,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 8.57/4.56        = ( abs_abs_rat @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2842_divide__eq__0__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ( divide_divide_rat @ A @ B )
% 8.57/4.56          = zero_zero_rat )
% 8.57/4.56        = ( ( A = zero_zero_rat )
% 8.57/4.56          | ( B = zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2843_divide__cancel__left,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ( divide_divide_rat @ C @ A )
% 8.57/4.56          = ( divide_divide_rat @ C @ B ) )
% 8.57/4.56        = ( ( C = zero_zero_rat )
% 8.57/4.56          | ( A = B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2844_divide__cancel__right,axiom,
% 8.57/4.56      ! [A: rat,C: rat,B: rat] :
% 8.57/4.56        ( ( ( divide_divide_rat @ A @ C )
% 8.57/4.56          = ( divide_divide_rat @ B @ C ) )
% 8.57/4.56        = ( ( C = zero_zero_rat )
% 8.57/4.56          | ( A = B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2845_division__ring__divide__zero,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 8.57/4.56        = zero_zero_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2846_div__0,axiom,
% 8.57/4.56      ! [A: nat] :
% 8.57/4.56        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 8.57/4.56        = zero_zero_nat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2847_div__0,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( divide_divide_int @ zero_zero_int @ A )
% 8.57/4.56        = zero_zero_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2848_div__0,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.56        = zero_z3403309356797280102nteger ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2849_div__0,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 8.57/4.56        = zero_zero_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2850_div__0,axiom,
% 8.57/4.56      ! [A: code_natural] :
% 8.57/4.56        ( ( divide5121882707175180666atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.56        = zero_z2226904508553997617atural ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2851_div__by__0,axiom,
% 8.57/4.56      ! [A: nat] :
% 8.57/4.56        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 8.57/4.56        = zero_zero_nat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2852_div__by__0,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( divide_divide_int @ A @ zero_zero_int )
% 8.57/4.56        = zero_zero_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2853_div__by__0,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.56        = zero_z3403309356797280102nteger ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2854_div__by__0,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 8.57/4.56        = zero_zero_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2855_div__by__0,axiom,
% 8.57/4.56      ! [A: code_natural] :
% 8.57/4.56        ( ( divide5121882707175180666atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.56        = zero_z2226904508553997617atural ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2856_div__by__1,axiom,
% 8.57/4.56      ! [A: nat] :
% 8.57/4.56        ( ( divide_divide_nat @ A @ one_one_nat )
% 8.57/4.56        = A ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2857_div__by__1,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( divide_divide_int @ A @ one_one_int )
% 8.57/4.56        = A ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2858_div__by__1,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 8.57/4.56        = A ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2859_div__by__1,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( divide_divide_rat @ A @ one_one_rat )
% 8.57/4.56        = A ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2860_div__by__1,axiom,
% 8.57/4.56      ! [A: code_natural] :
% 8.57/4.56        ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 8.57/4.56        = A ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2861_abs__0__eq,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( zero_zero_int
% 8.57/4.56          = ( abs_abs_int @ A ) )
% 8.57/4.56        = ( A = zero_zero_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2862_abs__0__eq,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( zero_z3403309356797280102nteger
% 8.57/4.56          = ( abs_abs_Code_integer @ A ) )
% 8.57/4.56        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2863_abs__0__eq,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( zero_zero_rat
% 8.57/4.56          = ( abs_abs_rat @ A ) )
% 8.57/4.56        = ( A = zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2864_abs__eq__0,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( ( abs_abs_int @ A )
% 8.57/4.56          = zero_zero_int )
% 8.57/4.56        = ( A = zero_zero_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2865_abs__eq__0,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( ( abs_abs_Code_integer @ A )
% 8.57/4.56          = zero_z3403309356797280102nteger )
% 8.57/4.56        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2866_abs__eq__0,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ( abs_abs_rat @ A )
% 8.57/4.56          = zero_zero_rat )
% 8.57/4.56        = ( A = zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2867_abs__zero,axiom,
% 8.57/4.56      ( ( abs_abs_int @ zero_zero_int )
% 8.57/4.56      = zero_zero_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2868_abs__zero,axiom,
% 8.57/4.56      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 8.57/4.56      = zero_z3403309356797280102nteger ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2869_abs__zero,axiom,
% 8.57/4.56      ( ( abs_abs_rat @ zero_zero_rat )
% 8.57/4.56      = zero_zero_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2870_abs__0,axiom,
% 8.57/4.56      ( ( abs_abs_int @ zero_zero_int )
% 8.57/4.56      = zero_zero_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2871_abs__0,axiom,
% 8.57/4.56      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 8.57/4.56      = zero_z3403309356797280102nteger ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2872_abs__0,axiom,
% 8.57/4.56      ( ( abs_abs_rat @ zero_zero_rat )
% 8.57/4.56      = zero_zero_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2873_abs__add__abs,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 8.57/4.56        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2874_abs__add__abs,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 8.57/4.56        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2875_abs__add__abs,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 8.57/4.56        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2876_abs__1,axiom,
% 8.57/4.56      ( ( abs_abs_int @ one_one_int )
% 8.57/4.56      = one_one_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2877_abs__1,axiom,
% 8.57/4.56      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 8.57/4.56      = one_one_Code_integer ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2878_abs__1,axiom,
% 8.57/4.56      ( ( abs_abs_rat @ one_one_rat )
% 8.57/4.56      = one_one_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2879_nat__mult__div__cancel__disj,axiom,
% 8.57/4.56      ! [K: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ( K = zero_zero_nat )
% 8.57/4.56         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.56            = zero_zero_nat ) )
% 8.57/4.56        & ( ( K != zero_zero_nat )
% 8.57/4.56         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.56            = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2880_abs__minus__cancel,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 8.57/4.56        = ( abs_abs_int @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2881_abs__minus__cancel,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 8.57/4.56        = ( abs_abs_Code_integer @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2882_abs__minus__cancel,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 8.57/4.56        = ( abs_abs_rat @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2883_abs__of__nat,axiom,
% 8.57/4.56      ! [N: nat] :
% 8.57/4.56        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.56        = ( semiri1314217659103216013at_int @ N ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2884_abs__of__nat,axiom,
% 8.57/4.56      ! [N: nat] :
% 8.57/4.56        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 8.57/4.56        = ( semiri4939895301339042750nteger @ N ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2885_abs__of__nat,axiom,
% 8.57/4.56      ! [N: nat] :
% 8.57/4.56        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 8.57/4.56        = ( semiri681578069525770553at_rat @ N ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2886_slice__eq__bounds__empty,axiom,
% 8.57/4.56      ! [I: nat,Xs: list_int] :
% 8.57/4.56        ( ( slice_int @ I @ I @ Xs )
% 8.57/4.56        = nil_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2887_slice__eq__bounds__empty,axiom,
% 8.57/4.56      ! [I: nat,Xs: list_nat] :
% 8.57/4.56        ( ( slice_nat @ I @ I @ Xs )
% 8.57/4.56        = nil_nat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2888_slice__eq__bounds__empty,axiom,
% 8.57/4.56      ! [I: nat,Xs: list_char] :
% 8.57/4.56        ( ( slice_char @ I @ I @ Xs )
% 8.57/4.56        = nil_char ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2889_slice__Nil,axiom,
% 8.57/4.56      ! [Begin: nat,End: nat] :
% 8.57/4.56        ( ( slice_int @ Begin @ End @ nil_int )
% 8.57/4.56        = nil_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2890_slice__Nil,axiom,
% 8.57/4.56      ! [Begin: nat,End: nat] :
% 8.57/4.56        ( ( slice_nat @ Begin @ End @ nil_nat )
% 8.57/4.56        = nil_nat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2891_slice__Nil,axiom,
% 8.57/4.56      ! [Begin: nat,End: nat] :
% 8.57/4.56        ( ( slice_char @ Begin @ End @ nil_char )
% 8.57/4.56        = nil_char ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2892_nonzero__mult__div__cancel__left,axiom,
% 8.57/4.56      ! [A: nat,B: nat] :
% 8.57/4.56        ( ( A != zero_zero_nat )
% 8.57/4.56       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 8.57/4.56          = B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2893_nonzero__mult__div__cancel__left,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( A != zero_zero_int )
% 8.57/4.56       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 8.57/4.56          = B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2894_nonzero__mult__div__cancel__left,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( A != zero_z3403309356797280102nteger )
% 8.57/4.56       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 8.57/4.56          = B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2895_nonzero__mult__div__cancel__left,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( A != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 8.57/4.56          = B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2896_nonzero__mult__div__cancel__left,axiom,
% 8.57/4.56      ! [A: code_natural,B: code_natural] :
% 8.57/4.56        ( ( A != zero_z2226904508553997617atural )
% 8.57/4.56       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ A )
% 8.57/4.56          = B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2897_nonzero__mult__div__cancel__right,axiom,
% 8.57/4.56      ! [B: nat,A: nat] :
% 8.57/4.56        ( ( B != zero_zero_nat )
% 8.57/4.56       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2898_nonzero__mult__div__cancel__right,axiom,
% 8.57/4.56      ! [B: int,A: int] :
% 8.57/4.56        ( ( B != zero_zero_int )
% 8.57/4.56       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2899_nonzero__mult__div__cancel__right,axiom,
% 8.57/4.56      ! [B: code_integer,A: code_integer] :
% 8.57/4.56        ( ( B != zero_z3403309356797280102nteger )
% 8.57/4.56       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2900_nonzero__mult__div__cancel__right,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( B != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2901_nonzero__mult__div__cancel__right,axiom,
% 8.57/4.56      ! [B: code_natural,A: code_natural] :
% 8.57/4.56        ( ( B != zero_z2226904508553997617atural )
% 8.57/4.56       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2902_nonzero__mult__divide__mult__cancel__right2,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( C != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2903_nonzero__mult__divide__mult__cancel__right,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( C != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.57/4.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2904_nonzero__mult__divide__mult__cancel__left2,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( C != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 8.57/4.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2905_nonzero__mult__divide__mult__cancel__left,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( C != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2906_mult__divide__mult__cancel__left__if,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ( C = zero_zero_rat )
% 8.57/4.56         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.56            = zero_zero_rat ) )
% 8.57/4.56        & ( ( C != zero_zero_rat )
% 8.57/4.56         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.57/4.56            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2907_zero__eq__1__divide__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( zero_zero_rat
% 8.57/4.56          = ( divide_divide_rat @ one_one_rat @ A ) )
% 8.57/4.56        = ( A = zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2908_one__divide__eq__0__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 8.57/4.56          = zero_zero_rat )
% 8.57/4.56        = ( A = zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2909_eq__divide__eq__1,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( one_one_rat
% 8.57/4.56          = ( divide_divide_rat @ B @ A ) )
% 8.57/4.56        = ( ( A != zero_zero_rat )
% 8.57/4.56          & ( A = B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2910_divide__eq__eq__1,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( ( divide_divide_rat @ B @ A )
% 8.57/4.56          = one_one_rat )
% 8.57/4.56        = ( ( A != zero_zero_rat )
% 8.57/4.56          & ( A = B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2911_divide__self__if,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ( A = zero_zero_rat )
% 8.57/4.56         => ( ( divide_divide_rat @ A @ A )
% 8.57/4.56            = zero_zero_rat ) )
% 8.57/4.56        & ( ( A != zero_zero_rat )
% 8.57/4.56         => ( ( divide_divide_rat @ A @ A )
% 8.57/4.56            = one_one_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2912_divide__self,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( A != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ A @ A )
% 8.57/4.56          = one_one_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2913_one__eq__divide__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( one_one_rat
% 8.57/4.56          = ( divide_divide_rat @ A @ B ) )
% 8.57/4.56        = ( ( B != zero_zero_rat )
% 8.57/4.56          & ( A = B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2914_divide__eq__1__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ( divide_divide_rat @ A @ B )
% 8.57/4.56          = one_one_rat )
% 8.57/4.56        = ( ( B != zero_zero_rat )
% 8.57/4.56          & ( A = B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2915_div__self,axiom,
% 8.57/4.56      ! [A: nat] :
% 8.57/4.56        ( ( A != zero_zero_nat )
% 8.57/4.56       => ( ( divide_divide_nat @ A @ A )
% 8.57/4.56          = one_one_nat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2916_div__self,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( A != zero_zero_int )
% 8.57/4.56       => ( ( divide_divide_int @ A @ A )
% 8.57/4.56          = one_one_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2917_div__self,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( A != zero_z3403309356797280102nteger )
% 8.57/4.56       => ( ( divide6298287555418463151nteger @ A @ A )
% 8.57/4.56          = one_one_Code_integer ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2918_div__self,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( A != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ A @ A )
% 8.57/4.56          = one_one_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2919_div__self,axiom,
% 8.57/4.56      ! [A: code_natural] :
% 8.57/4.56        ( ( A != zero_z2226904508553997617atural )
% 8.57/4.56       => ( ( divide5121882707175180666atural @ A @ A )
% 8.57/4.56          = one_one_Code_natural ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2920_abs__le__zero__iff,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 8.57/4.56        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2921_abs__le__zero__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 8.57/4.56        = ( A = zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2922_abs__le__zero__iff,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 8.57/4.56        = ( A = zero_zero_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2923_abs__le__self__iff,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 8.57/4.56        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2924_abs__le__self__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 8.57/4.56        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2925_abs__le__self__iff,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 8.57/4.56        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2926_abs__of__nonneg,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.56       => ( ( abs_abs_Code_integer @ A )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2927_abs__of__nonneg,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( abs_abs_rat @ A )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2928_abs__of__nonneg,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.56       => ( ( abs_abs_int @ A )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2929_zero__less__abs__iff,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 8.57/4.56        = ( A != zero_z3403309356797280102nteger ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2930_zero__less__abs__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 8.57/4.56        = ( A != zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2931_zero__less__abs__iff,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 8.57/4.56        = ( A != zero_zero_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2932_divide__minus1,axiom,
% 8.57/4.56      ! [X2: rat] :
% 8.57/4.56        ( ( divide_divide_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.57/4.56        = ( uminus_uminus_rat @ X2 ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2933_abs__neg__one,axiom,
% 8.57/4.56      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.56      = one_one_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2934_abs__neg__one,axiom,
% 8.57/4.56      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.57/4.56      = one_one_Code_integer ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2935_abs__neg__one,axiom,
% 8.57/4.56      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.57/4.56      = one_one_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2936_abs__power__int__minus,axiom,
% 8.57/4.56      ! [A: rat,N: int] :
% 8.57/4.56        ( ( abs_abs_rat @ ( power_int_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 8.57/4.56        = ( abs_abs_rat @ ( power_int_rat @ A @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2937_of__int__abs,axiom,
% 8.57/4.56      ! [X2: int] :
% 8.57/4.56        ( ( ring_18347121197199848620nteger @ ( abs_abs_int @ X2 ) )
% 8.57/4.56        = ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2938_of__int__abs,axiom,
% 8.57/4.56      ! [X2: int] :
% 8.57/4.56        ( ( ring_1_of_int_rat @ ( abs_abs_int @ X2 ) )
% 8.57/4.56        = ( abs_abs_rat @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2939_of__int__abs,axiom,
% 8.57/4.56      ! [X2: int] :
% 8.57/4.56        ( ( ring_1_of_int_int @ ( abs_abs_int @ X2 ) )
% 8.57/4.56        = ( abs_abs_int @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2940_frac__eq__0__iff,axiom,
% 8.57/4.56      ! [X2: rat] :
% 8.57/4.56        ( ( ( archimedean_frac_rat @ X2 )
% 8.57/4.56          = zero_zero_rat )
% 8.57/4.56        = ( member_rat @ X2 @ ring_1_Ints_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2941_slice__complete,axiom,
% 8.57/4.56      ! [Xs: list_nat] :
% 8.57/4.56        ( ( slice_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) @ Xs )
% 8.57/4.56        = Xs ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2942_slice__complete,axiom,
% 8.57/4.56      ! [Xs: list_int] :
% 8.57/4.56        ( ( slice_int @ zero_zero_nat @ ( size_size_list_int @ Xs ) @ Xs )
% 8.57/4.56        = Xs ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2943_slice__complete,axiom,
% 8.57/4.56      ! [Xs: list_o] :
% 8.57/4.56        ( ( slice_o @ zero_zero_nat @ ( size_size_list_o @ Xs ) @ Xs )
% 8.57/4.56        = Xs ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2944_zero__le__divide__1__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 8.57/4.56        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2945_divide__le__0__1__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 8.57/4.56        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2946_zero__less__divide__1__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 8.57/4.56        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2947_less__divide__eq__1__pos,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.57/4.56          = ( ord_less_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2948_less__divide__eq__1__neg,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.57/4.56          = ( ord_less_rat @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2949_divide__less__eq__1__pos,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.57/4.56          = ( ord_less_rat @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2950_divide__less__eq__1__neg,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.57/4.56          = ( ord_less_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2951_divide__less__0__1__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 8.57/4.56        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2952_nonzero__divide__mult__cancel__right,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( B != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 8.57/4.56          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2953_nonzero__divide__mult__cancel__left,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( A != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 8.57/4.56          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2954_abs__of__nonpos,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.56       => ( ( abs_abs_Code_integer @ A )
% 8.57/4.56          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2955_abs__of__nonpos,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.56       => ( ( abs_abs_rat @ A )
% 8.57/4.56          = ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2956_abs__of__nonpos,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.56       => ( ( abs_abs_int @ A )
% 8.57/4.56          = ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2957_zero__le__divide__abs__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 8.57/4.56        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56          | ( B = zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2958_divide__le__0__abs__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 8.57/4.56        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.56          | ( B = zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2959_zabs__less__one__iff,axiom,
% 8.57/4.56      ! [Z2: int] :
% 8.57/4.56        ( ( ord_less_int @ ( abs_abs_int @ Z2 ) @ one_one_int )
% 8.57/4.56        = ( Z2 = zero_zero_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2960_floor__add2,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 8.57/4.56          | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 8.57/4.56       => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 8.57/4.56          = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2961_frac__gt__0__iff,axiom,
% 8.57/4.56      ! [X2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) )
% 8.57/4.56        = ( ~ ( member_rat @ X2 @ ring_1_Ints_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2962_le__divide__eq__1__pos,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.57/4.56          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2963_le__divide__eq__1__neg,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.57/4.56          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2964_divide__le__eq__1__pos,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.57/4.56          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2965_divide__le__eq__1__neg,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.57/4.56          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2966_div__abs__eq__div__nat,axiom,
% 8.57/4.56      ! [K: int,L: int] :
% 8.57/4.56        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 8.57/4.56        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2967_zdiv__int,axiom,
% 8.57/4.56      ! [A: nat,B: nat] :
% 8.57/4.56        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 8.57/4.56        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2968_Ints__abs,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( member_int @ A @ ring_1_Ints_int )
% 8.57/4.56       => ( member_int @ ( abs_abs_int @ A ) @ ring_1_Ints_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2969_Ints__abs,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( member_Code_integer @ ( abs_abs_Code_integer @ A ) @ ring_11222124179247155820nteger ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2970_Ints__abs,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56       => ( member_rat @ ( abs_abs_rat @ A ) @ ring_1_Ints_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2971_nonzero__abs__divide,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( B != zero_zero_rat )
% 8.57/4.56       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 8.57/4.56          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2972_abs__div__pos,axiom,
% 8.57/4.56      ! [Y: rat,X2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.57/4.56       => ( ( divide_divide_rat @ ( abs_abs_rat @ X2 ) @ Y )
% 8.57/4.56          = ( abs_abs_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2973_abs__ge__self,axiom,
% 8.57/4.56      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2974_abs__ge__self,axiom,
% 8.57/4.56      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2975_abs__ge__self,axiom,
% 8.57/4.56      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2976_abs__le__D1,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.57/4.56       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2977_abs__le__D1,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 8.57/4.56       => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2978_abs__le__D1,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 8.57/4.56       => ( ord_less_eq_int @ A @ B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2979_abs__eq__0__iff,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( ( abs_abs_int @ A )
% 8.57/4.56          = zero_zero_int )
% 8.57/4.56        = ( A = zero_zero_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2980_abs__eq__0__iff,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( ( abs_abs_Code_integer @ A )
% 8.57/4.56          = zero_z3403309356797280102nteger )
% 8.57/4.56        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2981_abs__eq__0__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ( abs_abs_rat @ A )
% 8.57/4.56          = zero_zero_rat )
% 8.57/4.56        = ( A = zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2982_floor__divide__of__int__eq,axiom,
% 8.57/4.56      ! [K: int,L: int] :
% 8.57/4.56        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 8.57/4.56        = ( divide_divide_int @ K @ L ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2983_abs__one,axiom,
% 8.57/4.56      ( ( abs_abs_int @ one_one_int )
% 8.57/4.56      = one_one_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2984_abs__one,axiom,
% 8.57/4.56      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 8.57/4.56      = one_one_Code_integer ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2985_abs__one,axiom,
% 8.57/4.56      ( ( abs_abs_rat @ one_one_rat )
% 8.57/4.56      = one_one_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2986_abs__minus__commute,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.57/4.56        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2987_abs__minus__commute,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 8.57/4.56        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2988_abs__minus__commute,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 8.57/4.56        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2989_add__divide__distrib,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.57/4.56        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2990_power__int__abs,axiom,
% 8.57/4.56      ! [A: rat,N: int] :
% 8.57/4.56        ( ( abs_abs_rat @ ( power_int_rat @ A @ N ) )
% 8.57/4.56        = ( power_int_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2991_nat__div__as__int,axiom,
% 8.57/4.56      ( divide_divide_nat
% 8.57/4.56      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2992_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2993_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: nat,Y: nat,C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.57/4.56          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2994_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: nat,Y: nat,C: nat,A: nat,B: nat] :
% 8.57/4.56        ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.57/4.56          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2995_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: nat,Y: nat,C: int,A: int,B: int] :
% 8.57/4.56        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.57/4.56          = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2996_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2997_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: int,Y: int,C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.57/4.56          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2998_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: int,Y: int,C: nat,A: nat,B: nat] :
% 8.57/4.56        ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.57/4.56          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_2999_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: int,Y: int,C: int,A: int,B: int] :
% 8.57/4.56        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.57/4.56          = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3000_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer,C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3001_distrib__right__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X2 @ Y ) @ C )
% 8.57/4.56       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.57/4.56          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3002_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.56        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3003_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: nat,Y: nat,A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.56          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3004_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: nat,Y: nat,A: nat,B: nat,C: nat] :
% 8.57/4.56        ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 8.57/4.56          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3005_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: nat,Y: nat,A: int,B: int,C: int] :
% 8.57/4.56        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.57/4.56          = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3006_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.56        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3007_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: int,Y: int,A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.56          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3008_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: int,Y: int,A: nat,B: nat,C: nat] :
% 8.57/4.56        ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 8.57/4.56          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3009_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: int,Y: int,A: int,B: int,C: int] :
% 8.57/4.56        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.57/4.56          = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3010_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer,A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.56        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3011_distrib__left__NO__MATCH,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X2 @ Y ) @ A )
% 8.57/4.56       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.56          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3012_power__int__divide__distrib,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat,M: int] :
% 8.57/4.56        ( ( power_int_rat @ ( divide_divide_rat @ X2 @ Y ) @ M )
% 8.57/4.56        = ( divide_divide_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ Y @ M ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3013_Ints__0,axiom,
% 8.57/4.56      member_int @ zero_zero_int @ ring_1_Ints_int ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3014_Ints__0,axiom,
% 8.57/4.56      member_Code_integer @ zero_z3403309356797280102nteger @ ring_11222124179247155820nteger ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3015_Ints__0,axiom,
% 8.57/4.56      member_rat @ zero_zero_rat @ ring_1_Ints_rat ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3016_Ints__add,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ( member_Code_integer @ B @ ring_11222124179247155820nteger )
% 8.57/4.56         => ( member_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) @ ring_11222124179247155820nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3017_Ints__add,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56       => ( ( member_rat @ B @ ring_1_Ints_rat )
% 8.57/4.56         => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3018_Ints__add,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( member_int @ A @ ring_1_Ints_int )
% 8.57/4.56       => ( ( member_int @ B @ ring_1_Ints_int )
% 8.57/4.56         => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3019_Ints__mult,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ( member_Code_integer @ B @ ring_11222124179247155820nteger )
% 8.57/4.56         => ( member_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ring_11222124179247155820nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3020_Ints__mult,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56       => ( ( member_rat @ B @ ring_1_Ints_rat )
% 8.57/4.56         => ( member_rat @ ( times_times_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3021_Ints__mult,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( member_int @ A @ ring_1_Ints_int )
% 8.57/4.56       => ( ( member_int @ B @ ring_1_Ints_int )
% 8.57/4.56         => ( member_int @ ( times_times_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3022_Ints__1,axiom,
% 8.57/4.56      member_int @ one_one_int @ ring_1_Ints_int ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3023_Ints__1,axiom,
% 8.57/4.56      member_Code_integer @ one_one_Code_integer @ ring_11222124179247155820nteger ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3024_Ints__1,axiom,
% 8.57/4.56      member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3025_Ints__diff,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ( member_Code_integer @ B @ ring_11222124179247155820nteger )
% 8.57/4.56         => ( member_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) @ ring_11222124179247155820nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3026_Ints__diff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56       => ( ( member_rat @ B @ ring_1_Ints_rat )
% 8.57/4.56         => ( member_rat @ ( minus_minus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3027_Ints__diff,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( member_int @ A @ ring_1_Ints_int )
% 8.57/4.56       => ( ( member_int @ B @ ring_1_Ints_int )
% 8.57/4.56         => ( member_int @ ( minus_minus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3028_minus__in__Ints__iff,axiom,
% 8.57/4.56      ! [X2: int] :
% 8.57/4.56        ( ( member_int @ ( uminus_uminus_int @ X2 ) @ ring_1_Ints_int )
% 8.57/4.56        = ( member_int @ X2 @ ring_1_Ints_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3029_minus__in__Ints__iff,axiom,
% 8.57/4.56      ! [X2: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ ( uminus1351360451143612070nteger @ X2 ) @ ring_11222124179247155820nteger )
% 8.57/4.56        = ( member_Code_integer @ X2 @ ring_11222124179247155820nteger ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3030_minus__in__Ints__iff,axiom,
% 8.57/4.56      ! [X2: rat] :
% 8.57/4.56        ( ( member_rat @ ( uminus_uminus_rat @ X2 ) @ ring_1_Ints_rat )
% 8.57/4.56        = ( member_rat @ X2 @ ring_1_Ints_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3031_Ints__minus,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( member_int @ A @ ring_1_Ints_int )
% 8.57/4.56       => ( member_int @ ( uminus_uminus_int @ A ) @ ring_1_Ints_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3032_Ints__minus,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( member_Code_integer @ ( uminus1351360451143612070nteger @ A ) @ ring_11222124179247155820nteger ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3033_Ints__minus,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56       => ( member_rat @ ( uminus_uminus_rat @ A ) @ ring_1_Ints_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3034_Ints__of__nat,axiom,
% 8.57/4.56      ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ring_1_Ints_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3035_Ints__of__nat,axiom,
% 8.57/4.56      ! [N: nat] : ( member_Code_integer @ ( semiri4939895301339042750nteger @ N ) @ ring_11222124179247155820nteger ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3036_Ints__of__nat,axiom,
% 8.57/4.56      ! [N: nat] : ( member_rat @ ( semiri681578069525770553at_rat @ N ) @ ring_1_Ints_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3037_Ints__of__int,axiom,
% 8.57/4.56      ! [Z2: int] : ( member_Code_integer @ ( ring_18347121197199848620nteger @ Z2 ) @ ring_11222124179247155820nteger ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3038_Ints__of__int,axiom,
% 8.57/4.56      ! [Z2: int] : ( member_rat @ ( ring_1_of_int_rat @ Z2 ) @ ring_1_Ints_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3039_Ints__of__int,axiom,
% 8.57/4.56      ! [Z2: int] : ( member_int @ ( ring_1_of_int_int @ Z2 ) @ ring_1_Ints_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3040_Ints__induct,axiom,
% 8.57/4.56      ! [Q2: code_integer,P: code_integer > $o] :
% 8.57/4.56        ( ( member_Code_integer @ Q2 @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ! [Z4: int] : ( P @ ( ring_18347121197199848620nteger @ Z4 ) )
% 8.57/4.56         => ( P @ Q2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3041_Ints__induct,axiom,
% 8.57/4.56      ! [Q2: rat,P: rat > $o] :
% 8.57/4.56        ( ( member_rat @ Q2 @ ring_1_Ints_rat )
% 8.57/4.56       => ( ! [Z4: int] : ( P @ ( ring_1_of_int_rat @ Z4 ) )
% 8.57/4.56         => ( P @ Q2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3042_Ints__induct,axiom,
% 8.57/4.56      ! [Q2: int,P: int > $o] :
% 8.57/4.56        ( ( member_int @ Q2 @ ring_1_Ints_int )
% 8.57/4.56       => ( ! [Z4: int] : ( P @ ( ring_1_of_int_int @ Z4 ) )
% 8.57/4.56         => ( P @ Q2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3043_Ints__cases,axiom,
% 8.57/4.56      ! [Q2: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ Q2 @ ring_11222124179247155820nteger )
% 8.57/4.56       => ~ ! [Z4: int] :
% 8.57/4.56              ( Q2
% 8.57/4.56             != ( ring_18347121197199848620nteger @ Z4 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3044_Ints__cases,axiom,
% 8.57/4.56      ! [Q2: rat] :
% 8.57/4.56        ( ( member_rat @ Q2 @ ring_1_Ints_rat )
% 8.57/4.56       => ~ ! [Z4: int] :
% 8.57/4.56              ( Q2
% 8.57/4.56             != ( ring_1_of_int_rat @ Z4 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3045_Ints__cases,axiom,
% 8.57/4.56      ! [Q2: int] :
% 8.57/4.56        ( ( member_int @ Q2 @ ring_1_Ints_int )
% 8.57/4.56       => ~ ! [Z4: int] :
% 8.57/4.56              ( Q2
% 8.57/4.56             != ( ring_1_of_int_int @ Z4 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3046_Ints__nonzero__abs__ge1,axiom,
% 8.57/4.56      ! [X2: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ( X2 != zero_z3403309356797280102nteger )
% 8.57/4.56         => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3047_Ints__nonzero__abs__ge1,axiom,
% 8.57/4.56      ! [X2: rat] :
% 8.57/4.56        ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 8.57/4.56       => ( ( X2 != zero_zero_rat )
% 8.57/4.56         => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3048_Ints__nonzero__abs__ge1,axiom,
% 8.57/4.56      ! [X2: int] :
% 8.57/4.56        ( ( member_int @ X2 @ ring_1_Ints_int )
% 8.57/4.56       => ( ( X2 != zero_zero_int )
% 8.57/4.56         => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3049_Ints__nonzero__abs__less1,axiom,
% 8.57/4.56      ! [X2: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer )
% 8.57/4.56         => ( X2 = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3050_Ints__nonzero__abs__less1,axiom,
% 8.57/4.56      ! [X2: rat] :
% 8.57/4.56        ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 8.57/4.56       => ( ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat )
% 8.57/4.56         => ( X2 = zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3051_Ints__nonzero__abs__less1,axiom,
% 8.57/4.56      ! [X2: int] :
% 8.57/4.56        ( ( member_int @ X2 @ ring_1_Ints_int )
% 8.57/4.56       => ( ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int )
% 8.57/4.56         => ( X2 = zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3052_Ints__eq__abs__less1,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 8.57/4.56         => ( ( X2 = Y )
% 8.57/4.56            = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3053_Ints__eq__abs__less1,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 8.57/4.56       => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 8.57/4.56         => ( ( X2 = Y )
% 8.57/4.56            = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ Y ) ) @ one_one_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3054_Ints__eq__abs__less1,axiom,
% 8.57/4.56      ! [X2: int,Y: int] :
% 8.57/4.56        ( ( member_int @ X2 @ ring_1_Ints_int )
% 8.57/4.56       => ( ( member_int @ Y @ ring_1_Ints_int )
% 8.57/4.56         => ( ( X2 = Y )
% 8.57/4.56            = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Y ) ) @ one_one_int ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3055_floor__divide__of__nat__eq,axiom,
% 8.57/4.56      ! [M: nat,N: nat] :
% 8.57/4.56        ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 8.57/4.56        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3056_abs__ge__zero,axiom,
% 8.57/4.56      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3057_abs__ge__zero,axiom,
% 8.57/4.56      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3058_abs__ge__zero,axiom,
% 8.57/4.56      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3059_abs__not__less__zero,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3060_abs__not__less__zero,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3061_abs__not__less__zero,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3062_abs__of__pos,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.56       => ( ( abs_abs_Code_integer @ A )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3063_abs__of__pos,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56       => ( ( abs_abs_rat @ A )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3064_abs__of__pos,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.56       => ( ( abs_abs_int @ A )
% 8.57/4.56          = A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3065_abs__triangle__ineq,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3066_abs__triangle__ineq,axiom,
% 8.57/4.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3067_abs__triangle__ineq,axiom,
% 8.57/4.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3068_abs__triangle__ineq2__sym,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3069_abs__triangle__ineq2__sym,axiom,
% 8.57/4.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3070_abs__triangle__ineq2__sym,axiom,
% 8.57/4.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3071_abs__triangle__ineq3,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3072_abs__triangle__ineq3,axiom,
% 8.57/4.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3073_abs__triangle__ineq3,axiom,
% 8.57/4.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3074_abs__triangle__ineq2,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3075_abs__triangle__ineq2,axiom,
% 8.57/4.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3076_abs__triangle__ineq2,axiom,
% 8.57/4.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3077_abs__leI,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.57/4.56         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3078_abs__leI,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.57/4.56         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3079_abs__leI,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.56       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 8.57/4.56         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3080_abs__le__D2,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.57/4.56       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3081_abs__le__D2,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 8.57/4.56       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3082_abs__le__D2,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 8.57/4.56       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3083_abs__le__iff,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.57/4.56        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.56          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3084_abs__le__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 8.57/4.56        = ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.56          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3085_abs__le__iff,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 8.57/4.56        = ( ( ord_less_eq_int @ A @ B )
% 8.57/4.56          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3086_abs__ge__minus__self,axiom,
% 8.57/4.56      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3087_abs__ge__minus__self,axiom,
% 8.57/4.56      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3088_abs__ge__minus__self,axiom,
% 8.57/4.56      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3089_divide__right__mono__neg,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.56       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3090_divide__nonpos__nonpos,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 8.57/4.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3091_divide__nonpos__nonneg,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.57/4.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3092_divide__nonneg__nonpos,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 8.57/4.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3093_divide__nonneg__nonneg,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.57/4.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3094_zero__le__divide__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 8.57/4.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 8.57/4.56          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.56            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3095_divide__right__mono,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3096_divide__le__0__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 8.57/4.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 8.57/4.56          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.57/4.56            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3097_divide__neg__neg,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.57/4.56         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3098_divide__neg__pos,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.57/4.56         => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3099_divide__pos__neg,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.57/4.56         => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3100_divide__pos__pos,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.57/4.56         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3101_divide__less__0__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 8.57/4.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3102_divide__less__cancel,axiom,
% 8.57/4.56      ! [A: rat,C: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_rat @ A @ B ) )
% 8.57/4.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_rat @ B @ A ) )
% 8.57/4.56          & ( C != zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3103_zero__less__divide__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 8.57/4.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3104_divide__strict__right__mono,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ B )
% 8.57/4.56       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3105_divide__strict__right__mono__neg,axiom,
% 8.57/4.56      ! [B: rat,A: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_rat @ B @ A )
% 8.57/4.56       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3106_nonzero__eq__divide__eq,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( C != zero_zero_rat )
% 8.57/4.56       => ( ( A
% 8.57/4.56            = ( divide_divide_rat @ B @ C ) )
% 8.57/4.56          = ( ( times_times_rat @ A @ C )
% 8.57/4.56            = B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3107_nonzero__divide__eq__eq,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( C != zero_zero_rat )
% 8.57/4.56       => ( ( ( divide_divide_rat @ B @ C )
% 8.57/4.56            = A )
% 8.57/4.56          = ( B
% 8.57/4.56            = ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3108_eq__divide__imp,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( C != zero_zero_rat )
% 8.57/4.56       => ( ( ( times_times_rat @ A @ C )
% 8.57/4.56            = B )
% 8.57/4.56         => ( A
% 8.57/4.56            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3109_divide__eq__imp,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( C != zero_zero_rat )
% 8.57/4.56       => ( ( B
% 8.57/4.56            = ( times_times_rat @ A @ C ) )
% 8.57/4.56         => ( ( divide_divide_rat @ B @ C )
% 8.57/4.56            = A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3110_eq__divide__eq,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( A
% 8.57/4.56          = ( divide_divide_rat @ B @ C ) )
% 8.57/4.56        = ( ( ( C != zero_zero_rat )
% 8.57/4.56           => ( ( times_times_rat @ A @ C )
% 8.57/4.56              = B ) )
% 8.57/4.56          & ( ( C = zero_zero_rat )
% 8.57/4.56           => ( A = zero_zero_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3111_divide__eq__eq,axiom,
% 8.57/4.56      ! [B: rat,C: rat,A: rat] :
% 8.57/4.56        ( ( ( divide_divide_rat @ B @ C )
% 8.57/4.56          = A )
% 8.57/4.56        = ( ( ( C != zero_zero_rat )
% 8.57/4.56           => ( B
% 8.57/4.56              = ( times_times_rat @ A @ C ) ) )
% 8.57/4.56          & ( ( C = zero_zero_rat )
% 8.57/4.56           => ( A = zero_zero_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3112_frac__eq__eq,axiom,
% 8.57/4.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 8.57/4.56        ( ( Y != zero_zero_rat )
% 8.57/4.56       => ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( ( divide_divide_rat @ X2 @ Y )
% 8.57/4.56              = ( divide_divide_rat @ W2 @ Z2 ) )
% 8.57/4.56            = ( ( times_times_rat @ X2 @ Z2 )
% 8.57/4.56              = ( times_times_rat @ W2 @ Y ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3113_right__inverse__eq,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( B != zero_zero_rat )
% 8.57/4.56       => ( ( ( divide_divide_rat @ A @ B )
% 8.57/4.56            = one_one_rat )
% 8.57/4.56          = ( A = B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3114_nonzero__minus__divide__right,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( B != zero_zero_rat )
% 8.57/4.56       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 8.57/4.56          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3115_nonzero__minus__divide__divide,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( B != zero_zero_rat )
% 8.57/4.56       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 8.57/4.56          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3116_abs__zmult__eq__1,axiom,
% 8.57/4.56      ! [M: int,N: int] :
% 8.57/4.56        ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 8.57/4.56          = one_one_int )
% 8.57/4.56       => ( ( abs_abs_int @ M )
% 8.57/4.56          = one_one_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3117_div__neg__pos__less0,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_int @ A @ zero_zero_int )
% 8.57/4.56       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.56         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3118_neg__imp__zdiv__neg__iff,axiom,
% 8.57/4.56      ! [B: int,A: int] :
% 8.57/4.56        ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.56       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 8.57/4.56          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3119_pos__imp__zdiv__neg__iff,axiom,
% 8.57/4.56      ! [B: int,A: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.56       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 8.57/4.56          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3120_power__int__one__over,axiom,
% 8.57/4.56      ! [X2: rat,N: int] :
% 8.57/4.56        ( ( power_int_rat @ ( divide_divide_rat @ one_one_rat @ X2 ) @ N )
% 8.57/4.56        = ( divide_divide_rat @ one_one_rat @ ( power_int_rat @ X2 @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3121_Ints__double__eq__0__iff,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( member_int @ A @ ring_1_Ints_int )
% 8.57/4.56       => ( ( ( plus_plus_int @ A @ A )
% 8.57/4.56            = zero_zero_int )
% 8.57/4.56          = ( A = zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3122_Ints__double__eq__0__iff,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 8.57/4.56            = zero_z3403309356797280102nteger )
% 8.57/4.56          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3123_Ints__double__eq__0__iff,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56       => ( ( ( plus_plus_rat @ A @ A )
% 8.57/4.56            = zero_zero_rat )
% 8.57/4.56          = ( A = zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3124_dense__eq0__I,axiom,
% 8.57/4.56      ! [X2: rat] :
% 8.57/4.56        ( ! [E3: rat] :
% 8.57/4.56            ( ( ord_less_rat @ zero_zero_rat @ E3 )
% 8.57/4.56           => ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ E3 ) )
% 8.57/4.56       => ( X2 = zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3125_abs__eq__mult,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.56            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 8.57/4.56          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.56            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 8.57/4.56       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.57/4.56          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3126_abs__eq__mult,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 8.57/4.56          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.56            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 8.57/4.56       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 8.57/4.56          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3127_abs__eq__mult,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.56            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 8.57/4.56          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.56            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 8.57/4.56       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 8.57/4.56          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3128_abs__mult__pos,axiom,
% 8.57/4.56      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 8.57/4.56       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X2 )
% 8.57/4.56          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3129_abs__mult__pos,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X2 )
% 8.57/4.56          = ( abs_abs_rat @ ( times_times_rat @ Y @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3130_abs__mult__pos,axiom,
% 8.57/4.56      ! [X2: int,Y: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.56       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X2 )
% 8.57/4.56          = ( abs_abs_int @ ( times_times_int @ Y @ X2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3131_abs__minus__le__zero,axiom,
% 8.57/4.56      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3132_abs__minus__le__zero,axiom,
% 8.57/4.56      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3133_abs__minus__le__zero,axiom,
% 8.57/4.56      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3134_eq__abs__iff_H,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( A
% 8.57/4.56          = ( abs_abs_Code_integer @ B ) )
% 8.57/4.56        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.56          & ( ( B = A )
% 8.57/4.56            | ( B
% 8.57/4.56              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3135_eq__abs__iff_H,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( A
% 8.57/4.56          = ( abs_abs_rat @ B ) )
% 8.57/4.56        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.56          & ( ( B = A )
% 8.57/4.56            | ( B
% 8.57/4.56              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3136_eq__abs__iff_H,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( A
% 8.57/4.56          = ( abs_abs_int @ B ) )
% 8.57/4.56        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.56          & ( ( B = A )
% 8.57/4.56            | ( B
% 8.57/4.56              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3137_abs__eq__iff_H,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ( abs_abs_Code_integer @ A )
% 8.57/4.56          = B )
% 8.57/4.56        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.56          & ( ( A = B )
% 8.57/4.56            | ( A
% 8.57/4.56              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3138_abs__eq__iff_H,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ( abs_abs_rat @ A )
% 8.57/4.56          = B )
% 8.57/4.56        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.56          & ( ( A = B )
% 8.57/4.56            | ( A
% 8.57/4.56              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3139_abs__eq__iff_H,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ( abs_abs_int @ A )
% 8.57/4.56          = B )
% 8.57/4.56        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.56          & ( ( A = B )
% 8.57/4.56            | ( A
% 8.57/4.56              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3140_abs__diff__triangle__ineq,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3141_abs__diff__triangle__ineq,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3142_abs__diff__triangle__ineq,axiom,
% 8.57/4.56      ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3143_abs__triangle__ineq4,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3144_abs__triangle__ineq4,axiom,
% 8.57/4.56      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3145_abs__triangle__ineq4,axiom,
% 8.57/4.56      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3146_abs__diff__le__iff,axiom,
% 8.57/4.56      ! [X2: code_integer,A: code_integer,R: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 8.57/4.56        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 8.57/4.56          & ( ord_le3102999989581377725nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3147_abs__diff__le__iff,axiom,
% 8.57/4.56      ! [X2: rat,A: rat,R: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 8.57/4.56        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 8.57/4.56          & ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3148_abs__diff__le__iff,axiom,
% 8.57/4.56      ! [X2: int,A: int,R: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 8.57/4.56        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 8.57/4.56          & ( ord_less_eq_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3149_abs__if,axiom,
% 8.57/4.56      ( abs_abs_int
% 8.57/4.56      = ( ^ [A2: int] : ( if_int @ ( ord_less_int @ A2 @ zero_zero_int ) @ ( uminus_uminus_int @ A2 ) @ A2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3150_abs__if,axiom,
% 8.57/4.56      ( abs_abs_Code_integer
% 8.57/4.56      = ( ^ [A2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A2 ) @ A2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3151_abs__if,axiom,
% 8.57/4.56      ( abs_abs_rat
% 8.57/4.56      = ( ^ [A2: rat] : ( if_rat @ ( ord_less_rat @ A2 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A2 ) @ A2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3152_abs__of__neg,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( ord_less_int @ A @ zero_zero_int )
% 8.57/4.56       => ( ( abs_abs_int @ A )
% 8.57/4.56          = ( uminus_uminus_int @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3153_abs__of__neg,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.56       => ( ( abs_abs_Code_integer @ A )
% 8.57/4.56          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3154_abs__of__neg,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56       => ( ( abs_abs_rat @ A )
% 8.57/4.56          = ( uminus_uminus_rat @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3155_abs__if__raw,axiom,
% 8.57/4.56      ( abs_abs_int
% 8.57/4.56      = ( ^ [A2: int] : ( if_int @ ( ord_less_int @ A2 @ zero_zero_int ) @ ( uminus_uminus_int @ A2 ) @ A2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3156_abs__if__raw,axiom,
% 8.57/4.56      ( abs_abs_Code_integer
% 8.57/4.56      = ( ^ [A2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A2 ) @ A2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3157_abs__if__raw,axiom,
% 8.57/4.56      ( abs_abs_rat
% 8.57/4.56      = ( ^ [A2: rat] : ( if_rat @ ( ord_less_rat @ A2 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A2 ) @ A2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3158_abs__diff__less__iff,axiom,
% 8.57/4.56      ! [X2: code_integer,A: code_integer,R: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 8.57/4.56        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 8.57/4.56          & ( ord_le6747313008572928689nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3159_abs__diff__less__iff,axiom,
% 8.57/4.56      ! [X2: rat,A: rat,R: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 8.57/4.56        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 8.57/4.56          & ( ord_less_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3160_abs__diff__less__iff,axiom,
% 8.57/4.56      ! [X2: int,A: int,R: int] :
% 8.57/4.56        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 8.57/4.56        = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 8.57/4.56          & ( ord_less_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3161_div__positive,axiom,
% 8.57/4.56      ! [B: code_integer,A: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.56       => ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.57/4.56         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3162_div__positive,axiom,
% 8.57/4.56      ! [B: nat,A: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.56       => ( ( ord_less_eq_nat @ B @ A )
% 8.57/4.56         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3163_div__positive,axiom,
% 8.57/4.56      ! [B: int,A: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.56       => ( ( ord_less_eq_int @ B @ A )
% 8.57/4.56         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3164_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 8.57/4.56      ! [A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.56       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.56         => ( ( divide6298287555418463151nteger @ A @ B )
% 8.57/4.56            = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3165_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 8.57/4.56      ! [A: nat,B: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.56       => ( ( ord_less_nat @ A @ B )
% 8.57/4.56         => ( ( divide_divide_nat @ A @ B )
% 8.57/4.56            = zero_zero_nat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3166_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.56       => ( ( ord_less_int @ A @ B )
% 8.57/4.56         => ( ( divide_divide_int @ A @ B )
% 8.57/4.56            = zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3167_divide__nonpos__pos,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.57/4.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3168_divide__nonpos__neg,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.57/4.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3169_divide__nonneg__pos,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.57/4.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3170_divide__nonneg__neg,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.57/4.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3171_divide__le__cancel,axiom,
% 8.57/4.56      ! [A: rat,C: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ A @ B ) )
% 8.57/4.56          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3172_frac__less2,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat,W2: rat,Z2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.56         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 8.57/4.56           => ( ( ord_less_rat @ W2 @ Z2 )
% 8.57/4.56             => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3173_frac__less,axiom,
% 8.57/4.56      ! [X2: rat,Y: rat,W2: rat,Z2: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 8.57/4.56       => ( ( ord_less_rat @ X2 @ Y )
% 8.57/4.56         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 8.57/4.56           => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 8.57/4.56             => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3174_frac__le,axiom,
% 8.57/4.56      ! [Y: rat,X2: rat,W2: rat,Z2: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.57/4.56       => ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.56         => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 8.57/4.56           => ( ( ord_less_eq_rat @ W2 @ Z2 )
% 8.57/4.56             => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3175_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 8.57/4.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.56       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.56          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3176_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 8.57/4.56      ! [C: nat,A: nat,B: nat] :
% 8.57/4.56        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.56       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 8.57/4.56          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3177_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 8.57/4.56      ! [C: int,A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.56       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 8.57/4.56          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3178_divide__less__eq,axiom,
% 8.57/4.56      ! [B: rat,C: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 8.57/4.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 8.57/4.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3179_less__divide__eq,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 8.57/4.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 8.57/4.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3180_neg__divide__less__eq,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.57/4.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3181_neg__less__divide__eq,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.56          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3182_pos__divide__less__eq,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.57/4.56          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3183_pos__less__divide__eq,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3184_mult__imp__div__pos__less,axiom,
% 8.57/4.56      ! [Y: rat,X2: rat,Z2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.57/4.56       => ( ( ord_less_rat @ X2 @ ( times_times_rat @ Z2 @ Y ) )
% 8.57/4.56         => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3185_mult__imp__less__div__pos,axiom,
% 8.57/4.56      ! [Y: rat,Z2: rat,X2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.57/4.56       => ( ( ord_less_rat @ ( times_times_rat @ Z2 @ Y ) @ X2 )
% 8.57/4.56         => ( ord_less_rat @ Z2 @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3186_divide__strict__left__mono,axiom,
% 8.57/4.56      ! [B: rat,A: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_rat @ B @ A )
% 8.57/4.56       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.57/4.56           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3187_divide__strict__left__mono__neg,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ B )
% 8.57/4.56       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.57/4.56           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3188_less__divide__eq__1,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56            & ( ord_less_rat @ A @ B ) )
% 8.57/4.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3189_divide__less__eq__1,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56            & ( ord_less_rat @ B @ A ) )
% 8.57/4.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56            & ( ord_less_rat @ A @ B ) )
% 8.57/4.56          | ( A = zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3190_add__divide__eq__if__simps_I2_J,axiom,
% 8.57/4.56      ! [Z2: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ( Z2 = zero_zero_rat )
% 8.57/4.56         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 8.57/4.56            = B ) )
% 8.57/4.56        & ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 8.57/4.56            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3191_add__divide__eq__if__simps_I1_J,axiom,
% 8.57/4.56      ! [Z2: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ( Z2 = zero_zero_rat )
% 8.57/4.56         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 8.57/4.56            = A ) )
% 8.57/4.56        & ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 8.57/4.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3192_add__frac__eq,axiom,
% 8.57/4.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 8.57/4.56        ( ( Y != zero_zero_rat )
% 8.57/4.56       => ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 8.57/4.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3193_add__frac__num,axiom,
% 8.57/4.56      ! [Y: rat,X2: rat,Z2: rat] :
% 8.57/4.56        ( ( Y != zero_zero_rat )
% 8.57/4.56       => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z2 )
% 8.57/4.56          = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3194_add__num__frac,axiom,
% 8.57/4.56      ! [Y: rat,Z2: rat,X2: rat] :
% 8.57/4.56        ( ( Y != zero_zero_rat )
% 8.57/4.56       => ( ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ X2 @ Y ) )
% 8.57/4.56          = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3195_add__divide__eq__iff,axiom,
% 8.57/4.56      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.56        ( ( Z2 != zero_zero_rat )
% 8.57/4.56       => ( ( plus_plus_rat @ X2 @ ( divide_divide_rat @ Y @ Z2 ) )
% 8.57/4.56          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3196_divide__add__eq__iff,axiom,
% 8.57/4.56      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.56        ( ( Z2 != zero_zero_rat )
% 8.57/4.56       => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ Y )
% 8.57/4.56          = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3197_divide__diff__eq__iff,axiom,
% 8.57/4.56      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.56        ( ( Z2 != zero_zero_rat )
% 8.57/4.56       => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Z2 ) @ Y )
% 8.57/4.56          = ( divide_divide_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3198_diff__divide__eq__iff,axiom,
% 8.57/4.56      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.56        ( ( Z2 != zero_zero_rat )
% 8.57/4.56       => ( ( minus_minus_rat @ X2 @ ( divide_divide_rat @ Y @ Z2 ) )
% 8.57/4.56          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3199_diff__frac__eq,axiom,
% 8.57/4.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 8.57/4.56        ( ( Y != zero_zero_rat )
% 8.57/4.56       => ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 8.57/4.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3200_add__divide__eq__if__simps_I4_J,axiom,
% 8.57/4.56      ! [Z2: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ( Z2 = zero_zero_rat )
% 8.57/4.56         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 8.57/4.56            = A ) )
% 8.57/4.56        & ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 8.57/4.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3201_less__half__sum,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ B )
% 8.57/4.56       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3202_gt__half__sum,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ B )
% 8.57/4.56       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3203_eq__minus__divide__eq,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( A
% 8.57/4.56          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.57/4.56        = ( ( ( C != zero_zero_rat )
% 8.57/4.56           => ( ( times_times_rat @ A @ C )
% 8.57/4.56              = ( uminus_uminus_rat @ B ) ) )
% 8.57/4.56          & ( ( C = zero_zero_rat )
% 8.57/4.56           => ( A = zero_zero_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3204_minus__divide__eq__eq,axiom,
% 8.57/4.56      ! [B: rat,C: rat,A: rat] :
% 8.57/4.56        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.56          = A )
% 8.57/4.56        = ( ( ( C != zero_zero_rat )
% 8.57/4.56           => ( ( uminus_uminus_rat @ B )
% 8.57/4.56              = ( times_times_rat @ A @ C ) ) )
% 8.57/4.56          & ( ( C = zero_zero_rat )
% 8.57/4.56           => ( A = zero_zero_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3205_nonzero__neg__divide__eq__eq,axiom,
% 8.57/4.56      ! [B: rat,A: rat,C: rat] :
% 8.57/4.56        ( ( B != zero_zero_rat )
% 8.57/4.56       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 8.57/4.56            = C )
% 8.57/4.56          = ( ( uminus_uminus_rat @ A )
% 8.57/4.56            = ( times_times_rat @ C @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3206_nonzero__neg__divide__eq__eq2,axiom,
% 8.57/4.56      ! [B: rat,C: rat,A: rat] :
% 8.57/4.56        ( ( B != zero_zero_rat )
% 8.57/4.56       => ( ( C
% 8.57/4.56            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 8.57/4.56          = ( ( times_times_rat @ C @ B )
% 8.57/4.56            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3207_divide__eq__minus__1__iff,axiom,
% 8.57/4.56      ! [A: rat,B: rat] :
% 8.57/4.56        ( ( ( divide_divide_rat @ A @ B )
% 8.57/4.56          = ( uminus_uminus_rat @ one_one_rat ) )
% 8.57/4.56        = ( ( B != zero_zero_rat )
% 8.57/4.56          & ( A
% 8.57/4.56            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3208_zabs__def,axiom,
% 8.57/4.56      ( abs_abs_int
% 8.57/4.56      = ( ^ [I2: int] : ( if_int @ ( ord_less_int @ I2 @ zero_zero_int ) @ ( uminus_uminus_int @ I2 ) @ I2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3209_nat__mult__div__cancel1,axiom,
% 8.57/4.56      ! [K: nat,M: nat,N: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.56       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.56          = ( divide_divide_nat @ M @ N ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3210_nat__abs__mult__distrib,axiom,
% 8.57/4.56      ! [W2: int,Z2: int] :
% 8.57/4.56        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W2 @ Z2 ) ) )
% 8.57/4.56        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W2 ) ) @ ( nat2 @ ( abs_abs_int @ Z2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3211_nonneg1__imp__zdiv__pos__iff,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.56       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 8.57/4.56          = ( ( ord_less_eq_int @ B @ A )
% 8.57/4.56            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3212_pos__imp__zdiv__nonneg__iff,axiom,
% 8.57/4.56      ! [B: int,A: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 8.57/4.56          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3213_neg__imp__zdiv__nonneg__iff,axiom,
% 8.57/4.56      ! [B: int,A: int] :
% 8.57/4.56        ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 8.57/4.56          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3214_pos__imp__zdiv__pos__iff,axiom,
% 8.57/4.56      ! [K: int,I: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.56       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 8.57/4.56          = ( ord_less_eq_int @ K @ I ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3215_div__nonpos__pos__le0,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.56       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.56         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3216_div__nonneg__neg__le0,axiom,
% 8.57/4.56      ! [A: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.56       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.56         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3217_div__positive__int,axiom,
% 8.57/4.56      ! [L: int,K: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ L @ K )
% 8.57/4.56       => ( ( ord_less_int @ zero_zero_int @ L )
% 8.57/4.56         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3218_div__int__pos__iff,axiom,
% 8.57/4.56      ! [K: int,L: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 8.57/4.56        = ( ( K = zero_zero_int )
% 8.57/4.56          | ( L = zero_zero_int )
% 8.57/4.56          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.56            & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 8.57/4.56          | ( ( ord_less_int @ K @ zero_zero_int )
% 8.57/4.56            & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3219_zdiv__mono2__neg,axiom,
% 8.57/4.56      ! [A: int,B5: int,B: int] :
% 8.57/4.56        ( ( ord_less_int @ A @ zero_zero_int )
% 8.57/4.56       => ( ( ord_less_int @ zero_zero_int @ B5 )
% 8.57/4.56         => ( ( ord_less_eq_int @ B5 @ B )
% 8.57/4.56           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B5 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3220_zdiv__mono1__neg,axiom,
% 8.57/4.56      ! [A: int,A5: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ A @ A5 )
% 8.57/4.56       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.56         => ( ord_less_eq_int @ ( divide_divide_int @ A5 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3221_zdiv__eq__0__iff,axiom,
% 8.57/4.56      ! [I: int,K: int] :
% 8.57/4.56        ( ( ( divide_divide_int @ I @ K )
% 8.57/4.56          = zero_zero_int )
% 8.57/4.56        = ( ( K = zero_zero_int )
% 8.57/4.56          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 8.57/4.56            & ( ord_less_int @ I @ K ) )
% 8.57/4.56          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 8.57/4.56            & ( ord_less_int @ K @ I ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3222_zdiv__mono2,axiom,
% 8.57/4.56      ! [A: int,B5: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.56       => ( ( ord_less_int @ zero_zero_int @ B5 )
% 8.57/4.56         => ( ( ord_less_eq_int @ B5 @ B )
% 8.57/4.56           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B5 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3223_zdiv__mono1,axiom,
% 8.57/4.56      ! [A: int,A5: int,B: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ A @ A5 )
% 8.57/4.56       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.56         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A5 @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3224_int__div__less__self,axiom,
% 8.57/4.56      ! [X2: int,K: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ X2 )
% 8.57/4.56       => ( ( ord_less_int @ one_one_int @ K )
% 8.57/4.56         => ( ord_less_int @ ( divide_divide_int @ X2 @ K ) @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3225_power__int__diff,axiom,
% 8.57/4.56      ! [X2: rat,M: int,N: int] :
% 8.57/4.56        ( ( ( X2 != zero_zero_rat )
% 8.57/4.56          | ( M != N ) )
% 8.57/4.56       => ( ( power_int_rat @ X2 @ ( minus_minus_int @ M @ N ) )
% 8.57/4.56          = ( divide_divide_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ X2 @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3226_Ints__odd__nonzero,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( member_int @ A @ ring_1_Ints_int )
% 8.57/4.56       => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 8.57/4.56         != zero_zero_int ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3227_Ints__odd__nonzero,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A )
% 8.57/4.56         != zero_z3403309356797280102nteger ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3228_Ints__odd__nonzero,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56       => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 8.57/4.56         != zero_zero_rat ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3229_abs__add__one__gt__zero,axiom,
% 8.57/4.56      ! [X2: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3230_abs__add__one__gt__zero,axiom,
% 8.57/4.56      ! [X2: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3231_abs__add__one__gt__zero,axiom,
% 8.57/4.56      ! [X2: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3232_of__int__leD,axiom,
% 8.57/4.56      ! [N: int,X2: code_integer] :
% 8.57/4.56        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 8.57/4.56       => ( ( N = zero_zero_int )
% 8.57/4.56          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3233_of__int__leD,axiom,
% 8.57/4.56      ! [N: int,X2: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 8.57/4.56       => ( ( N = zero_zero_int )
% 8.57/4.56          | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3234_of__int__leD,axiom,
% 8.57/4.56      ! [N: int,X2: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 8.57/4.56       => ( ( N = zero_zero_int )
% 8.57/4.56          | ( ord_less_eq_int @ one_one_int @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3235_of__int__lessD,axiom,
% 8.57/4.56      ! [N: int,X2: code_integer] :
% 8.57/4.56        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 8.57/4.56       => ( ( N = zero_zero_int )
% 8.57/4.56          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3236_of__int__lessD,axiom,
% 8.57/4.56      ! [N: int,X2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 8.57/4.56       => ( ( N = zero_zero_int )
% 8.57/4.56          | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3237_of__int__lessD,axiom,
% 8.57/4.56      ! [N: int,X2: int] :
% 8.57/4.56        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 8.57/4.56       => ( ( N = zero_zero_int )
% 8.57/4.56          | ( ord_less_int @ one_one_int @ X2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3238_divide__le__eq,axiom,
% 8.57/4.56      ! [B: rat,C: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 8.57/4.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 8.57/4.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3239_le__divide__eq,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 8.57/4.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 8.57/4.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3240_divide__left__mono,axiom,
% 8.57/4.56      ! [B: rat,A: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ B @ A )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.57/4.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.57/4.56           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3241_neg__divide__le__eq,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.57/4.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3242_neg__le__divide__eq,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.56          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3243_pos__divide__le__eq,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.57/4.56          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3244_pos__le__divide__eq,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3245_mult__imp__div__pos__le,axiom,
% 8.57/4.56      ! [Y: rat,X2: rat,Z2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.57/4.56       => ( ( ord_less_eq_rat @ X2 @ ( times_times_rat @ Z2 @ Y ) )
% 8.57/4.56         => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3246_mult__imp__le__div__pos,axiom,
% 8.57/4.56      ! [Y: rat,Z2: rat,X2: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ Y ) @ X2 )
% 8.57/4.56         => ( ord_less_eq_rat @ Z2 @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3247_divide__left__mono__neg,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.56       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.57/4.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.57/4.56           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3248_le__divide__eq__1,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56            & ( ord_less_eq_rat @ A @ B ) )
% 8.57/4.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3249_divide__le__eq__1,axiom,
% 8.57/4.56      ! [B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.56            & ( ord_less_eq_rat @ B @ A ) )
% 8.57/4.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.57/4.56            & ( ord_less_eq_rat @ A @ B ) )
% 8.57/4.56          | ( A = zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3250_frac__le__eq,axiom,
% 8.57/4.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 8.57/4.56        ( ( Y != zero_zero_rat )
% 8.57/4.56       => ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 8.57/4.56            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3251_frac__less__eq,axiom,
% 8.57/4.56      ! [Y: rat,Z2: rat,X2: rat,W2: rat] :
% 8.57/4.56        ( ( Y != zero_zero_rat )
% 8.57/4.56       => ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W2 @ Z2 ) )
% 8.57/4.56            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z2 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3252_pos__minus__divide__less__eq,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.57/4.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3253_pos__less__minus__divide__eq,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.57/4.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3254_neg__minus__divide__less__eq,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.57/4.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3255_neg__less__minus__divide__eq,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.57/4.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3256_minus__divide__less__eq,axiom,
% 8.57/4.56      ! [B: rat,C: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 8.57/4.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 8.57/4.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3257_less__minus__divide__eq,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 8.57/4.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 8.57/4.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3258_minus__divide__add__eq__iff,axiom,
% 8.57/4.56      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.56        ( ( Z2 != zero_zero_rat )
% 8.57/4.56       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z2 ) ) @ Y )
% 8.57/4.56          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3259_add__divide__eq__if__simps_I3_J,axiom,
% 8.57/4.56      ! [Z2: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ( Z2 = zero_zero_rat )
% 8.57/4.56         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 8.57/4.56            = B ) )
% 8.57/4.56        & ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 8.57/4.56            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3260_add__divide__eq__if__simps_I6_J,axiom,
% 8.57/4.56      ! [Z2: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ( Z2 = zero_zero_rat )
% 8.57/4.56         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 8.57/4.56            = ( uminus_uminus_rat @ B ) ) )
% 8.57/4.56        & ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 8.57/4.56            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3261_add__divide__eq__if__simps_I5_J,axiom,
% 8.57/4.56      ! [Z2: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ( Z2 = zero_zero_rat )
% 8.57/4.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 8.57/4.56            = ( uminus_uminus_rat @ B ) ) )
% 8.57/4.56        & ( ( Z2 != zero_zero_rat )
% 8.57/4.56         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 8.57/4.56            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3262_minus__divide__diff__eq__iff,axiom,
% 8.57/4.56      ! [Z2: rat,X2: rat,Y: rat] :
% 8.57/4.56        ( ( Z2 != zero_zero_rat )
% 8.57/4.56       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z2 ) ) @ Y )
% 8.57/4.56          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3263_nat__abs__triangle__ineq,axiom,
% 8.57/4.56      ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3264_div__geq,axiom,
% 8.57/4.56      ! [N: nat,M: nat] :
% 8.57/4.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.56       => ( ~ ( ord_less_nat @ M @ N )
% 8.57/4.56         => ( ( divide_divide_nat @ M @ N )
% 8.57/4.56            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3265_verit__less__mono__div__int2,axiom,
% 8.57/4.56      ! [A4: int,B4: int,N: int] :
% 8.57/4.56        ( ( ord_less_eq_int @ A4 @ B4 )
% 8.57/4.56       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 8.57/4.56         => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A4 @ N ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3266_div__eq__minus1,axiom,
% 8.57/4.56      ! [B: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.56       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 8.57/4.56          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3267_Ints__odd__less__0,axiom,
% 8.57/4.56      ! [A: code_integer] :
% 8.57/4.56        ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 8.57/4.56       => ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A ) @ zero_z3403309356797280102nteger )
% 8.57/4.56          = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3268_Ints__odd__less__0,axiom,
% 8.57/4.56      ! [A: rat] :
% 8.57/4.56        ( ( member_rat @ A @ ring_1_Ints_rat )
% 8.57/4.56       => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 8.57/4.56          = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3269_Ints__odd__less__0,axiom,
% 8.57/4.56      ! [A: int] :
% 8.57/4.56        ( ( member_int @ A @ ring_1_Ints_int )
% 8.57/4.56       => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 8.57/4.56          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3270_scaling__mono,axiom,
% 8.57/4.56      ! [U: rat,V: rat,R: rat,S: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ U @ V )
% 8.57/4.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 8.57/4.56         => ( ( ord_less_eq_rat @ R @ S )
% 8.57/4.56           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3271_pos__minus__divide__le__eq,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.57/4.56          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3272_pos__le__minus__divide__eq,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.57/4.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3273_neg__minus__divide__le__eq,axiom,
% 8.57/4.56      ! [C: rat,B: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.57/4.56          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3274_neg__le__minus__divide__eq,axiom,
% 8.57/4.56      ! [C: rat,A: rat,B: rat] :
% 8.57/4.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.57/4.56          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3275_minus__divide__le__eq,axiom,
% 8.57/4.56      ! [B: rat,C: rat,A: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 8.57/4.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 8.57/4.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3276_le__minus__divide__eq,axiom,
% 8.57/4.56      ! [A: rat,B: rat,C: rat] :
% 8.57/4.56        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.57/4.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 8.57/4.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 8.57/4.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.56               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3277_nat__approx__posE,axiom,
% 8.57/4.56      ! [E: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ E )
% 8.57/4.56       => ~ ! [N2: nat] :
% 8.57/4.56              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ E ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3278_nat__abs__int__diff,axiom,
% 8.57/4.56      ! [A: nat,B: nat] :
% 8.57/4.56        ( ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.56         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 8.57/4.56            = ( minus_minus_nat @ B @ A ) ) )
% 8.57/4.56        & ( ~ ( ord_less_eq_nat @ A @ B )
% 8.57/4.56         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 8.57/4.56            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3279_split__zdiv,axiom,
% 8.57/4.56      ! [P: int > $o,N: int,K: int] :
% 8.57/4.56        ( ( P @ ( divide_divide_int @ N @ K ) )
% 8.57/4.56        = ( ( ( K = zero_zero_int )
% 8.57/4.56           => ( P @ zero_zero_int ) )
% 8.57/4.56          & ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.56           => ! [I2: int,J3: int] :
% 8.57/4.56                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 8.57/4.56                  & ( ord_less_int @ J3 @ K )
% 8.57/4.56                  & ( N
% 8.57/4.56                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 8.57/4.56               => ( P @ I2 ) ) )
% 8.57/4.56          & ( ( ord_less_int @ K @ zero_zero_int )
% 8.57/4.56           => ! [I2: int,J3: int] :
% 8.57/4.56                ( ( ( ord_less_int @ K @ J3 )
% 8.57/4.56                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 8.57/4.56                  & ( N
% 8.57/4.56                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 8.57/4.56               => ( P @ I2 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3280_int__div__neg__eq,axiom,
% 8.57/4.56      ! [A: int,B: int,Q2: int,R: int] :
% 8.57/4.56        ( ( A
% 8.57/4.56          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.57/4.56       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 8.57/4.56         => ( ( ord_less_int @ B @ R )
% 8.57/4.56           => ( ( divide_divide_int @ A @ B )
% 8.57/4.56              = Q2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3281_int__div__pos__eq,axiom,
% 8.57/4.56      ! [A: int,B: int,Q2: int,R: int] :
% 8.57/4.56        ( ( A
% 8.57/4.56          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.57/4.56       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 8.57/4.56         => ( ( ord_less_int @ R @ B )
% 8.57/4.56           => ( ( divide_divide_int @ A @ B )
% 8.57/4.56              = Q2 ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3282_frac__neg,axiom,
% 8.57/4.56      ! [X2: rat] :
% 8.57/4.56        ( ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 8.57/4.56         => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X2 ) )
% 8.57/4.56            = zero_zero_rat ) )
% 8.57/4.56        & ( ~ ( member_rat @ X2 @ ring_1_Ints_rat )
% 8.57/4.56         => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X2 ) )
% 8.57/4.56            = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X2 ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3283_nat__intermed__int__val,axiom,
% 8.57/4.56      ! [M: nat,N: nat,F: nat > int,K: int] :
% 8.57/4.56        ( ! [I3: nat] :
% 8.57/4.56            ( ( ( ord_less_eq_nat @ M @ I3 )
% 8.57/4.56              & ( ord_less_nat @ I3 @ N ) )
% 8.57/4.56           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 8.57/4.56       => ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.56         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 8.57/4.56           => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 8.57/4.56             => ? [I3: nat] :
% 8.57/4.56                  ( ( ord_less_eq_nat @ M @ I3 )
% 8.57/4.56                  & ( ord_less_eq_nat @ I3 @ N )
% 8.57/4.56                  & ( ( F @ I3 )
% 8.57/4.56                    = K ) ) ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3284_floor__divide__lower,axiom,
% 8.57/4.56      ! [Q2: rat,P3: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 8.57/4.56       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P3 @ Q2 ) ) ) @ Q2 ) @ P3 ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3285_ceiling__divide__upper,axiom,
% 8.57/4.56      ! [Q2: rat,P3: rat] :
% 8.57/4.56        ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 8.57/4.56       => ( ord_less_eq_rat @ P3 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P3 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3286_decr__lemma,axiom,
% 8.57/4.56      ! [D: int,X2: int,Z2: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ D )
% 8.57/4.56       => ( ord_less_int @ ( minus_minus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z2 ) ) @ one_one_int ) @ D ) ) @ Z2 ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3287_incr__lemma,axiom,
% 8.57/4.56      ! [D: int,Z2: int,X2: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ D )
% 8.57/4.56       => ( ord_less_int @ Z2 @ ( plus_plus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z2 ) ) @ one_one_int ) @ D ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3288_div__pos__geq,axiom,
% 8.57/4.56      ! [L: int,K: int] :
% 8.57/4.56        ( ( ord_less_int @ zero_zero_int @ L )
% 8.57/4.56       => ( ( ord_less_eq_int @ L @ K )
% 8.57/4.56         => ( ( divide_divide_int @ K @ L )
% 8.57/4.56            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3289_div__mult__self1,axiom,
% 8.57/4.56      ! [B: nat,A: nat,C: nat] :
% 8.57/4.56        ( ( B != zero_zero_nat )
% 8.57/4.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 8.57/4.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3290_div__mult__self1,axiom,
% 8.57/4.56      ! [B: int,A: int,C: int] :
% 8.57/4.56        ( ( B != zero_zero_int )
% 8.57/4.56       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 8.57/4.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3291_div__mult__self1,axiom,
% 8.57/4.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.56        ( ( B != zero_z3403309356797280102nteger )
% 8.57/4.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3292_div__mult__self1,axiom,
% 8.57/4.56      ! [B: code_natural,A: code_natural,C: code_natural] :
% 8.57/4.56        ( ( B != zero_z2226904508553997617atural )
% 8.57/4.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 8.57/4.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3293_div__mult__self2,axiom,
% 8.57/4.56      ! [B: nat,A: nat,C: nat] :
% 8.57/4.56        ( ( B != zero_zero_nat )
% 8.57/4.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 8.57/4.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3294_div__mult__self2,axiom,
% 8.57/4.56      ! [B: int,A: int,C: int] :
% 8.57/4.56        ( ( B != zero_zero_int )
% 8.57/4.56       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 8.57/4.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3295_div__mult__self2,axiom,
% 8.57/4.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.56        ( ( B != zero_z3403309356797280102nteger )
% 8.57/4.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3296_div__mult__self2,axiom,
% 8.57/4.56      ! [B: code_natural,A: code_natural,C: code_natural] :
% 8.57/4.56        ( ( B != zero_z2226904508553997617atural )
% 8.57/4.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 8.57/4.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3297_div__mult__self3,axiom,
% 8.57/4.56      ! [B: nat,C: nat,A: nat] :
% 8.57/4.56        ( ( B != zero_zero_nat )
% 8.57/4.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 8.57/4.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3298_div__mult__self3,axiom,
% 8.57/4.56      ! [B: int,C: int,A: int] :
% 8.57/4.56        ( ( B != zero_zero_int )
% 8.57/4.56       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 8.57/4.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3299_div__mult__self3,axiom,
% 8.57/4.56      ! [B: code_integer,C: code_integer,A: code_integer] :
% 8.57/4.56        ( ( B != zero_z3403309356797280102nteger )
% 8.57/4.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3300_div__mult__self3,axiom,
% 8.57/4.56      ! [B: code_natural,C: code_natural,A: code_natural] :
% 8.57/4.56        ( ( B != zero_z2226904508553997617atural )
% 8.57/4.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 8.57/4.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3301_div__mult__self4,axiom,
% 8.57/4.56      ! [B: nat,C: nat,A: nat] :
% 8.57/4.56        ( ( B != zero_zero_nat )
% 8.57/4.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 8.57/4.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3302_div__mult__self4,axiom,
% 8.57/4.56      ! [B: int,C: int,A: int] :
% 8.57/4.56        ( ( B != zero_zero_int )
% 8.57/4.56       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 8.57/4.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3303_div__mult__self4,axiom,
% 8.57/4.56      ! [B: code_integer,C: code_integer,A: code_integer] :
% 8.57/4.56        ( ( B != zero_z3403309356797280102nteger )
% 8.57/4.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 8.57/4.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.57/4.56  
% 8.57/4.56  thf(fact_3304_div__mult__self4,axiom,
% 8.57/4.56      ! [B: code_natural,C: code_natural,A: code_natural] :
% 8.57/4.57        ( ( B != zero_z2226904508553997617atural )
% 8.57/4.57       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 8.57/4.57          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3305_div__pos__pos__trivial,axiom,
% 8.57/4.57      ! [K: int,L: int] :
% 8.57/4.57        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.57       => ( ( ord_less_int @ K @ L )
% 8.57/4.57         => ( ( divide_divide_int @ K @ L )
% 8.57/4.57            = zero_zero_int ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3306_div__neg__neg__trivial,axiom,
% 8.57/4.57      ! [K: int,L: int] :
% 8.57/4.57        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 8.57/4.57       => ( ( ord_less_int @ L @ K )
% 8.57/4.57         => ( ( divide_divide_int @ K @ L )
% 8.57/4.57            = zero_zero_int ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3307_div__mult__mult1__if,axiom,
% 8.57/4.57      ! [C: nat,A: nat,B: nat] :
% 8.57/4.57        ( ( ( C = zero_zero_nat )
% 8.57/4.57         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.57/4.57            = zero_zero_nat ) )
% 8.57/4.57        & ( ( C != zero_zero_nat )
% 8.57/4.57         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.57/4.57            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3308_div__mult__mult1__if,axiom,
% 8.57/4.57      ! [C: int,A: int,B: int] :
% 8.57/4.57        ( ( ( C = zero_zero_int )
% 8.57/4.57         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.57            = zero_zero_int ) )
% 8.57/4.57        & ( ( C != zero_zero_int )
% 8.57/4.57         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.57            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3309_div__mult__mult1__if,axiom,
% 8.57/4.57      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.57        ( ( ( C = zero_z3403309356797280102nteger )
% 8.57/4.57         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.57            = zero_z3403309356797280102nteger ) )
% 8.57/4.57        & ( ( C != zero_z3403309356797280102nteger )
% 8.57/4.57         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.57            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3310_div__mult__mult1__if,axiom,
% 8.57/4.57      ! [C: code_natural,A: code_natural,B: code_natural] :
% 8.57/4.57        ( ( ( C = zero_z2226904508553997617atural )
% 8.57/4.57         => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 8.57/4.57            = zero_z2226904508553997617atural ) )
% 8.57/4.57        & ( ( C != zero_z2226904508553997617atural )
% 8.57/4.57         => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 8.57/4.57            = ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3311_div__mult__mult2,axiom,
% 8.57/4.57      ! [C: nat,A: nat,B: nat] :
% 8.57/4.57        ( ( C != zero_zero_nat )
% 8.57/4.57       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 8.57/4.57          = ( divide_divide_nat @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3312_div__mult__mult2,axiom,
% 8.57/4.57      ! [C: int,A: int,B: int] :
% 8.57/4.57        ( ( C != zero_zero_int )
% 8.57/4.57       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.57/4.57          = ( divide_divide_int @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3313_div__mult__mult2,axiom,
% 8.57/4.57      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.57        ( ( C != zero_z3403309356797280102nteger )
% 8.57/4.57       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.57          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3314_div__mult__mult2,axiom,
% 8.57/4.57      ! [C: code_natural,A: code_natural,B: code_natural] :
% 8.57/4.57        ( ( C != zero_z2226904508553997617atural )
% 8.57/4.57       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 8.57/4.57          = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3315_div__mult__mult1,axiom,
% 8.57/4.57      ! [C: nat,A: nat,B: nat] :
% 8.57/4.57        ( ( C != zero_zero_nat )
% 8.57/4.57       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.57/4.57          = ( divide_divide_nat @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3316_div__mult__mult1,axiom,
% 8.57/4.57      ! [C: int,A: int,B: int] :
% 8.57/4.57        ( ( C != zero_zero_int )
% 8.57/4.57       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.57/4.57          = ( divide_divide_int @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3317_div__mult__mult1,axiom,
% 8.57/4.57      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.57        ( ( C != zero_z3403309356797280102nteger )
% 8.57/4.57       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.57/4.57          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3318_div__mult__mult1,axiom,
% 8.57/4.57      ! [C: code_natural,A: code_natural,B: code_natural] :
% 8.57/4.57        ( ( C != zero_z2226904508553997617atural )
% 8.57/4.57       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 8.57/4.57          = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3319_div__minus1__right,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.57        = ( uminus_uminus_int @ A ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3320_div__minus1__right,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.57/4.57        = ( uminus1351360451143612070nteger @ A ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3321_div__by__Suc__0,axiom,
% 8.57/4.57      ! [M: nat] :
% 8.57/4.57        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 8.57/4.57        = M ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3322_div__less,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ M @ N )
% 8.57/4.57       => ( ( divide_divide_nat @ M @ N )
% 8.57/4.57          = zero_zero_nat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3323_div__mult__self__is__m,axiom,
% 8.57/4.57      ! [N: nat,M: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 8.57/4.57          = M ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3324_div__mult__self1__is__m,axiom,
% 8.57/4.57      ! [N: nat,M: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 8.57/4.57          = M ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3325_div__le__dividend,axiom,
% 8.57/4.57      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3326_div__le__mono,axiom,
% 8.57/4.57      ! [M: nat,N: nat,K: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3327_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ( divide_divide_nat @ M @ N )
% 8.57/4.57          = zero_zero_nat )
% 8.57/4.57        = ( ( ord_less_nat @ M @ N )
% 8.57/4.57          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3328_Suc__div__le__mono,axiom,
% 8.57/4.57      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3329_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 8.57/4.57        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3330_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 8.57/4.57        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3331_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( semiri4939895301339042750nteger @ ( divide_divide_nat @ M @ N ) )
% 8.57/4.57        = ( divide6298287555418463151nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3332_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( semiri3763490453095760265atural @ ( divide_divide_nat @ M @ N ) )
% 8.57/4.57        = ( divide5121882707175180666atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3333_div__times__less__eq__dividend,axiom,
% 8.57/4.57      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3334_times__div__less__eq__dividend,axiom,
% 8.57/4.57      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3335_div__mult2__eq_H,axiom,
% 8.57/4.57      ! [A: int,M: nat,N: nat] :
% 8.57/4.57        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.57/4.57        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3336_div__mult2__eq_H,axiom,
% 8.57/4.57      ! [A: nat,M: nat,N: nat] :
% 8.57/4.57        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 8.57/4.57        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3337_div__mult2__eq_H,axiom,
% 8.57/4.57      ! [A: code_integer,M: nat,N: nat] :
% 8.57/4.57        ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 8.57/4.57        = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3338_div__mult2__eq_H,axiom,
% 8.57/4.57      ! [A: code_natural,M: nat,N: nat] :
% 8.57/4.57        ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) )
% 8.57/4.57        = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3339_div__le__mono2,axiom,
% 8.57/4.57      ! [M: nat,N: nat,K: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.57       => ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3340_div__greater__zero__iff,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 8.57/4.57        = ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3341_div__less__iff__less__mult,axiom,
% 8.57/4.57      ! [Q2: nat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 8.57/4.57       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 8.57/4.57          = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3342_div__eq__dividend__iff,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.57       => ( ( ( divide_divide_nat @ M @ N )
% 8.57/4.57            = M )
% 8.57/4.57          = ( N = one_one_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3343_div__less__dividend,axiom,
% 8.57/4.57      ! [N: nat,M: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ N )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.57         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3344_zdiv__zmult2__eq,axiom,
% 8.57/4.57      ! [C: int,A: int,B: int] :
% 8.57/4.57        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.57       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 8.57/4.57          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3345_nat__div__distrib,axiom,
% 8.57/4.57      ! [X2: int,Y: int] :
% 8.57/4.57        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.57       => ( ( nat2 @ ( divide_divide_int @ X2 @ Y ) )
% 8.57/4.57          = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3346_nat__div__distrib_H,axiom,
% 8.57/4.57      ! [Y: int,X2: int] :
% 8.57/4.57        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.57       => ( ( nat2 @ ( divide_divide_int @ X2 @ Y ) )
% 8.57/4.57          = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3347_div__add__self2,axiom,
% 8.57/4.57      ! [B: nat,A: nat] :
% 8.57/4.57        ( ( B != zero_zero_nat )
% 8.57/4.57       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.57/4.57          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3348_div__add__self2,axiom,
% 8.57/4.57      ! [B: int,A: int] :
% 8.57/4.57        ( ( B != zero_zero_int )
% 8.57/4.57       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.57/4.57          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3349_div__add__self2,axiom,
% 8.57/4.57      ! [B: code_integer,A: code_integer] :
% 8.57/4.57        ( ( B != zero_z3403309356797280102nteger )
% 8.57/4.57       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 8.57/4.57          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3350_div__add__self2,axiom,
% 8.57/4.57      ! [B: code_natural,A: code_natural] :
% 8.57/4.57        ( ( B != zero_z2226904508553997617atural )
% 8.57/4.57       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 8.57/4.57          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3351_div__add__self1,axiom,
% 8.57/4.57      ! [B: nat,A: nat] :
% 8.57/4.57        ( ( B != zero_zero_nat )
% 8.57/4.57       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.57/4.57          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3352_div__add__self1,axiom,
% 8.57/4.57      ! [B: int,A: int] :
% 8.57/4.57        ( ( B != zero_zero_int )
% 8.57/4.57       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.57/4.57          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3353_div__add__self1,axiom,
% 8.57/4.57      ! [B: code_integer,A: code_integer] :
% 8.57/4.57        ( ( B != zero_z3403309356797280102nteger )
% 8.57/4.57       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 8.57/4.57          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3354_div__add__self1,axiom,
% 8.57/4.57      ! [B: code_natural,A: code_natural] :
% 8.57/4.57        ( ( B != zero_z2226904508553997617atural )
% 8.57/4.57       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 8.57/4.57          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3355_div__if,axiom,
% 8.57/4.57      ( divide_divide_nat
% 8.57/4.57      = ( ^ [M2: nat,N3: nat] :
% 8.57/4.57            ( if_nat
% 8.57/4.57            @ ( ( ord_less_nat @ M2 @ N3 )
% 8.57/4.57              | ( N3 = zero_zero_nat ) )
% 8.57/4.57            @ zero_zero_nat
% 8.57/4.57            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N3 ) @ N3 ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3356_less__eq__div__iff__mult__less__eq,axiom,
% 8.57/4.57      ! [Q2: nat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 8.57/4.57       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 8.57/4.57          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3357_div__nat__eqI,axiom,
% 8.57/4.57      ! [N: nat,Q2: nat,M: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 8.57/4.57       => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 8.57/4.57         => ( ( divide_divide_nat @ M @ N )
% 8.57/4.57            = Q2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3358_split__div,axiom,
% 8.57/4.57      ! [P: nat > $o,M: nat,N: nat] :
% 8.57/4.57        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 8.57/4.57        = ( ( ( N = zero_zero_nat )
% 8.57/4.57           => ( P @ zero_zero_nat ) )
% 8.57/4.57          & ( ( N != zero_zero_nat )
% 8.57/4.57           => ! [I2: nat,J3: nat] :
% 8.57/4.57                ( ( ord_less_nat @ J3 @ N )
% 8.57/4.57               => ( ( M
% 8.57/4.57                    = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 8.57/4.57                 => ( P @ I2 ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3359_dividend__less__div__times,axiom,
% 8.57/4.57      ! [N: nat,M: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3360_dividend__less__times__div,axiom,
% 8.57/4.57      ! [N: nat,M: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3361_le__div__geq,axiom,
% 8.57/4.57      ! [N: nat,M: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57         => ( ( divide_divide_nat @ M @ N )
% 8.57/4.57            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3362_split__div_H,axiom,
% 8.57/4.57      ! [P: nat > $o,M: nat,N: nat] :
% 8.57/4.57        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 8.57/4.57        = ( ( ( N = zero_zero_nat )
% 8.57/4.57            & ( P @ zero_zero_nat ) )
% 8.57/4.57          | ? [Q6: nat] :
% 8.57/4.57              ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q6 ) @ M )
% 8.57/4.57              & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q6 ) ) )
% 8.57/4.57              & ( P @ Q6 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3363_div__pos__neg__trivial,axiom,
% 8.57/4.57      ! [K: int,L: int] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.57       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 8.57/4.57         => ( ( divide_divide_int @ K @ L )
% 8.57/4.57            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3364_bits__div__by__1,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( divide_divide_nat @ A @ one_one_nat )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3365_bits__div__by__1,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( divide_divide_int @ A @ one_one_int )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3366_bits__div__by__1,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3367_bits__div__by__1,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3368_bits__div__by__0,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 8.57/4.57        = zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3369_bits__div__by__0,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( divide_divide_int @ A @ zero_zero_int )
% 8.57/4.57        = zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3370_bits__div__by__0,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.57        = zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3371_bits__div__by__0,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( divide5121882707175180666atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.57        = zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3372_bits__div__0,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 8.57/4.57        = zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3373_bits__div__0,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( divide_divide_int @ zero_zero_int @ A )
% 8.57/4.57        = zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3374_bits__div__0,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57        = zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3375_bits__div__0,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( divide5121882707175180666atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57        = zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3376_int__power__div__base,axiom,
% 8.57/4.57      ! [M: nat,K: int] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.57       => ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.57         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 8.57/4.57            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3377_gbinomial__absorption_H,axiom,
% 8.57/4.57      ! [K: nat,A: rat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.57       => ( ( gbinomial_rat @ A @ K )
% 8.57/4.57          = ( 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 ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3378_pochhammer__absorb__comp,axiom,
% 8.57/4.57      ! [R: int,K: nat] :
% 8.57/4.57        ( ( times_times_int @ ( minus_minus_int @ R @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R ) @ K ) )
% 8.57/4.57        = ( times_times_int @ R @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R ) @ one_one_int ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3379_pochhammer__absorb__comp,axiom,
% 8.57/4.57      ! [R: code_integer,K: nat] :
% 8.57/4.57        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R ) @ K ) )
% 8.57/4.57        = ( times_3573771949741848930nteger @ R @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3380_pochhammer__absorb__comp,axiom,
% 8.57/4.57      ! [R: rat,K: nat] :
% 8.57/4.57        ( ( times_times_rat @ ( minus_minus_rat @ R @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R ) @ K ) )
% 8.57/4.57        = ( times_times_rat @ R @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R ) @ one_one_rat ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3381_fact__reduce,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( semiri1406184849735516958ct_int @ N )
% 8.57/4.57          = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3382_fact__reduce,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( semiri3624122377584611663nteger @ N )
% 8.57/4.57          = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3383_fact__reduce,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( semiri773545260158071498ct_rat @ N )
% 8.57/4.57          = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3384_fact__reduce,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( semiri2447717529341329178atural @ N )
% 8.57/4.57          = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( semiri2447717529341329178atural @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3385_fact__reduce,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( semiri1408675320244567234ct_nat @ N )
% 8.57/4.57          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3386_power__one,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N )
% 8.57/4.57        = one_one_Code_integer ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3387_power__one,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_power_rat @ one_one_rat @ N )
% 8.57/4.57        = one_one_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3388_power__one,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_7079662738309270450atural @ one_one_Code_natural @ N )
% 8.57/4.57        = one_one_Code_natural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3389_power__one,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_power_int @ one_one_int @ N )
% 8.57/4.57        = one_one_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3390_power__one,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_power_nat @ one_one_nat @ N )
% 8.57/4.57        = one_one_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3391_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ( semiri1314217659103216013at_int @ X2 )
% 8.57/4.57          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 8.57/4.57        = ( X2
% 8.57/4.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3392_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ( semiri1316708129612266289at_nat @ X2 )
% 8.57/4.57          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 8.57/4.57        = ( X2
% 8.57/4.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3393_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ( semiri4939895301339042750nteger @ X2 )
% 8.57/4.57          = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 8.57/4.57        = ( X2
% 8.57/4.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3394_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ( semiri681578069525770553at_rat @ X2 )
% 8.57/4.57          = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 8.57/4.57        = ( X2
% 8.57/4.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3395_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ( semiri3763490453095760265atural @ X2 )
% 8.57/4.57          = ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) )
% 8.57/4.57        = ( X2
% 8.57/4.57          = ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3396_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 )
% 8.57/4.57          = ( semiri1314217659103216013at_int @ X2 ) )
% 8.57/4.57        = ( ( power_power_nat @ B @ W2 )
% 8.57/4.57          = X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3397_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 )
% 8.57/4.57          = ( semiri1316708129612266289at_nat @ X2 ) )
% 8.57/4.57        = ( ( power_power_nat @ B @ W2 )
% 8.57/4.57          = X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3398_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 )
% 8.57/4.57          = ( semiri4939895301339042750nteger @ X2 ) )
% 8.57/4.57        = ( ( power_power_nat @ B @ W2 )
% 8.57/4.57          = X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3399_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 )
% 8.57/4.57          = ( semiri681578069525770553at_rat @ X2 ) )
% 8.57/4.57        = ( ( power_power_nat @ B @ W2 )
% 8.57/4.57          = X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3400_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 )
% 8.57/4.57          = ( semiri3763490453095760265atural @ X2 ) )
% 8.57/4.57        = ( ( power_power_nat @ B @ W2 )
% 8.57/4.57          = X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3401_of__nat__power,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 8.57/4.57        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3402_of__nat__power,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 8.57/4.57        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3403_of__nat__power,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( semiri4939895301339042750nteger @ ( power_power_nat @ M @ N ) )
% 8.57/4.57        = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ M ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3404_of__nat__power,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 8.57/4.57        = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3405_of__nat__power,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( semiri3763490453095760265atural @ ( power_power_nat @ M @ N ) )
% 8.57/4.57        = ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ M ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3406_power__one__right,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( power_power_int @ A @ one_one_nat )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3407_power__one__right,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( power_power_nat @ A @ one_one_nat )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3408_of__nat__fact,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri1314217659103216013at_int @ ( semiri1408675320244567234ct_nat @ N ) )
% 8.57/4.57        = ( semiri1406184849735516958ct_int @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3409_of__nat__fact,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri4939895301339042750nteger @ ( semiri1408675320244567234ct_nat @ N ) )
% 8.57/4.57        = ( semiri3624122377584611663nteger @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3410_of__nat__fact,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri681578069525770553at_rat @ ( semiri1408675320244567234ct_nat @ N ) )
% 8.57/4.57        = ( semiri773545260158071498ct_rat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3411_of__nat__fact,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri3763490453095760265atural @ ( semiri1408675320244567234ct_nat @ N ) )
% 8.57/4.57        = ( semiri2447717529341329178atural @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3412_of__nat__fact,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri1316708129612266289at_nat @ ( semiri1408675320244567234ct_nat @ N ) )
% 8.57/4.57        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3413_power__inject__exp,axiom,
% 8.57/4.57      ! [A: code_natural,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 8.57/4.57       => ( ( ( power_7079662738309270450atural @ A @ M )
% 8.57/4.57            = ( power_7079662738309270450atural @ A @ N ) )
% 8.57/4.57          = ( M = N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3414_power__inject__exp,axiom,
% 8.57/4.57      ! [A: code_integer,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.57/4.57       => ( ( ( power_8256067586552552935nteger @ A @ M )
% 8.57/4.57            = ( power_8256067586552552935nteger @ A @ N ) )
% 8.57/4.57          = ( M = N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3415_power__inject__exp,axiom,
% 8.57/4.57      ! [A: rat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.57       => ( ( ( power_power_rat @ A @ M )
% 8.57/4.57            = ( power_power_rat @ A @ N ) )
% 8.57/4.57          = ( M = N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3416_power__inject__exp,axiom,
% 8.57/4.57      ! [A: nat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ A )
% 8.57/4.57       => ( ( ( power_power_nat @ A @ M )
% 8.57/4.57            = ( power_power_nat @ A @ N ) )
% 8.57/4.57          = ( M = N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3417_power__inject__exp,axiom,
% 8.57/4.57      ! [A: int,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ one_one_int @ A )
% 8.57/4.57       => ( ( ( power_power_int @ A @ M )
% 8.57/4.57            = ( power_power_int @ A @ N ) )
% 8.57/4.57          = ( M = N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3418_power__0__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( suc @ N ) )
% 8.57/4.57        = zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3419_power__0__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 8.57/4.57        = zero_zero_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3420_power__0__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ ( suc @ N ) )
% 8.57/4.57        = zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3421_power__0__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 8.57/4.57        = zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3422_power__0__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.57/4.57        = zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3423_power__Suc0__right,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3424_power__Suc0__right,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3425_gbinomial__0_I2_J,axiom,
% 8.57/4.57      ! [K: nat] :
% 8.57/4.57        ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 8.57/4.57        = zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3426_gbinomial__0_I2_J,axiom,
% 8.57/4.57      ! [K: nat] :
% 8.57/4.57        ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 8.57/4.57        = zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3427_gbinomial__0_I2_J,axiom,
% 8.57/4.57      ! [K: nat] :
% 8.57/4.57        ( ( gbinom8545251970709558553nteger @ zero_z3403309356797280102nteger @ ( suc @ K ) )
% 8.57/4.57        = zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3428_gbinomial__0_I2_J,axiom,
% 8.57/4.57      ! [K: nat] :
% 8.57/4.57        ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 8.57/4.57        = zero_zero_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3429_gbinomial__0_I2_J,axiom,
% 8.57/4.57      ! [K: nat] :
% 8.57/4.57        ( ( gbinom7368847122466276068atural @ zero_z2226904508553997617atural @ ( suc @ K ) )
% 8.57/4.57        = zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3430_fact__0,axiom,
% 8.57/4.57      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 8.57/4.57      = one_one_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3431_fact__0,axiom,
% 8.57/4.57      ( ( semiri3624122377584611663nteger @ zero_zero_nat )
% 8.57/4.57      = one_one_Code_integer ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3432_fact__0,axiom,
% 8.57/4.57      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 8.57/4.57      = one_one_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3433_fact__0,axiom,
% 8.57/4.57      ( ( semiri2447717529341329178atural @ zero_zero_nat )
% 8.57/4.57      = one_one_Code_natural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3434_fact__0,axiom,
% 8.57/4.57      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 8.57/4.57      = one_one_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3435_gbinomial__0_I1_J,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( gbinomial_int @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3436_gbinomial__0_I1_J,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3437_gbinomial__0_I1_J,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( gbinom8545251970709558553nteger @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_Code_integer ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3438_gbinomial__0_I1_J,axiom,
% 8.57/4.57      ! [A: rat] :
% 8.57/4.57        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3439_gbinomial__0_I1_J,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( gbinom7368847122466276068atural @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_Code_natural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3440_pochhammer__0,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3441_pochhammer__0,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3442_pochhammer__0,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( comm_s8582702949713902594nteger @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_Code_integer ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3443_pochhammer__0,axiom,
% 8.57/4.57      ! [A: rat] :
% 8.57/4.57        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3444_pochhammer__0,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( comm_s7406298101470620109atural @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_Code_natural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3445_fact__1,axiom,
% 8.57/4.57      ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 8.57/4.57      = one_one_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3446_fact__1,axiom,
% 8.57/4.57      ( ( semiri3624122377584611663nteger @ one_one_nat )
% 8.57/4.57      = one_one_Code_integer ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3447_fact__1,axiom,
% 8.57/4.57      ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 8.57/4.57      = one_one_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3448_fact__1,axiom,
% 8.57/4.57      ( ( semiri2447717529341329178atural @ one_one_nat )
% 8.57/4.57      = one_one_Code_natural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3449_fact__1,axiom,
% 8.57/4.57      ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 8.57/4.57      = one_one_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3450_of__int__power,axiom,
% 8.57/4.57      ! [Z2: int,N: nat] :
% 8.57/4.57        ( ( ring_18347121197199848620nteger @ ( power_power_int @ Z2 @ N ) )
% 8.57/4.57        = ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3451_of__int__power,axiom,
% 8.57/4.57      ! [Z2: int,N: nat] :
% 8.57/4.57        ( ( ring_1_of_int_rat @ ( power_power_int @ Z2 @ N ) )
% 8.57/4.57        = ( power_power_rat @ ( ring_1_of_int_rat @ Z2 ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3452_of__int__power,axiom,
% 8.57/4.57      ! [Z2: int,N: nat] :
% 8.57/4.57        ( ( ring_1_of_int_int @ ( power_power_int @ Z2 @ N ) )
% 8.57/4.57        = ( power_power_int @ ( ring_1_of_int_int @ Z2 ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3453_of__int__eq__of__int__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: int,W2: nat,X2: int] :
% 8.57/4.57        ( ( ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 )
% 8.57/4.57          = ( ring_18347121197199848620nteger @ X2 ) )
% 8.57/4.57        = ( ( power_power_int @ B @ W2 )
% 8.57/4.57          = X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3454_of__int__eq__of__int__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: int,W2: nat,X2: int] :
% 8.57/4.57        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 )
% 8.57/4.57          = ( ring_1_of_int_rat @ X2 ) )
% 8.57/4.57        = ( ( power_power_int @ B @ W2 )
% 8.57/4.57          = X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3455_of__int__eq__of__int__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: int,W2: nat,X2: int] :
% 8.57/4.57        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 )
% 8.57/4.57          = ( ring_1_of_int_int @ X2 ) )
% 8.57/4.57        = ( ( power_power_int @ B @ W2 )
% 8.57/4.57          = X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3456_of__int__power__eq__of__int__cancel__iff,axiom,
% 8.57/4.57      ! [X2: int,B: int,W2: nat] :
% 8.57/4.57        ( ( ( ring_18347121197199848620nteger @ X2 )
% 8.57/4.57          = ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) )
% 8.57/4.57        = ( X2
% 8.57/4.57          = ( power_power_int @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3457_of__int__power__eq__of__int__cancel__iff,axiom,
% 8.57/4.57      ! [X2: int,B: int,W2: nat] :
% 8.57/4.57        ( ( ( ring_1_of_int_rat @ X2 )
% 8.57/4.57          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 8.57/4.57        = ( X2
% 8.57/4.57          = ( power_power_int @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3458_of__int__power__eq__of__int__cancel__iff,axiom,
% 8.57/4.57      ! [X2: int,B: int,W2: nat] :
% 8.57/4.57        ( ( ( ring_1_of_int_int @ X2 )
% 8.57/4.57          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 8.57/4.57        = ( X2
% 8.57/4.57          = ( power_power_int @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3459_power__strict__increasing__iff,axiom,
% 8.57/4.57      ! [B: code_natural,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ B )
% 8.57/4.57       => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ B @ X2 ) @ ( power_7079662738309270450atural @ B @ Y ) )
% 8.57/4.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3460_power__strict__increasing__iff,axiom,
% 8.57/4.57      ! [B: code_integer,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 8.57/4.57       => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X2 ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 8.57/4.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3461_power__strict__increasing__iff,axiom,
% 8.57/4.57      ! [B: rat,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_less_rat @ one_one_rat @ B )
% 8.57/4.57       => ( ( ord_less_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y ) )
% 8.57/4.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3462_power__strict__increasing__iff,axiom,
% 8.57/4.57      ! [B: nat,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ B )
% 8.57/4.57       => ( ( ord_less_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y ) )
% 8.57/4.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3463_power__strict__increasing__iff,axiom,
% 8.57/4.57      ! [B: int,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_less_int @ one_one_int @ B )
% 8.57/4.57       => ( ( ord_less_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y ) )
% 8.57/4.57          = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3464_minus__one__mult__self,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 8.57/4.57        = one_one_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3465_minus__one__mult__self,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 8.57/4.57        = one_one_Code_integer ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3466_minus__one__mult__self,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 8.57/4.57        = one_one_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3467_left__minus__one__mult__self,axiom,
% 8.57/4.57      ! [N: nat,A: int] :
% 8.57/4.57        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3468_left__minus__one__mult__self,axiom,
% 8.57/4.57      ! [N: nat,A: code_integer] :
% 8.57/4.57        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3469_left__minus__one__mult__self,axiom,
% 8.57/4.57      ! [N: nat,A: rat] :
% 8.57/4.57        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3470_power__eq__0__iff,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ( power_8256067586552552935nteger @ A @ N )
% 8.57/4.57          = zero_z3403309356797280102nteger )
% 8.57/4.57        = ( ( A = zero_z3403309356797280102nteger )
% 8.57/4.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3471_power__eq__0__iff,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ( power_power_rat @ A @ N )
% 8.57/4.57          = zero_zero_rat )
% 8.57/4.57        = ( ( A = zero_zero_rat )
% 8.57/4.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3472_power__eq__0__iff,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ( power_7079662738309270450atural @ A @ N )
% 8.57/4.57          = zero_z2226904508553997617atural )
% 8.57/4.57        = ( ( A = zero_z2226904508553997617atural )
% 8.57/4.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3473_power__eq__0__iff,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ( power_power_int @ A @ N )
% 8.57/4.57          = zero_zero_int )
% 8.57/4.57        = ( ( A = zero_zero_int )
% 8.57/4.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3474_power__eq__0__iff,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ( power_power_nat @ A @ N )
% 8.57/4.57          = zero_zero_nat )
% 8.57/4.57        = ( ( A = zero_zero_nat )
% 8.57/4.57          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3475_of__nat__less__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 8.57/4.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3476_of__nat__less__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 8.57/4.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3477_of__nat__less__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 8.57/4.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3478_of__nat__less__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 8.57/4.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3479_of__nat__less__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) @ ( semiri3763490453095760265atural @ X2 ) )
% 8.57/4.57        = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3480_of__nat__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3481_of__nat__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3482_of__nat__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3483_of__nat__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3484_of__nat__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ X2 ) @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3485_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3486_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ X2 ) @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3487_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3488_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3489_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.57      ! [X2: nat,B: nat,W2: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3490_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3491_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ B ) @ W2 ) @ ( semiri3763490453095760265atural @ X2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3492_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3493_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3494_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: nat,W2: nat,X2: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 8.57/4.57        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3495_fact__Suc__0,axiom,
% 8.57/4.57      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 8.57/4.57      = one_one_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3496_fact__Suc__0,axiom,
% 8.57/4.57      ( ( semiri3624122377584611663nteger @ ( suc @ zero_zero_nat ) )
% 8.57/4.57      = one_one_Code_integer ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3497_fact__Suc__0,axiom,
% 8.57/4.57      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 8.57/4.57      = one_one_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3498_fact__Suc__0,axiom,
% 8.57/4.57      ( ( semiri2447717529341329178atural @ ( suc @ zero_zero_nat ) )
% 8.57/4.57      = one_one_Code_natural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3499_fact__Suc__0,axiom,
% 8.57/4.57      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 8.57/4.57      = one_one_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3500_fact__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3501_fact__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri3624122377584611663nteger @ ( suc @ N ) )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3502_fact__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3503_fact__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri2447717529341329178atural @ ( suc @ N ) )
% 8.57/4.57        = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ ( suc @ N ) ) @ ( semiri2447717529341329178atural @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3504_fact__Suc,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3505_power__strict__decreasing__iff,axiom,
% 8.57/4.57      ! [B: code_natural,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.57       => ( ( ord_le5570908160329646204atural @ B @ one_one_Code_natural )
% 8.57/4.57         => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ B @ M ) @ ( power_7079662738309270450atural @ B @ N ) )
% 8.57/4.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3506_power__strict__decreasing__iff,axiom,
% 8.57/4.57      ! [B: code_integer,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.57       => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 8.57/4.57         => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 8.57/4.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3507_power__strict__decreasing__iff,axiom,
% 8.57/4.57      ! [B: rat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.57/4.57       => ( ( ord_less_rat @ B @ one_one_rat )
% 8.57/4.57         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 8.57/4.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3508_power__strict__decreasing__iff,axiom,
% 8.57/4.57      ! [B: nat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.57       => ( ( ord_less_nat @ B @ one_one_nat )
% 8.57/4.57         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 8.57/4.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3509_power__strict__decreasing__iff,axiom,
% 8.57/4.57      ! [B: int,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.57       => ( ( ord_less_int @ B @ one_one_int )
% 8.57/4.57         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 8.57/4.57            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3510_power__mono__iff,axiom,
% 8.57/4.57      ! [A: code_integer,B: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 8.57/4.57              = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3511_power__mono__iff,axiom,
% 8.57/4.57      ! [A: code_natural,B: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ B @ N ) )
% 8.57/4.57              = ( ord_le1926595141338095240atural @ A @ B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3512_power__mono__iff,axiom,
% 8.57/4.57      ! [A: rat,B: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 8.57/4.57              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3513_power__mono__iff,axiom,
% 8.57/4.57      ! [A: nat,B: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 8.57/4.57              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3514_power__mono__iff,axiom,
% 8.57/4.57      ! [A: int,B: int,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 8.57/4.57              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3515_power__increasing__iff,axiom,
% 8.57/4.57      ! [B: code_natural,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ B )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ B @ X2 ) @ ( power_7079662738309270450atural @ B @ Y ) )
% 8.57/4.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3516_power__increasing__iff,axiom,
% 8.57/4.57      ! [B: code_integer,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X2 ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 8.57/4.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3517_power__increasing__iff,axiom,
% 8.57/4.57      ! [B: rat,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_less_rat @ one_one_rat @ B )
% 8.57/4.57       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y ) )
% 8.57/4.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3518_power__increasing__iff,axiom,
% 8.57/4.57      ! [B: nat,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ B )
% 8.57/4.57       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y ) )
% 8.57/4.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3519_power__increasing__iff,axiom,
% 8.57/4.57      ! [B: int,X2: nat,Y: nat] :
% 8.57/4.57        ( ( ord_less_int @ one_one_int @ B )
% 8.57/4.57       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y ) )
% 8.57/4.57          = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3520_zero__less__power__abs__iff,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 8.57/4.57        = ( ( A != zero_z3403309356797280102nteger )
% 8.57/4.57          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3521_zero__less__power__abs__iff,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 8.57/4.57        = ( ( A != zero_zero_rat )
% 8.57/4.57          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3522_zero__less__power__abs__iff,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 8.57/4.57        = ( ( A != zero_zero_int )
% 8.57/4.57          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3523_of__int__le__of__int__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: int,W2: nat,X2: int] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) @ ( ring_18347121197199848620nteger @ X2 ) )
% 8.57/4.57        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3524_of__int__le__of__int__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: int,W2: nat,X2: int] :
% 8.57/4.57        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X2 ) )
% 8.57/4.57        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3525_of__int__le__of__int__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: int,W2: nat,X2: int] :
% 8.57/4.57        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X2 ) )
% 8.57/4.57        = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3526_of__int__power__le__of__int__cancel__iff,axiom,
% 8.57/4.57      ! [X2: int,B: int,W2: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3527_of__int__power__le__of__int__cancel__iff,axiom,
% 8.57/4.57      ! [X2: int,B: int,W2: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3528_of__int__power__le__of__int__cancel__iff,axiom,
% 8.57/4.57      ! [X2: int,B: int,W2: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3529_of__int__less__of__int__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: int,W2: nat,X2: int] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) @ ( ring_18347121197199848620nteger @ X2 ) )
% 8.57/4.57        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3530_of__int__less__of__int__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: int,W2: nat,X2: int] :
% 8.57/4.57        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X2 ) )
% 8.57/4.57        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3531_of__int__less__of__int__power__cancel__iff,axiom,
% 8.57/4.57      ! [B: int,W2: nat,X2: int] :
% 8.57/4.57        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X2 ) )
% 8.57/4.57        = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3532_of__int__power__less__of__int__cancel__iff,axiom,
% 8.57/4.57      ! [X2: int,B: int,W2: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3533_of__int__power__less__of__int__cancel__iff,axiom,
% 8.57/4.57      ! [X2: int,B: int,W2: nat] :
% 8.57/4.57        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3534_of__int__power__less__of__int__cancel__iff,axiom,
% 8.57/4.57      ! [X2: int,B: int,W2: nat] :
% 8.57/4.57        ( ( ord_less_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 8.57/4.57        = ( ord_less_int @ X2 @ ( power_power_int @ B @ W2 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3535_power__decreasing__iff,axiom,
% 8.57/4.57      ! [B: code_natural,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.57       => ( ( ord_le5570908160329646204atural @ B @ one_one_Code_natural )
% 8.57/4.57         => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ B @ M ) @ ( power_7079662738309270450atural @ B @ N ) )
% 8.57/4.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3536_power__decreasing__iff,axiom,
% 8.57/4.57      ! [B: code_integer,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.57       => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 8.57/4.57         => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 8.57/4.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3537_power__decreasing__iff,axiom,
% 8.57/4.57      ! [B: rat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.57/4.57       => ( ( ord_less_rat @ B @ one_one_rat )
% 8.57/4.57         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 8.57/4.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3538_power__decreasing__iff,axiom,
% 8.57/4.57      ! [B: nat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.57       => ( ( ord_less_nat @ B @ one_one_nat )
% 8.57/4.57         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 8.57/4.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3539_power__decreasing__iff,axiom,
% 8.57/4.57      ! [B: int,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.57       => ( ( ord_less_int @ B @ one_one_int )
% 8.57/4.57         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 8.57/4.57            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3540_of__nat__zero__less__power__iff,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X2 ) @ N ) )
% 8.57/4.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 8.57/4.57          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3541_of__nat__zero__less__power__iff,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N ) )
% 8.57/4.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 8.57/4.57          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3542_of__nat__zero__less__power__iff,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X2 ) @ N ) )
% 8.57/4.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 8.57/4.57          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3543_of__nat__zero__less__power__iff,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N ) )
% 8.57/4.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 8.57/4.57          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3544_of__nat__zero__less__power__iff,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( power_7079662738309270450atural @ ( semiri3763490453095760265atural @ X2 ) @ N ) )
% 8.57/4.57        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 8.57/4.57          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3545_pochhammer__of__nat,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( comm_s4660882817536571857er_int @ ( semiri1314217659103216013at_int @ X2 ) @ N )
% 8.57/4.57        = ( semiri1314217659103216013at_int @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3546_pochhammer__of__nat,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( comm_s4663373288045622133er_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N )
% 8.57/4.57        = ( semiri1316708129612266289at_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3547_pochhammer__of__nat,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( comm_s8582702949713902594nteger @ ( semiri4939895301339042750nteger @ X2 ) @ N )
% 8.57/4.57        = ( semiri4939895301339042750nteger @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3548_pochhammer__of__nat,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( comm_s4028243227959126397er_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N )
% 8.57/4.57        = ( semiri681578069525770553at_rat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3549_pochhammer__of__nat,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( comm_s7406298101470620109atural @ ( semiri3763490453095760265atural @ X2 ) @ N )
% 8.57/4.57        = ( semiri3763490453095760265atural @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3550_pochhammer__fact,axiom,
% 8.57/4.57      ( semiri1406184849735516958ct_int
% 8.57/4.57      = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3551_pochhammer__fact,axiom,
% 8.57/4.57      ( semiri3624122377584611663nteger
% 8.57/4.57      = ( comm_s8582702949713902594nteger @ one_one_Code_integer ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3552_pochhammer__fact,axiom,
% 8.57/4.57      ( semiri773545260158071498ct_rat
% 8.57/4.57      = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3553_pochhammer__fact,axiom,
% 8.57/4.57      ( semiri2447717529341329178atural
% 8.57/4.57      = ( comm_s7406298101470620109atural @ one_one_Code_natural ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3554_pochhammer__fact,axiom,
% 8.57/4.57      ( semiri1408675320244567234ct_nat
% 8.57/4.57      = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3555_of__nat__gbinomial,axiom,
% 8.57/4.57      ! [N: nat,K: nat] :
% 8.57/4.57        ( ( semiri681578069525770553at_rat @ ( gbinomial_nat @ N @ K ) )
% 8.57/4.57        = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3556_gbinomial__pochhammer,axiom,
% 8.57/4.57      ( gbinomial_rat
% 8.57/4.57      = ( ^ [A2: rat,K2: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A2 ) @ K2 ) ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3557_gbinomial__ge__n__over__k__pow__k,axiom,
% 8.57/4.57      ! [K: nat,A: rat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 8.57/4.57       => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3558_fact__mono__nat,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3559_fact__ge__self,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3560_power__not__zero,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( A != zero_z3403309356797280102nteger )
% 8.57/4.57       => ( ( power_8256067586552552935nteger @ A @ N )
% 8.57/4.57         != zero_z3403309356797280102nteger ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3561_power__not__zero,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( A != zero_zero_rat )
% 8.57/4.57       => ( ( power_power_rat @ A @ N )
% 8.57/4.57         != zero_zero_rat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3562_power__not__zero,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( A != zero_z2226904508553997617atural )
% 8.57/4.57       => ( ( power_7079662738309270450atural @ A @ N )
% 8.57/4.57         != zero_z2226904508553997617atural ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3563_power__not__zero,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( A != zero_zero_int )
% 8.57/4.57       => ( ( power_power_int @ A @ N )
% 8.57/4.57         != zero_zero_int ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3564_power__not__zero,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( A != zero_zero_nat )
% 8.57/4.57       => ( ( power_power_nat @ A @ N )
% 8.57/4.57         != zero_zero_nat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3565_fact__nonzero,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri1406184849735516958ct_int @ N )
% 8.57/4.57       != zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3566_fact__nonzero,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri3624122377584611663nteger @ N )
% 8.57/4.57       != zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3567_fact__nonzero,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri773545260158071498ct_rat @ N )
% 8.57/4.57       != zero_zero_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3568_fact__nonzero,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri2447717529341329178atural @ N )
% 8.57/4.57       != zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3569_fact__nonzero,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( semiri1408675320244567234ct_nat @ N )
% 8.57/4.57       != zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3570_pochhammer__same,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 8.57/4.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3571_pochhammer__same,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3572_pochhammer__same,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 8.57/4.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3573_Ints__power,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( member_int @ A @ ring_1_Ints_int )
% 8.57/4.57       => ( member_int @ ( power_power_int @ A @ N ) @ ring_1_Ints_int ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3574_gbinomial__pochhammer_H,axiom,
% 8.57/4.57      ( gbinomial_rat
% 8.57/4.57      = ( ^ [A2: rat,K2: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A2 @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3575_gbinomial__index__swap,axiom,
% 8.57/4.57      ! [K: nat,N: nat] :
% 8.57/4.57        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 8.57/4.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3576_gbinomial__negated__upper,axiom,
% 8.57/4.57      ( gbinomial_rat
% 8.57/4.57      = ( ^ [A2: rat,K2: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A2 ) @ one_one_rat ) @ K2 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3577_fact__less__mono__nat,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.57       => ( ( ord_less_nat @ M @ N )
% 8.57/4.57         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3578_zero__le__power,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3579_zero__le__power,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57       => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3580_zero__le__power,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3581_zero__le__power,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3582_zero__le__power,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3583_power__mono,axiom,
% 8.57/4.57      ! [A: code_integer,B: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3584_power__mono,axiom,
% 8.57/4.57      ! [A: code_natural,B: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ A @ B )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57         => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ B @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3585_power__mono,axiom,
% 8.57/4.57      ! [A: rat,B: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ A @ B )
% 8.57/4.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3586_power__mono,axiom,
% 8.57/4.57      ! [A: nat,B: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ A @ B )
% 8.57/4.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3587_power__mono,axiom,
% 8.57/4.57      ! [A: int,B: int,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ A @ B )
% 8.57/4.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3588_zero__less__power,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57       => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3589_zero__less__power,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57       => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3590_zero__less__power,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.57       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3591_zero__less__power,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.57       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3592_zero__less__power,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.57       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3593_gbinomial__Suc__Suc,axiom,
% 8.57/4.57      ! [A: rat,K: nat] :
% 8.57/4.57        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 8.57/4.57        = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3594_one__le__power,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 8.57/4.57       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3595_one__le__power,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ A )
% 8.57/4.57       => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3596_one__le__power,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.57/4.57       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3597_one__le__power,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 8.57/4.57       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3598_one__le__power,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ one_one_int @ A )
% 8.57/4.57       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3599_left__right__inverse__power,axiom,
% 8.57/4.57      ! [X2: code_natural,Y: code_natural,N: nat] :
% 8.57/4.57        ( ( ( times_2397367101498566445atural @ X2 @ Y )
% 8.57/4.57          = one_one_Code_natural )
% 8.57/4.57       => ( ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ X2 @ N ) @ ( power_7079662738309270450atural @ Y @ N ) )
% 8.57/4.57          = one_one_Code_natural ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3600_left__right__inverse__power,axiom,
% 8.57/4.57      ! [X2: code_integer,Y: code_integer,N: nat] :
% 8.57/4.57        ( ( ( times_3573771949741848930nteger @ X2 @ Y )
% 8.57/4.57          = one_one_Code_integer )
% 8.57/4.57       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 8.57/4.57          = one_one_Code_integer ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3601_left__right__inverse__power,axiom,
% 8.57/4.57      ! [X2: rat,Y: rat,N: nat] :
% 8.57/4.57        ( ( ( times_times_rat @ X2 @ Y )
% 8.57/4.57          = one_one_rat )
% 8.57/4.57       => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y @ N ) )
% 8.57/4.57          = one_one_rat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3602_left__right__inverse__power,axiom,
% 8.57/4.57      ! [X2: nat,Y: nat,N: nat] :
% 8.57/4.57        ( ( ( times_times_nat @ X2 @ Y )
% 8.57/4.57          = one_one_nat )
% 8.57/4.57       => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y @ N ) )
% 8.57/4.57          = one_one_nat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3603_left__right__inverse__power,axiom,
% 8.57/4.57      ! [X2: int,Y: int,N: nat] :
% 8.57/4.57        ( ( ( times_times_int @ X2 @ Y )
% 8.57/4.57          = one_one_int )
% 8.57/4.57       => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y @ N ) )
% 8.57/4.57          = one_one_int ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3604_power__0,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_Code_integer ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3605_power__0,axiom,
% 8.57/4.57      ! [A: rat] :
% 8.57/4.57        ( ( power_power_rat @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3606_power__0,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( power_7079662738309270450atural @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_Code_natural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3607_power__0,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( power_power_int @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3608_power__0,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( power_power_nat @ A @ zero_zero_nat )
% 8.57/4.57        = one_one_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3609_power__one__over,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 8.57/4.57        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3610_power__add,axiom,
% 8.57/4.57      ! [A: code_integer,M: nat,N: nat] :
% 8.57/4.57        ( ( power_8256067586552552935nteger @ A @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3611_power__add,axiom,
% 8.57/4.57      ! [A: rat,M: nat,N: nat] :
% 8.57/4.57        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.57        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3612_power__add,axiom,
% 8.57/4.57      ! [A: nat,M: nat,N: nat] :
% 8.57/4.57        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.57        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3613_power__add,axiom,
% 8.57/4.57      ! [A: int,M: nat,N: nat] :
% 8.57/4.57        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.57        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3614_fact__ge__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri3624122377584611663nteger @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3615_fact__ge__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( semiri2447717529341329178atural @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3616_fact__ge__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3617_fact__ge__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3618_fact__ge__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3619_gbinomial__of__nat__symmetric,axiom,
% 8.57/4.57      ! [K: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.57       => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 8.57/4.57          = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3620_fact__gt__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( semiri2447717529341329178atural @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3621_fact__gt__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri3624122377584611663nteger @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3622_fact__gt__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3623_fact__gt__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3624_fact__gt__zero,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3625_fact__not__neg,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ~ ( ord_le5570908160329646204atural @ ( semiri2447717529341329178atural @ N ) @ zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3626_fact__not__neg,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ~ ( ord_le6747313008572928689nteger @ ( semiri3624122377584611663nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3627_fact__not__neg,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3628_fact__not__neg,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3629_fact__not__neg,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3630_fact__ge__1,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3631_fact__ge__1,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( semiri2447717529341329178atural @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3632_fact__ge__1,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3633_fact__ge__1,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3634_fact__ge__1,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3635_fact__mono,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3636_fact__mono,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3637_fact__mono,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3638_pochhammer__pos,axiom,
% 8.57/4.57      ! [X2: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ X2 )
% 8.57/4.57       => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( comm_s7406298101470620109atural @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3639_pochhammer__pos,axiom,
% 8.57/4.57      ! [X2: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X2 )
% 8.57/4.57       => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( comm_s8582702949713902594nteger @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3640_pochhammer__pos,axiom,
% 8.57/4.57      ! [X2: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 8.57/4.57       => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3641_pochhammer__pos,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 8.57/4.57       => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3642_pochhammer__pos,axiom,
% 8.57/4.57      ! [X2: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ X2 )
% 8.57/4.57       => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3643_pochhammer__neq__0__mono,axiom,
% 8.57/4.57      ! [A: rat,M: nat,N: nat] :
% 8.57/4.57        ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 8.57/4.57         != zero_zero_rat )
% 8.57/4.57       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57         => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 8.57/4.57           != zero_zero_rat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3644_pochhammer__eq__0__mono,axiom,
% 8.57/4.57      ! [A: rat,N: nat,M: nat] :
% 8.57/4.57        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 8.57/4.57          = zero_zero_rat )
% 8.57/4.57       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57         => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 8.57/4.57            = zero_zero_rat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3645_gbinomial__minus,axiom,
% 8.57/4.57      ! [A: rat,K: nat] :
% 8.57/4.57        ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 8.57/4.57        = ( 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 ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3646_gbinomial__addition__formula,axiom,
% 8.57/4.57      ! [A: rat,K: nat] :
% 8.57/4.57        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 8.57/4.57        = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3647_gbinomial__absorb__comp,axiom,
% 8.57/4.57      ! [A: rat,K: nat] :
% 8.57/4.57        ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 8.57/4.57        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3648_gbinomial__mult__1_H,axiom,
% 8.57/4.57      ! [A: rat,K: nat] :
% 8.57/4.57        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 8.57/4.57        = ( 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 ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3649_gbinomial__mult__1,axiom,
% 8.57/4.57      ! [A: rat,K: nat] :
% 8.57/4.57        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 8.57/4.57        = ( 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 ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3650_fact__ge__Suc__0__nat,axiom,
% 8.57/4.57      ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3651_pochhammer__minus,axiom,
% 8.57/4.57      ! [B: int,K: nat] :
% 8.57/4.57        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 8.57/4.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3652_pochhammer__minus,axiom,
% 8.57/4.57      ! [B: code_integer,K: nat] :
% 8.57/4.57        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3653_pochhammer__minus,axiom,
% 8.57/4.57      ! [B: rat,K: nat] :
% 8.57/4.57        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 8.57/4.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3654_pochhammer__minus_H,axiom,
% 8.57/4.57      ! [B: int,K: nat] :
% 8.57/4.57        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 8.57/4.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3655_pochhammer__minus_H,axiom,
% 8.57/4.57      ! [B: code_integer,K: nat] :
% 8.57/4.57        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3656_pochhammer__minus_H,axiom,
% 8.57/4.57      ! [B: rat,K: nat] :
% 8.57/4.57        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 8.57/4.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3657_power__less__imp__less__base,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat,B: code_natural] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ B @ N ) )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.57         => ( ord_le5570908160329646204atural @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3658_power__less__imp__less__base,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat,B: code_integer] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.57         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3659_power__less__imp__less__base,axiom,
% 8.57/4.57      ! [A: rat,N: nat,B: rat] :
% 8.57/4.57        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 8.57/4.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.57         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3660_power__less__imp__less__base,axiom,
% 8.57/4.57      ! [A: nat,N: nat,B: nat] :
% 8.57/4.57        ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 8.57/4.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.57         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3661_power__less__imp__less__base,axiom,
% 8.57/4.57      ! [A: int,N: nat,B: int] :
% 8.57/4.57        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 8.57/4.57       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.57         => ( ord_less_int @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3662_power__le__one,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 8.57/4.57         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3663_power__le__one,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 8.57/4.57         => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N ) @ one_one_Code_natural ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3664_power__le__one,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.57/4.57         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3665_power__le__one,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.57/4.57         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3666_power__le__one,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57       => ( ( ord_less_eq_int @ A @ one_one_int )
% 8.57/4.57         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3667_power__le__imp__le__base,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat,B: code_integer] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ ( power_8256067586552552935nteger @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.57         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3668_power__le__imp__le__base,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat,B: code_natural] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) @ ( power_7079662738309270450atural @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.57         => ( ord_le1926595141338095240atural @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3669_power__le__imp__le__base,axiom,
% 8.57/4.57      ! [A: rat,N: nat,B: rat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.57         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3670_power__le__imp__le__base,axiom,
% 8.57/4.57      ! [A: nat,N: nat,B: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.57         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3671_power__le__imp__le__base,axiom,
% 8.57/4.57      ! [A: int,N: nat,B: int] :
% 8.57/4.57        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.57         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3672_power__inject__base,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat,B: code_integer] :
% 8.57/4.57        ( ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 8.57/4.57          = ( power_8256067586552552935nteger @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.57           => ( A = B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3673_power__inject__base,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat,B: code_natural] :
% 8.57/4.57        ( ( ( power_7079662738309270450atural @ A @ ( suc @ N ) )
% 8.57/4.57          = ( power_7079662738309270450atural @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.57           => ( A = B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3674_power__inject__base,axiom,
% 8.57/4.57      ! [A: rat,N: nat,B: rat] :
% 8.57/4.57        ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 8.57/4.57          = ( power_power_rat @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.57           => ( A = B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3675_power__inject__base,axiom,
% 8.57/4.57      ! [A: nat,N: nat,B: nat] :
% 8.57/4.57        ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 8.57/4.57          = ( power_power_nat @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.57           => ( A = B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3676_power__inject__base,axiom,
% 8.57/4.57      ! [A: int,N: nat,B: int] :
% 8.57/4.57        ( ( ( power_power_int @ A @ ( suc @ N ) )
% 8.57/4.57          = ( power_power_int @ B @ ( suc @ N ) ) )
% 8.57/4.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.57           => ( A = B ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3677_power__gt1__lemma,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 8.57/4.57       => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3678_power__gt1__lemma,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.57/4.57       => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3679_power__gt1__lemma,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.57       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3680_power__gt1__lemma,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ A )
% 8.57/4.57       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3681_power__gt1__lemma,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ one_one_int @ A )
% 8.57/4.57       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3682_power__less__power__Suc,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 8.57/4.57       => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N ) @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3683_power__less__power__Suc,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.57/4.57       => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3684_power__less__power__Suc,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.57       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3685_power__less__power__Suc,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ A )
% 8.57/4.57       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3686_power__less__power__Suc,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ one_one_int @ A )
% 8.57/4.57       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3687_power__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 8.57/4.57            = one_one_Code_integer ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 8.57/4.57            = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3688_power__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( power_power_rat @ zero_zero_rat @ N )
% 8.57/4.57            = one_one_rat ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( power_power_rat @ zero_zero_rat @ N )
% 8.57/4.57            = zero_zero_rat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3689_power__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N )
% 8.57/4.57            = one_one_Code_natural ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N )
% 8.57/4.57            = zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3690_power__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( power_power_int @ zero_zero_int @ N )
% 8.57/4.57            = one_one_int ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( power_power_int @ zero_zero_int @ N )
% 8.57/4.57            = zero_zero_int ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3691_power__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( power_power_nat @ zero_zero_nat @ N )
% 8.57/4.57            = one_one_nat ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( power_power_nat @ zero_zero_nat @ N )
% 8.57/4.57            = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3692_power__gt1,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 8.57/4.57       => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3693_power__gt1,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.57/4.57       => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3694_power__gt1,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.57       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3695_power__gt1,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ A )
% 8.57/4.57       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3696_power__gt1,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ one_one_int @ A )
% 8.57/4.57       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3697_power__less__imp__less__exp,axiom,
% 8.57/4.57      ! [A: code_natural,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 8.57/4.57       => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 8.57/4.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3698_power__less__imp__less__exp,axiom,
% 8.57/4.57      ! [A: code_integer,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.57/4.57       => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 8.57/4.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3699_power__less__imp__less__exp,axiom,
% 8.57/4.57      ! [A: rat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.57       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 8.57/4.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3700_power__less__imp__less__exp,axiom,
% 8.57/4.57      ! [A: nat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ A )
% 8.57/4.57       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 8.57/4.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3701_power__less__imp__less__exp,axiom,
% 8.57/4.57      ! [A: int,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ one_one_int @ A )
% 8.57/4.57       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 8.57/4.57         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3702_power__strict__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: code_natural] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 8.57/4.57         => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3703_power__strict__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: code_integer] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.57/4.57         => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3704_power__strict__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: rat] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.57         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3705_power__strict__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: nat] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_nat @ one_one_nat @ A )
% 8.57/4.57         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3706_power__strict__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: int] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_int @ one_one_int @ A )
% 8.57/4.57         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3707_power__minus,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 8.57/4.57        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3708_power__minus,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3709_power__minus,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 8.57/4.57        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3710_power__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: code_integer] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 8.57/4.57         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3711_power__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: code_natural] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ A )
% 8.57/4.57         => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3712_power__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: rat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.57/4.57         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3713_power__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 8.57/4.57         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3714_power__increasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: int] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_eq_int @ one_one_int @ A )
% 8.57/4.57         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3715_zero__power,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 8.57/4.57          = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3716_zero__power,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( power_power_rat @ zero_zero_rat @ N )
% 8.57/4.57          = zero_zero_rat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3717_zero__power,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N )
% 8.57/4.57          = zero_z2226904508553997617atural ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3718_zero__power,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( power_power_int @ zero_zero_int @ N )
% 8.57/4.57          = zero_zero_int ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3719_zero__power,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( power_power_nat @ zero_zero_nat @ N )
% 8.57/4.57          = zero_zero_nat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3720_zero__le__power__abs,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3721_zero__le__power__abs,axiom,
% 8.57/4.57      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3722_zero__le__power__abs,axiom,
% 8.57/4.57      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3723_fact__less__mono,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.57       => ( ( ord_less_nat @ M @ N )
% 8.57/4.57         => ( ord_le6747313008572928689nteger @ ( semiri3624122377584611663nteger @ M ) @ ( semiri3624122377584611663nteger @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3724_fact__less__mono,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.57       => ( ( ord_less_nat @ M @ N )
% 8.57/4.57         => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3725_fact__less__mono,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.57       => ( ( ord_less_nat @ M @ N )
% 8.57/4.57         => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3726_fact__less__mono,axiom,
% 8.57/4.57      ! [M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.57       => ( ( ord_less_nat @ M @ N )
% 8.57/4.57         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3727_pochhammer__nonneg,axiom,
% 8.57/4.57      ! [X2: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ X2 )
% 8.57/4.57       => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( comm_s7406298101470620109atural @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3728_pochhammer__nonneg,axiom,
% 8.57/4.57      ! [X2: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X2 )
% 8.57/4.57       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( comm_s8582702949713902594nteger @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3729_pochhammer__nonneg,axiom,
% 8.57/4.57      ! [X2: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 8.57/4.57       => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3730_pochhammer__nonneg,axiom,
% 8.57/4.57      ! [X2: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 8.57/4.57       => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3731_pochhammer__nonneg,axiom,
% 8.57/4.57      ! [X2: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ X2 )
% 8.57/4.57       => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3732_pochhammer__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 8.57/4.57            = one_one_nat ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 8.57/4.57            = zero_zero_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3733_pochhammer__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 8.57/4.57            = one_one_int ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 8.57/4.57            = zero_zero_int ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3734_pochhammer__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 8.57/4.57            = one_one_Code_integer ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 8.57/4.57            = zero_z3403309356797280102nteger ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3735_pochhammer__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 8.57/4.57            = one_one_rat ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 8.57/4.57            = zero_zero_rat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3736_pochhammer__0__left,axiom,
% 8.57/4.57      ! [N: nat] :
% 8.57/4.57        ( ( ( N = zero_zero_nat )
% 8.57/4.57         => ( ( comm_s7406298101470620109atural @ zero_z2226904508553997617atural @ N )
% 8.57/4.57            = one_one_Code_natural ) )
% 8.57/4.57        & ( ( N != zero_zero_nat )
% 8.57/4.57         => ( ( comm_s7406298101470620109atural @ zero_z2226904508553997617atural @ N )
% 8.57/4.57            = zero_z2226904508553997617atural ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3737_Suc__times__gbinomial,axiom,
% 8.57/4.57      ! [K: nat,A: rat] :
% 8.57/4.57        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 8.57/4.57        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3738_gbinomial__absorption,axiom,
% 8.57/4.57      ! [K: nat,A: rat] :
% 8.57/4.57        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 8.57/4.57        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3739_gbinomial__trinomial__revision,axiom,
% 8.57/4.57      ! [K: nat,M: nat,A: rat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ K @ M )
% 8.57/4.57       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 8.57/4.57          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3740_power__Suc__less,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57       => ( ( ord_le5570908160329646204atural @ A @ one_one_Code_natural )
% 8.57/4.57         => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3741_power__Suc__less,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57       => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 8.57/4.57         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3742_power__Suc__less,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.57       => ( ( ord_less_rat @ A @ one_one_rat )
% 8.57/4.57         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3743_power__Suc__less,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.57       => ( ( ord_less_nat @ A @ one_one_nat )
% 8.57/4.57         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3744_power__Suc__less,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.57       => ( ( ord_less_int @ A @ one_one_int )
% 8.57/4.57         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3745_power__Suc__le__self,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 8.57/4.57         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3746_power__Suc__le__self,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 8.57/4.57         => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3747_power__Suc__le__self,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.57/4.57         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3748_power__Suc__le__self,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.57/4.57         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3749_power__Suc__le__self,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57       => ( ( ord_less_eq_int @ A @ one_one_int )
% 8.57/4.57         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3750_power__Suc__less__one,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57       => ( ( ord_le5570908160329646204atural @ A @ one_one_Code_natural )
% 8.57/4.57         => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) @ one_one_Code_natural ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3751_power__Suc__less__one,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57       => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 8.57/4.57         => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3752_power__Suc__less__one,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.57       => ( ( ord_less_rat @ A @ one_one_rat )
% 8.57/4.57         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3753_power__Suc__less__one,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.57       => ( ( ord_less_nat @ A @ one_one_nat )
% 8.57/4.57         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3754_power__Suc__less__one,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.57       => ( ( ord_less_int @ A @ one_one_int )
% 8.57/4.57         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3755_power__strict__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: code_natural] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57         => ( ( ord_le5570908160329646204atural @ A @ one_one_Code_natural )
% 8.57/4.57           => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N4 ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3756_power__strict__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: code_integer] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57         => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 8.57/4.57           => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3757_power__strict__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: rat] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.57/4.57         => ( ( ord_less_rat @ A @ one_one_rat )
% 8.57/4.57           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3758_power__strict__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: nat] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.57/4.57         => ( ( ord_less_nat @ A @ one_one_nat )
% 8.57/4.57           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3759_power__strict__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: int] :
% 8.57/4.57        ( ( ord_less_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_int @ zero_zero_int @ A )
% 8.57/4.57         => ( ( ord_less_int @ A @ one_one_int )
% 8.57/4.57           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3760_power__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: code_integer] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57         => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 8.57/4.57           => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3761_power__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: code_natural] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57         => ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 8.57/4.57           => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N4 ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3762_power__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: rat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.57/4.57           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3763_power__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.57/4.57           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3764_power__decreasing,axiom,
% 8.57/4.57      ! [N: nat,N4: nat,A: int] :
% 8.57/4.57        ( ( ord_less_eq_nat @ N @ N4 )
% 8.57/4.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57         => ( ( ord_less_eq_int @ A @ one_one_int )
% 8.57/4.57           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3765_power__eq__imp__eq__base,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat,B: code_integer] :
% 8.57/4.57        ( ( ( power_8256067586552552935nteger @ A @ N )
% 8.57/4.57          = ( power_8256067586552552935nteger @ B @ N ) )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57             => ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3766_power__eq__imp__eq__base,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat,B: code_natural] :
% 8.57/4.57        ( ( ( power_7079662738309270450atural @ A @ N )
% 8.57/4.57          = ( power_7079662738309270450atural @ B @ N ) )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57             => ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3767_power__eq__imp__eq__base,axiom,
% 8.57/4.57      ! [A: rat,N: nat,B: rat] :
% 8.57/4.57        ( ( ( power_power_rat @ A @ N )
% 8.57/4.57          = ( power_power_rat @ B @ N ) )
% 8.57/4.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57             => ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3768_power__eq__imp__eq__base,axiom,
% 8.57/4.57      ! [A: nat,N: nat,B: nat] :
% 8.57/4.57        ( ( ( power_power_nat @ A @ N )
% 8.57/4.57          = ( power_power_nat @ B @ N ) )
% 8.57/4.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57             => ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3769_power__eq__imp__eq__base,axiom,
% 8.57/4.57      ! [A: int,N: nat,B: int] :
% 8.57/4.57        ( ( ( power_power_int @ A @ N )
% 8.57/4.57          = ( power_power_int @ B @ N ) )
% 8.57/4.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.57           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57             => ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3770_power__eq__iff__eq__base,axiom,
% 8.57/4.57      ! [N: nat,A: code_integer,B: code_integer] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.57           => ( ( ( power_8256067586552552935nteger @ A @ N )
% 8.57/4.57                = ( power_8256067586552552935nteger @ B @ N ) )
% 8.57/4.57              = ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3771_power__eq__iff__eq__base,axiom,
% 8.57/4.57      ! [N: nat,A: code_natural,B: code_natural] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57         => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 8.57/4.57           => ( ( ( power_7079662738309270450atural @ A @ N )
% 8.57/4.57                = ( power_7079662738309270450atural @ B @ N ) )
% 8.57/4.57              = ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3772_power__eq__iff__eq__base,axiom,
% 8.57/4.57      ! [N: nat,A: rat,B: rat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.57/4.57           => ( ( ( power_power_rat @ A @ N )
% 8.57/4.57                = ( power_power_rat @ B @ N ) )
% 8.57/4.57              = ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3773_power__eq__iff__eq__base,axiom,
% 8.57/4.57      ! [N: nat,A: nat,B: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.57/4.57           => ( ( ( power_power_nat @ A @ N )
% 8.57/4.57                = ( power_power_nat @ B @ N ) )
% 8.57/4.57              = ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3774_power__eq__iff__eq__base,axiom,
% 8.57/4.57      ! [N: nat,A: int,B: int] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.57/4.57           => ( ( ( power_power_int @ A @ N )
% 8.57/4.57                = ( power_power_int @ B @ N ) )
% 8.57/4.57              = ( A = B ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3775_power__le__imp__le__exp,axiom,
% 8.57/4.57      ! [A: code_natural,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 8.57/4.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3776_power__le__imp__le__exp,axiom,
% 8.57/4.57      ! [A: code_integer,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 8.57/4.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3777_power__le__imp__le__exp,axiom,
% 8.57/4.57      ! [A: rat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.57       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 8.57/4.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3778_power__le__imp__le__exp,axiom,
% 8.57/4.57      ! [A: nat,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ A )
% 8.57/4.57       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 8.57/4.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3779_power__le__imp__le__exp,axiom,
% 8.57/4.57      ! [A: int,M: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ one_one_int @ A )
% 8.57/4.57       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 8.57/4.57         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3780_self__le__power,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3781_self__le__power,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_le1926595141338095240atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3782_self__le__power,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3783_self__le__power,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3784_self__le__power,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_int @ one_one_int @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3785_one__less__power,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3786_one__less__power,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3787_one__less__power,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ one_one_rat @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3788_one__less__power,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ one_one_nat @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3789_one__less__power,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ one_one_int @ A )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3790_power__diff,axiom,
% 8.57/4.57      ! [A: nat,N: nat,M: nat] :
% 8.57/4.57        ( ( A != zero_zero_nat )
% 8.57/4.57       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.57            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3791_power__diff,axiom,
% 8.57/4.57      ! [A: int,N: nat,M: nat] :
% 8.57/4.57        ( ( A != zero_zero_int )
% 8.57/4.57       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.57            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3792_power__diff,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat,M: nat] :
% 8.57/4.57        ( ( A != zero_z3403309356797280102nteger )
% 8.57/4.57       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57         => ( ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.57            = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3793_power__diff,axiom,
% 8.57/4.57      ! [A: rat,N: nat,M: nat] :
% 8.57/4.57        ( ( A != zero_zero_rat )
% 8.57/4.57       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.57            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3794_power__diff,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat,M: nat] :
% 8.57/4.57        ( ( A != zero_z2226904508553997617atural )
% 8.57/4.57       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57         => ( ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.57            = ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3795_pochhammer__rec,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( comm_s7406298101470620109atural @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_2397367101498566445atural @ A @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3796_pochhammer__rec,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3797_pochhammer__rec,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3798_pochhammer__rec,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3799_pochhammer__rec,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3800_pochhammer__Suc,axiom,
% 8.57/4.57      ! [A: int,N: nat] :
% 8.57/4.57        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3801_pochhammer__Suc,axiom,
% 8.57/4.57      ! [A: nat,N: nat] :
% 8.57/4.57        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3802_pochhammer__Suc,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat] :
% 8.57/4.57        ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3803_pochhammer__Suc,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3804_pochhammer__Suc,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat] :
% 8.57/4.57        ( ( comm_s7406298101470620109atural @ A @ ( suc @ N ) )
% 8.57/4.57        = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ A @ N ) @ ( plus_p4538020629002901425atural @ A @ ( semiri3763490453095760265atural @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3805_pochhammer__rec_H,axiom,
% 8.57/4.57      ! [Z2: int,N: nat] :
% 8.57/4.57        ( ( comm_s4660882817536571857er_int @ Z2 @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3806_pochhammer__rec_H,axiom,
% 8.57/4.57      ! [Z2: nat,N: nat] :
% 8.57/4.57        ( ( comm_s4663373288045622133er_nat @ Z2 @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3807_pochhammer__rec_H,axiom,
% 8.57/4.57      ! [Z2: code_integer,N: nat] :
% 8.57/4.57        ( ( comm_s8582702949713902594nteger @ Z2 @ ( suc @ N ) )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z2 @ ( semiri4939895301339042750nteger @ N ) ) @ ( comm_s8582702949713902594nteger @ Z2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3808_pochhammer__rec_H,axiom,
% 8.57/4.57      ! [Z2: rat,N: nat] :
% 8.57/4.57        ( ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N ) )
% 8.57/4.57        = ( times_times_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3809_pochhammer__rec_H,axiom,
% 8.57/4.57      ! [Z2: code_natural,N: nat] :
% 8.57/4.57        ( ( comm_s7406298101470620109atural @ Z2 @ ( suc @ N ) )
% 8.57/4.57        = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ Z2 @ ( semiri3763490453095760265atural @ N ) ) @ ( comm_s7406298101470620109atural @ Z2 @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3810_pochhammer__eq__0__iff,axiom,
% 8.57/4.57      ! [A: rat,N: nat] :
% 8.57/4.57        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 8.57/4.57          = zero_zero_rat )
% 8.57/4.57        = ( ? [K2: nat] :
% 8.57/4.57              ( ( ord_less_nat @ K2 @ N )
% 8.57/4.57              & ( A
% 8.57/4.57                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3811_pochhammer__of__nat__eq__0__iff,axiom,
% 8.57/4.57      ! [N: nat,K: nat] :
% 8.57/4.57        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 8.57/4.57          = zero_zero_int )
% 8.57/4.57        = ( ord_less_nat @ N @ K ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3812_pochhammer__of__nat__eq__0__iff,axiom,
% 8.57/4.57      ! [N: nat,K: nat] :
% 8.57/4.57        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 8.57/4.57          = zero_z3403309356797280102nteger )
% 8.57/4.57        = ( ord_less_nat @ N @ K ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3813_pochhammer__of__nat__eq__0__iff,axiom,
% 8.57/4.57      ! [N: nat,K: nat] :
% 8.57/4.57        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 8.57/4.57          = zero_zero_rat )
% 8.57/4.57        = ( ord_less_nat @ N @ K ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3814_pochhammer__of__nat__eq__0__lemma,axiom,
% 8.57/4.57      ! [N: nat,K: nat] :
% 8.57/4.57        ( ( ord_less_nat @ N @ K )
% 8.57/4.57       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 8.57/4.57          = zero_zero_int ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3815_pochhammer__of__nat__eq__0__lemma,axiom,
% 8.57/4.57      ! [N: nat,K: nat] :
% 8.57/4.57        ( ( ord_less_nat @ N @ K )
% 8.57/4.57       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 8.57/4.57          = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3816_pochhammer__of__nat__eq__0__lemma,axiom,
% 8.57/4.57      ! [N: nat,K: nat] :
% 8.57/4.57        ( ( ord_less_nat @ N @ K )
% 8.57/4.57       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 8.57/4.57          = zero_zero_rat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3817_gbinomial__rec,axiom,
% 8.57/4.57      ! [A: rat,K: nat] :
% 8.57/4.57        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 8.57/4.57        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3818_gbinomial__factors,axiom,
% 8.57/4.57      ! [A: rat,K: nat] :
% 8.57/4.57        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 8.57/4.57        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3819_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 8.57/4.57      ! [K: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.57       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 8.57/4.57         != zero_zero_int ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3820_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 8.57/4.57      ! [K: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.57       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 8.57/4.57         != zero_z3403309356797280102nteger ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3821_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 8.57/4.57      ! [K: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.57       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 8.57/4.57         != zero_zero_rat ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3822_pochhammer__product_H,axiom,
% 8.57/4.57      ! [Z2: int,N: nat,M: nat] :
% 8.57/4.57        ( ( comm_s4660882817536571857er_int @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 8.57/4.57        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3823_pochhammer__product_H,axiom,
% 8.57/4.57      ! [Z2: nat,N: nat,M: nat] :
% 8.57/4.57        ( ( comm_s4663373288045622133er_nat @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 8.57/4.57        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3824_pochhammer__product_H,axiom,
% 8.57/4.57      ! [Z2: code_integer,N: nat,M: nat] :
% 8.57/4.57        ( ( comm_s8582702949713902594nteger @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z2 @ N ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z2 @ ( semiri4939895301339042750nteger @ N ) ) @ M ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3825_pochhammer__product_H,axiom,
% 8.57/4.57      ! [Z2: rat,N: nat,M: nat] :
% 8.57/4.57        ( ( comm_s4028243227959126397er_rat @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 8.57/4.57        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3826_pochhammer__product_H,axiom,
% 8.57/4.57      ! [Z2: code_natural,N: nat,M: nat] :
% 8.57/4.57        ( ( comm_s7406298101470620109atural @ Z2 @ ( plus_plus_nat @ N @ M ) )
% 8.57/4.57        = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ Z2 @ N ) @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ Z2 @ ( semiri3763490453095760265atural @ N ) ) @ M ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3827_power__minus_H,axiom,
% 8.57/4.57      ! [X2: int,N: nat] :
% 8.57/4.57        ( ( nO_MATCH_int_int @ one_one_int @ X2 )
% 8.57/4.57       => ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ N )
% 8.57/4.57          = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ X2 @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3828_power__minus_H,axiom,
% 8.57/4.57      ! [X2: code_integer,N: nat] :
% 8.57/4.57        ( ( nO_MAT8252062027627875367nteger @ one_one_Code_integer @ X2 )
% 8.57/4.57       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ N )
% 8.57/4.57          = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ X2 @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3829_power__minus_H,axiom,
% 8.57/4.57      ! [X2: rat,N: nat] :
% 8.57/4.57        ( ( nO_MATCH_rat_rat @ one_one_rat @ X2 )
% 8.57/4.57       => ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ N )
% 8.57/4.57          = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ X2 @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3830_power__strict__mono,axiom,
% 8.57/4.57      ! [A: code_natural,B: code_natural,N: nat] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ A @ B )
% 8.57/4.57       => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ B @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3831_power__strict__mono,axiom,
% 8.57/4.57      ! [A: code_integer,B: code_integer,N: nat] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3832_power__strict__mono,axiom,
% 8.57/4.57      ! [A: rat,B: rat,N: nat] :
% 8.57/4.57        ( ( ord_less_rat @ A @ B )
% 8.57/4.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3833_power__strict__mono,axiom,
% 8.57/4.57      ! [A: nat,B: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ A @ B )
% 8.57/4.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3834_power__strict__mono,axiom,
% 8.57/4.57      ! [A: int,B: int,N: nat] :
% 8.57/4.57        ( ( ord_less_int @ A @ B )
% 8.57/4.57       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.57         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57           => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3835_power__diff__power__eq,axiom,
% 8.57/4.57      ! [A: nat,N: nat,M: nat] :
% 8.57/4.57        ( ( A != zero_zero_nat )
% 8.57/4.57       => ( ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 8.57/4.57              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 8.57/4.57          & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.57/4.57           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 8.57/4.57              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3836_power__diff__power__eq,axiom,
% 8.57/4.57      ! [A: int,N: nat,M: nat] :
% 8.57/4.57        ( ( A != zero_zero_int )
% 8.57/4.57       => ( ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 8.57/4.57              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 8.57/4.57          & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.57/4.57           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 8.57/4.57              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3837_power__diff__power__eq,axiom,
% 8.57/4.57      ! [A: code_integer,N: nat,M: nat] :
% 8.57/4.57        ( ( A != zero_z3403309356797280102nteger )
% 8.57/4.57       => ( ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 8.57/4.57              = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 8.57/4.57          & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.57/4.57           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 8.57/4.57              = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3838_power__diff__power__eq,axiom,
% 8.57/4.57      ! [A: code_natural,N: nat,M: nat] :
% 8.57/4.57        ( ( A != zero_z2226904508553997617atural )
% 8.57/4.57       => ( ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.57           => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 8.57/4.57              = ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 8.57/4.57          & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.57/4.57           => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 8.57/4.57              = ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3839_power__eq__if,axiom,
% 8.57/4.57      ( power_7079662738309270450atural
% 8.57/4.57      = ( ^ [P6: code_natural,M2: nat] : ( if_Code_natural @ ( M2 = zero_zero_nat ) @ one_one_Code_natural @ ( times_2397367101498566445atural @ P6 @ ( power_7079662738309270450atural @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3840_power__eq__if,axiom,
% 8.57/4.57      ( power_8256067586552552935nteger
% 8.57/4.57      = ( ^ [P6: code_integer,M2: nat] : ( if_Code_integer @ ( M2 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P6 @ ( power_8256067586552552935nteger @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3841_power__eq__if,axiom,
% 8.57/4.57      ( power_power_rat
% 8.57/4.57      = ( ^ [P6: rat,M2: nat] : ( if_rat @ ( M2 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3842_power__eq__if,axiom,
% 8.57/4.57      ( power_power_nat
% 8.57/4.57      = ( ^ [P6: nat,M2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3843_power__eq__if,axiom,
% 8.57/4.57      ( power_power_int
% 8.57/4.57      = ( ^ [P6: int,M2: nat] : ( if_int @ ( M2 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3844_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.57/4.57      ! [K: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.57       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 8.57/4.57          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3845_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.57/4.57      ! [K: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.57       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 8.57/4.57          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3846_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.57/4.57      ! [K: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.57       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 8.57/4.57          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3847_power__minus__mult,axiom,
% 8.57/4.57      ! [N: nat,A: code_integer] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.57/4.57          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3848_power__minus__mult,axiom,
% 8.57/4.57      ! [N: nat,A: rat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.57/4.57          = ( power_power_rat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3849_power__minus__mult,axiom,
% 8.57/4.57      ! [N: nat,A: nat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.57/4.57          = ( power_power_nat @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3850_power__minus__mult,axiom,
% 8.57/4.57      ! [N: nat,A: int] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.57/4.57          = ( power_power_int @ A @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3851_gbinomial__reduce__nat,axiom,
% 8.57/4.57      ! [K: nat,A: rat] :
% 8.57/4.57        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.57       => ( ( gbinomial_rat @ A @ K )
% 8.57/4.57          = ( 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 ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3852_pochhammer__product,axiom,
% 8.57/4.57      ! [M: nat,N: nat,Z2: int] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ( comm_s4660882817536571857er_int @ Z2 @ N )
% 8.57/4.57          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3853_pochhammer__product,axiom,
% 8.57/4.57      ! [M: nat,N: nat,Z2: nat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ( comm_s4663373288045622133er_nat @ Z2 @ N )
% 8.57/4.57          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3854_pochhammer__product,axiom,
% 8.57/4.57      ! [M: nat,N: nat,Z2: code_integer] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ( comm_s8582702949713902594nteger @ Z2 @ N )
% 8.57/4.57          = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z2 @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z2 @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3855_pochhammer__product,axiom,
% 8.57/4.57      ! [M: nat,N: nat,Z2: rat] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ( comm_s4028243227959126397er_rat @ Z2 @ N )
% 8.57/4.57          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3856_pochhammer__product,axiom,
% 8.57/4.57      ! [M: nat,N: nat,Z2: code_natural] :
% 8.57/4.57        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.57       => ( ( comm_s7406298101470620109atural @ Z2 @ N )
% 8.57/4.57          = ( times_2397367101498566445atural @ ( comm_s7406298101470620109atural @ Z2 @ M ) @ ( comm_s7406298101470620109atural @ ( plus_p4538020629002901425atural @ Z2 @ ( semiri3763490453095760265atural @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3857_fact__num__eq__if,axiom,
% 8.57/4.57      ( semiri1406184849735516958ct_int
% 8.57/4.57      = ( ^ [M2: nat] : ( if_int @ ( M2 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3858_fact__num__eq__if,axiom,
% 8.57/4.57      ( semiri3624122377584611663nteger
% 8.57/4.57      = ( ^ [M2: nat] : ( if_Code_integer @ ( M2 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3859_fact__num__eq__if,axiom,
% 8.57/4.57      ( semiri773545260158071498ct_rat
% 8.57/4.57      = ( ^ [M2: nat] : ( if_rat @ ( M2 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3860_fact__num__eq__if,axiom,
% 8.57/4.57      ( semiri2447717529341329178atural
% 8.57/4.57      = ( ^ [M2: nat] : ( if_Code_natural @ ( M2 = zero_zero_nat ) @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri2447717529341329178atural @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3861_fact__num__eq__if,axiom,
% 8.57/4.57      ( semiri1408675320244567234ct_nat
% 8.57/4.57      = ( ^ [M2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3862_gbinomial__code,axiom,
% 8.57/4.57      ( gbinomial_rat
% 8.57/4.57      = ( ^ [A2: rat,K2: nat] :
% 8.57/4.57            ( if_rat @ ( K2 = zero_zero_nat ) @ one_one_rat
% 8.57/4.57            @ ( divide_divide_rat
% 8.57/4.57              @ ( set_fo1949268297981939178at_rat
% 8.57/4.57                @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A2 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 8.57/4.57                @ zero_zero_nat
% 8.57/4.57                @ ( minus_minus_nat @ K2 @ one_one_nat )
% 8.57/4.57                @ one_one_rat )
% 8.57/4.57              @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3863_pochhammer__code,axiom,
% 8.57/4.57      ( comm_s4660882817536571857er_int
% 8.57/4.57      = ( ^ [A2: int,N3: nat] :
% 8.57/4.57            ( if_int @ ( N3 = zero_zero_nat ) @ one_one_int
% 8.57/4.57            @ ( set_fo2581907887559384638at_int
% 8.57/4.57              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A2 @ ( semiri1314217659103216013at_int @ O ) ) )
% 8.57/4.57              @ zero_zero_nat
% 8.57/4.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 8.57/4.57              @ one_one_int ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3864_pochhammer__code,axiom,
% 8.57/4.57      ( comm_s8582702949713902594nteger
% 8.57/4.57      = ( ^ [A2: code_integer,N3: nat] :
% 8.57/4.57            ( if_Code_integer @ ( N3 = zero_zero_nat ) @ one_one_Code_integer
% 8.57/4.57            @ ( set_fo1084959871951514735nteger
% 8.57/4.57              @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ ( semiri4939895301339042750nteger @ O ) ) )
% 8.57/4.57              @ zero_zero_nat
% 8.57/4.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 8.57/4.57              @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3865_pochhammer__code,axiom,
% 8.57/4.57      ( comm_s4028243227959126397er_rat
% 8.57/4.57      = ( ^ [A2: rat,N3: nat] :
% 8.57/4.57            ( if_rat @ ( N3 = zero_zero_nat ) @ one_one_rat
% 8.57/4.57            @ ( set_fo1949268297981939178at_rat
% 8.57/4.57              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A2 @ ( semiri681578069525770553at_rat @ O ) ) )
% 8.57/4.57              @ zero_zero_nat
% 8.57/4.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 8.57/4.57              @ one_one_rat ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3866_pochhammer__code,axiom,
% 8.57/4.57      ( comm_s7406298101470620109atural
% 8.57/4.57      = ( ^ [A2: code_natural,N3: nat] :
% 8.57/4.57            ( if_Code_natural @ ( N3 = zero_zero_nat ) @ one_one_Code_natural
% 8.57/4.57            @ ( set_fo9131927060563008058atural
% 8.57/4.57              @ ^ [O: nat] : ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A2 @ ( semiri3763490453095760265atural @ O ) ) )
% 8.57/4.57              @ zero_zero_nat
% 8.57/4.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 8.57/4.57              @ one_one_Code_natural ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3867_pochhammer__code,axiom,
% 8.57/4.57      ( comm_s4663373288045622133er_nat
% 8.57/4.57      = ( ^ [A2: nat,N3: nat] :
% 8.57/4.57            ( if_nat @ ( N3 = zero_zero_nat ) @ one_one_nat
% 8.57/4.57            @ ( set_fo2584398358068434914at_nat
% 8.57/4.57              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A2 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 8.57/4.57              @ zero_zero_nat
% 8.57/4.57              @ ( minus_minus_nat @ N3 @ one_one_nat )
% 8.57/4.57              @ one_one_nat ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3868_slice__nth,axiom,
% 8.57/4.57      ! [From: nat,To: nat,Xs: list_nat,I: nat] :
% 8.57/4.57        ( ( ord_less_nat @ From @ To )
% 8.57/4.57       => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 8.57/4.57         => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 8.57/4.57           => ( ( nth_nat @ ( slice_nat @ From @ To @ Xs ) @ I )
% 8.57/4.57              = ( nth_nat @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3869_slice__nth,axiom,
% 8.57/4.57      ! [From: nat,To: nat,Xs: list_int,I: nat] :
% 8.57/4.57        ( ( ord_less_nat @ From @ To )
% 8.57/4.57       => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 8.57/4.57         => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 8.57/4.57           => ( ( nth_int @ ( slice_int @ From @ To @ Xs ) @ I )
% 8.57/4.57              = ( nth_int @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3870_slice__nth,axiom,
% 8.57/4.57      ! [From: nat,To: nat,Xs: list_o,I: nat] :
% 8.57/4.57        ( ( ord_less_nat @ From @ To )
% 8.57/4.57       => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 8.57/4.57         => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 8.57/4.57           => ( ( nth_o @ ( slice_o @ From @ To @ Xs ) @ I )
% 8.57/4.57              = ( nth_o @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3871_split__pos__lemma,axiom,
% 8.57/4.57      ! [K: int,P: int > int > $o,N: int] :
% 8.57/4.57        ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.57       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 8.57/4.57          = ( ! [I2: int,J3: int] :
% 8.57/4.57                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 8.57/4.57                  & ( ord_less_int @ J3 @ K )
% 8.57/4.57                  & ( N
% 8.57/4.57                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 8.57/4.57               => ( P @ I2 @ J3 ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3872_split__neg__lemma,axiom,
% 8.57/4.57      ! [K: int,P: int > int > $o,N: int] :
% 8.57/4.57        ( ( ord_less_int @ K @ zero_zero_int )
% 8.57/4.57       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 8.57/4.57          = ( ! [I2: int,J3: int] :
% 8.57/4.57                ( ( ( ord_less_int @ K @ J3 )
% 8.57/4.57                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 8.57/4.57                  & ( N
% 8.57/4.57                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 8.57/4.57               => ( P @ I2 @ J3 ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3873_verit__le__mono__div__int,axiom,
% 8.57/4.57      ! [A4: int,B4: int,N: int] :
% 8.57/4.57        ( ( ord_less_int @ A4 @ B4 )
% 8.57/4.57       => ( ( ord_less_int @ zero_zero_int @ N )
% 8.57/4.57         => ( ord_less_eq_int
% 8.57/4.57            @ ( plus_plus_int @ ( divide_divide_int @ A4 @ N )
% 8.57/4.57              @ ( if_int
% 8.57/4.57                @ ( ( modulo_modulo_int @ B4 @ N )
% 8.57/4.57                  = zero_zero_int )
% 8.57/4.57                @ one_one_int
% 8.57/4.57                @ zero_zero_int ) )
% 8.57/4.57            @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3874_verit__le__mono__div,axiom,
% 8.57/4.57      ! [A4: nat,B4: nat,N: nat] :
% 8.57/4.57        ( ( ord_less_nat @ A4 @ B4 )
% 8.57/4.57       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.57         => ( ord_less_eq_nat
% 8.57/4.57            @ ( plus_plus_nat @ ( divide_divide_nat @ A4 @ N )
% 8.57/4.57              @ ( if_nat
% 8.57/4.57                @ ( ( modulo_modulo_nat @ B4 @ N )
% 8.57/4.57                  = zero_zero_nat )
% 8.57/4.57                @ one_one_nat
% 8.57/4.57                @ zero_zero_nat ) )
% 8.57/4.57            @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3875_le__divide__eq__numeral_I2_J,axiom,
% 8.57/4.57      ! [W2: num,B: rat,C: rat] :
% 8.57/4.57        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.57        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.57           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 8.57/4.57          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.57           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.57               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 8.57/4.57              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.57               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3876_numeral__eq__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ( numeral_numeral_int @ M )
% 8.57/4.57          = ( numeral_numeral_int @ N ) )
% 8.57/4.57        = ( M = N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3877_numeral__eq__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ( numeral_numeral_nat @ M )
% 8.57/4.57          = ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( M = N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3878_numeral__eq__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ( numera6620942414471956472nteger @ M )
% 8.57/4.57          = ( numera6620942414471956472nteger @ N ) )
% 8.57/4.57        = ( M = N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3879_numeral__eq__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ( numeral_numeral_rat @ M )
% 8.57/4.57          = ( numeral_numeral_rat @ N ) )
% 8.57/4.57        = ( M = N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3880_numeral__eq__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ( numera5444537566228673987atural @ M )
% 8.57/4.57          = ( numera5444537566228673987atural @ N ) )
% 8.57/4.57        = ( M = N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3881_int__eq__iff__numeral,axiom,
% 8.57/4.57      ! [M: nat,V: num] :
% 8.57/4.57        ( ( ( semiri1314217659103216013at_int @ M )
% 8.57/4.57          = ( numeral_numeral_int @ V ) )
% 8.57/4.57        = ( M
% 8.57/4.57          = ( numeral_numeral_nat @ V ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3882_nat__numeral,axiom,
% 8.57/4.57      ! [K: num] :
% 8.57/4.57        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 8.57/4.57        = ( numeral_numeral_nat @ K ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3883_numeral__le__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.57        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3884_numeral__le__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 8.57/4.57        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3885_numeral__le__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 8.57/4.57        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3886_numeral__le__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3887_numeral__le__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.57        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3888_numeral__less__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.57        = ( ord_less_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3889_numeral__less__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( ord_less_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3890_numeral__less__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.57        = ( ord_less_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3891_numeral__less__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 8.57/4.57        = ( ord_less_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3892_numeral__less__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 8.57/4.57        = ( ord_less_num @ M @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3893_numeral__plus__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.57        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3894_numeral__plus__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3895_numeral__plus__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.57        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3896_numeral__plus__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 8.57/4.57        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3897_numeral__plus__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 8.57/4.57        = ( numera5444537566228673987atural @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3898_add__numeral__left,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: int] :
% 8.57/4.57        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3899_add__numeral__left,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: nat] :
% 8.57/4.57        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3900_add__numeral__left,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: code_integer] :
% 8.57/4.57        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3901_add__numeral__left,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: rat] :
% 8.57/4.57        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3902_add__numeral__left,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: code_natural] :
% 8.57/4.57        ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ ( plus_plus_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3903_numeral__times__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.57        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3904_numeral__times__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3905_numeral__times__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.57        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3906_numeral__times__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 8.57/4.57        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3907_numeral__times__numeral,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 8.57/4.57        = ( numera5444537566228673987atural @ ( times_times_num @ M @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3908_mult__numeral__left__semiring__numeral,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: int] :
% 8.57/4.57        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3909_mult__numeral__left__semiring__numeral,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: nat] :
% 8.57/4.57        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3910_mult__numeral__left__semiring__numeral,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: code_integer] :
% 8.57/4.57        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3911_mult__numeral__left__semiring__numeral,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: rat] :
% 8.57/4.57        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3912_mult__numeral__left__semiring__numeral,axiom,
% 8.57/4.57      ! [V: num,W2: num,Z2: code_natural] :
% 8.57/4.57        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ W2 ) @ Z2 ) )
% 8.57/4.57        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( times_times_num @ V @ W2 ) ) @ Z2 ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3913_neg__numeral__eq__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 8.57/4.57          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.57        = ( M = N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3914_neg__numeral__eq__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 8.57/4.57          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.57/4.57        = ( M = N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3915_neg__numeral__eq__iff,axiom,
% 8.57/4.57      ! [M: num,N: num] :
% 8.57/4.57        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 8.57/4.57          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.57/4.57        = ( M = N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3916_power__zero__numeral,axiom,
% 8.57/4.57      ! [K: num] :
% 8.57/4.57        ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( numeral_numeral_nat @ K ) )
% 8.57/4.57        = zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3917_power__zero__numeral,axiom,
% 8.57/4.57      ! [K: num] :
% 8.57/4.57        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 8.57/4.57        = zero_zero_rat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3918_power__zero__numeral,axiom,
% 8.57/4.57      ! [K: num] :
% 8.57/4.57        ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ ( numeral_numeral_nat @ K ) )
% 8.57/4.57        = zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3919_power__zero__numeral,axiom,
% 8.57/4.57      ! [K: num] :
% 8.57/4.57        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 8.57/4.57        = zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3920_power__zero__numeral,axiom,
% 8.57/4.57      ! [K: num] :
% 8.57/4.57        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 8.57/4.57        = zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3921_mod__self,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( modulo_modulo_int @ A @ A )
% 8.57/4.57        = zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3922_mod__self,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( modulo_modulo_nat @ A @ A )
% 8.57/4.57        = zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3923_mod__self,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( modulo364778990260209775nteger @ A @ A )
% 8.57/4.57        = zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3924_mod__self,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( modulo8411746178871703098atural @ A @ A )
% 8.57/4.57        = zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3925_mod__by__0,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3926_mod__by__0,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3927_mod__by__0,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3928_mod__by__0,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( modulo8411746178871703098atural @ A @ zero_z2226904508553997617atural )
% 8.57/4.57        = A ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3929_mod__0,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 8.57/4.57        = zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3930_mod__0,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 8.57/4.57        = zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3931_mod__0,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57        = zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3932_mod__0,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57        = zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3933_bits__mod__0,axiom,
% 8.57/4.57      ! [A: int] :
% 8.57/4.57        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 8.57/4.57        = zero_zero_int ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3934_bits__mod__0,axiom,
% 8.57/4.57      ! [A: nat] :
% 8.57/4.57        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 8.57/4.57        = zero_zero_nat ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3935_bits__mod__0,axiom,
% 8.57/4.57      ! [A: code_integer] :
% 8.57/4.57        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.57        = zero_z3403309356797280102nteger ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3936_bits__mod__0,axiom,
% 8.57/4.57      ! [A: code_natural] :
% 8.57/4.57        ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 8.57/4.57        = zero_z2226904508553997617atural ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3937_power__add__numeral,axiom,
% 8.57/4.57      ! [A: code_integer,M: num,N: num] :
% 8.57/4.57        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.57/4.57        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3938_power__add__numeral,axiom,
% 8.57/4.57      ! [A: rat,M: num,N: num] :
% 8.57/4.57        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.57/4.57        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3939_power__add__numeral,axiom,
% 8.57/4.57      ! [A: nat,M: num,N: num] :
% 8.57/4.57        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.57/4.57        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3940_power__add__numeral,axiom,
% 8.57/4.57      ! [A: int,M: num,N: num] :
% 8.57/4.57        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.57/4.57        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3941_power__add__numeral2,axiom,
% 8.57/4.57      ! [A: code_integer,M: num,N: num,B: code_integer] :
% 8.57/4.57        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.57/4.57        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3942_power__add__numeral2,axiom,
% 8.57/4.57      ! [A: rat,M: num,N: num,B: rat] :
% 8.57/4.57        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.57/4.57        = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3943_power__add__numeral2,axiom,
% 8.57/4.57      ! [A: nat,M: num,N: num,B: nat] :
% 8.57/4.57        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.57/4.57        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3944_power__add__numeral2,axiom,
% 8.57/4.57      ! [A: int,M: num,N: num,B: int] :
% 8.57/4.57        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.57/4.57        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3945_of__nat__numeral,axiom,
% 8.57/4.57      ! [N: num] :
% 8.57/4.57        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( numeral_numeral_int @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3946_of__nat__numeral,axiom,
% 8.57/4.57      ! [N: num] :
% 8.57/4.57        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( numeral_numeral_nat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3947_of__nat__numeral,axiom,
% 8.57/4.57      ! [N: num] :
% 8.57/4.57        ( ( semiri4939895301339042750nteger @ ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3948_of__nat__numeral,axiom,
% 8.57/4.57      ! [N: num] :
% 8.57/4.57        ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3949_of__nat__numeral,axiom,
% 8.57/4.57      ! [N: num] :
% 8.57/4.57        ( ( semiri3763490453095760265atural @ ( numeral_numeral_nat @ N ) )
% 8.57/4.57        = ( numera5444537566228673987atural @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3950_mod__add__self1,axiom,
% 8.57/4.57      ! [B: int,A: int] :
% 8.57/4.57        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.57/4.57        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3951_mod__add__self1,axiom,
% 8.57/4.57      ! [B: nat,A: nat] :
% 8.57/4.57        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.57/4.57        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3952_mod__add__self1,axiom,
% 8.57/4.57      ! [B: code_integer,A: code_integer] :
% 8.57/4.57        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 8.57/4.57        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3953_mod__add__self1,axiom,
% 8.57/4.57      ! [B: code_natural,A: code_natural] :
% 8.57/4.57        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 8.57/4.57        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3954_mod__add__self2,axiom,
% 8.57/4.57      ! [A: int,B: int] :
% 8.57/4.57        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.57/4.57        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3955_mod__add__self2,axiom,
% 8.57/4.57      ! [A: nat,B: nat] :
% 8.57/4.57        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.57/4.57        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3956_mod__add__self2,axiom,
% 8.57/4.57      ! [A: code_integer,B: code_integer] :
% 8.57/4.57        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 8.57/4.57        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3957_mod__add__self2,axiom,
% 8.57/4.57      ! [A: code_natural,B: code_natural] :
% 8.57/4.57        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 8.57/4.57        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3958_abs__numeral,axiom,
% 8.57/4.57      ! [N: num] :
% 8.57/4.57        ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 8.57/4.57        = ( numeral_numeral_int @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3959_abs__numeral,axiom,
% 8.57/4.57      ! [N: num] :
% 8.57/4.57        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.57        = ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3960_abs__numeral,axiom,
% 8.57/4.57      ! [N: num] :
% 8.57/4.57        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 8.57/4.57        = ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3961_of__int__eq__numeral__iff,axiom,
% 8.57/4.57      ! [Z2: int,N: num] :
% 8.57/4.57        ( ( ( ring_1_of_int_int @ Z2 )
% 8.57/4.57          = ( numeral_numeral_int @ N ) )
% 8.57/4.57        = ( Z2
% 8.57/4.57          = ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3962_of__int__eq__numeral__iff,axiom,
% 8.57/4.57      ! [Z2: int,N: num] :
% 8.57/4.57        ( ( ( ring_18347121197199848620nteger @ Z2 )
% 8.57/4.57          = ( numera6620942414471956472nteger @ N ) )
% 8.57/4.57        = ( Z2
% 8.57/4.57          = ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3963_of__int__eq__numeral__iff,axiom,
% 8.57/4.57      ! [Z2: int,N: num] :
% 8.57/4.57        ( ( ( ring_1_of_int_rat @ Z2 )
% 8.57/4.57          = ( numeral_numeral_rat @ N ) )
% 8.57/4.57        = ( Z2
% 8.57/4.57          = ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3964_of__int__numeral,axiom,
% 8.57/4.57      ! [K: num] :
% 8.57/4.57        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 8.57/4.57        = ( numeral_numeral_int @ K ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3965_of__int__numeral,axiom,
% 8.57/4.57      ! [K: num] :
% 8.57/4.57        ( ( ring_18347121197199848620nteger @ ( numeral_numeral_int @ K ) )
% 8.57/4.57        = ( numera6620942414471956472nteger @ K ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3966_of__int__numeral,axiom,
% 8.57/4.57      ! [K: num] :
% 8.57/4.57        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 8.57/4.57        = ( numeral_numeral_rat @ K ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3967_power__int__add__numeral,axiom,
% 8.57/4.57      ! [X2: rat,M: num,N: num] :
% 8.57/4.57        ( ( times_times_rat @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ M ) ) @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.57        = ( power_int_rat @ X2 @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3968_power__int__add__numeral2,axiom,
% 8.57/4.57      ! [X2: rat,M: num,N: num,B: rat] :
% 8.57/4.57        ( ( times_times_rat @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ M ) ) @ ( times_times_rat @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ N ) ) @ B ) )
% 8.57/4.57        = ( times_times_rat @ ( power_int_rat @ X2 @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.57/4.57  
% 8.57/4.57  thf(fact_3969_floor__numeral,axiom,
% 8.57/4.57      ! [V: num] :
% 8.57/4.57        ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 8.57/4.57        = ( numeral_numeral_int @ V ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3970_ceiling__numeral,axiom,
% 8.57/4.58      ! [V: num] :
% 8.57/4.58        ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 8.57/4.58        = ( numeral_numeral_int @ V ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3971_distrib__right__numeral,axiom,
% 8.57/4.58      ! [A: int,B: int,V: num] :
% 8.57/4.58        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 8.57/4.58        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3972_distrib__right__numeral,axiom,
% 8.57/4.58      ! [A: nat,B: nat,V: num] :
% 8.57/4.58        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 8.57/4.58        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3973_distrib__right__numeral,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer,V: num] :
% 8.57/4.58        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3974_distrib__right__numeral,axiom,
% 8.57/4.58      ! [A: rat,B: rat,V: num] :
% 8.57/4.58        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 8.57/4.58        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3975_distrib__right__numeral,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural,V: num] :
% 8.57/4.58        ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ ( numera5444537566228673987atural @ V ) )
% 8.57/4.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ V ) ) @ ( times_2397367101498566445atural @ B @ ( numera5444537566228673987atural @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3976_distrib__left__numeral,axiom,
% 8.57/4.58      ! [V: num,B: int,C: int] :
% 8.57/4.58        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 8.57/4.58        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3977_distrib__left__numeral,axiom,
% 8.57/4.58      ! [V: num,B: nat,C: nat] :
% 8.57/4.58        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 8.57/4.58        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3978_distrib__left__numeral,axiom,
% 8.57/4.58      ! [V: num,B: code_integer,C: code_integer] :
% 8.57/4.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3979_distrib__left__numeral,axiom,
% 8.57/4.58      ! [V: num,B: rat,C: rat] :
% 8.57/4.58        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 8.57/4.58        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3980_distrib__left__numeral,axiom,
% 8.57/4.58      ! [V: num,B: code_natural,C: code_natural] :
% 8.57/4.58        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ B @ C ) )
% 8.57/4.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ B ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3981_neg__numeral__le__iff,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.57/4.58        = ( ord_less_eq_num @ N @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3982_neg__numeral__le__iff,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.57/4.58        = ( ord_less_eq_num @ N @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3983_neg__numeral__le__iff,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58        = ( ord_less_eq_num @ N @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3984_left__diff__distrib__numeral,axiom,
% 8.57/4.58      ! [A: int,B: int,V: num] :
% 8.57/4.58        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 8.57/4.58        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3985_left__diff__distrib__numeral,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer,V: num] :
% 8.57/4.58        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 8.57/4.58        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3986_left__diff__distrib__numeral,axiom,
% 8.57/4.58      ! [A: rat,B: rat,V: num] :
% 8.57/4.58        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 8.57/4.58        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3987_right__diff__distrib__numeral,axiom,
% 8.57/4.58      ! [V: num,B: int,C: int] :
% 8.57/4.58        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 8.57/4.58        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3988_right__diff__distrib__numeral,axiom,
% 8.57/4.58      ! [V: num,B: code_integer,C: code_integer] :
% 8.57/4.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 8.57/4.58        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3989_right__diff__distrib__numeral,axiom,
% 8.57/4.58      ! [V: num,B: rat,C: rat] :
% 8.57/4.58        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 8.57/4.58        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3990_neg__numeral__less__iff,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58        = ( ord_less_num @ N @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3991_neg__numeral__less__iff,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.57/4.58        = ( ord_less_num @ N @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3992_neg__numeral__less__iff,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.57/4.58        = ( ord_less_num @ N @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3993_semiring__norm_I168_J,axiom,
% 8.57/4.58      ! [V: num,W2: num,Y: int] :
% 8.57/4.58        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 8.57/4.58        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3994_semiring__norm_I168_J,axiom,
% 8.57/4.58      ! [V: num,W2: num,Y: code_integer] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3995_semiring__norm_I168_J,axiom,
% 8.57/4.58      ! [V: num,W2: num,Y: rat] :
% 8.57/4.58        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 8.57/4.58        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3996_add__neg__numeral__simps_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3997_add__neg__numeral__simps_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3998_add__neg__numeral__simps_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_3999_mult__neg__numeral__simps_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4000_mult__neg__numeral__simps_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4001_mult__neg__numeral__simps_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4002_mult__neg__numeral__simps_I2_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4003_mult__neg__numeral__simps_I2_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4004_mult__neg__numeral__simps_I2_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4005_mult__neg__numeral__simps_I1_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4006_mult__neg__numeral__simps_I1_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.57/4.58        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4007_mult__neg__numeral__simps_I1_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.57/4.58        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4008_diff__numeral__simps_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4009_diff__numeral__simps_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4010_diff__numeral__simps_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4011_diff__numeral__simps_I2_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4012_diff__numeral__simps_I2_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.57/4.58        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4013_diff__numeral__simps_I2_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.57/4.58        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4014_mod__mult__self2__is__0,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 8.57/4.58        = zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4015_mod__mult__self2__is__0,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 8.57/4.58        = zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4016_mod__mult__self2__is__0,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 8.57/4.58        = zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4017_mod__mult__self2__is__0,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 8.57/4.58        = zero_z2226904508553997617atural ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4018_mod__mult__self1__is__0,axiom,
% 8.57/4.58      ! [B: int,A: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 8.57/4.58        = zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4019_mod__mult__self1__is__0,axiom,
% 8.57/4.58      ! [B: nat,A: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 8.57/4.58        = zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4020_mod__mult__self1__is__0,axiom,
% 8.57/4.58      ! [B: code_integer,A: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 8.57/4.58        = zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4021_mod__mult__self1__is__0,axiom,
% 8.57/4.58      ! [B: code_natural,A: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 8.57/4.58        = zero_z2226904508553997617atural ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4022_mod__by__1,axiom,
% 8.57/4.58      ! [A: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ A @ one_one_int )
% 8.57/4.58        = zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4023_mod__by__1,axiom,
% 8.57/4.58      ! [A: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 8.57/4.58        = zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4024_mod__by__1,axiom,
% 8.57/4.58      ! [A: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 8.57/4.58        = zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4025_mod__by__1,axiom,
% 8.57/4.58      ! [A: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 8.57/4.58        = zero_z2226904508553997617atural ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4026_bits__mod__by__1,axiom,
% 8.57/4.58      ! [A: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ A @ one_one_int )
% 8.57/4.58        = zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4027_bits__mod__by__1,axiom,
% 8.57/4.58      ! [A: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 8.57/4.58        = zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4028_bits__mod__by__1,axiom,
% 8.57/4.58      ! [A: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 8.57/4.58        = zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4029_bits__mod__by__1,axiom,
% 8.57/4.58      ! [A: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 8.57/4.58        = zero_z2226904508553997617atural ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4030_mod__mult__self1,axiom,
% 8.57/4.58      ! [A: int,C: int,B: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 8.57/4.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4031_mod__mult__self1,axiom,
% 8.57/4.58      ! [A: nat,C: nat,B: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 8.57/4.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4032_mod__mult__self1,axiom,
% 8.57/4.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 8.57/4.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4033_mod__mult__self1,axiom,
% 8.57/4.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 8.57/4.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4034_mod__mult__self2,axiom,
% 8.57/4.58      ! [A: int,B: int,C: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 8.57/4.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4035_mod__mult__self2,axiom,
% 8.57/4.58      ! [A: nat,B: nat,C: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 8.57/4.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4036_mod__mult__self2,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 8.57/4.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4037_mod__mult__self2,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 8.57/4.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4038_mod__mult__self3,axiom,
% 8.57/4.58      ! [C: int,B: int,A: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 8.57/4.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4039_mod__mult__self3,axiom,
% 8.57/4.58      ! [C: nat,B: nat,A: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 8.57/4.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4040_mod__mult__self3,axiom,
% 8.57/4.58      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 8.57/4.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4041_mod__mult__self3,axiom,
% 8.57/4.58      ! [C: code_natural,B: code_natural,A: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 8.57/4.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4042_mod__mult__self4,axiom,
% 8.57/4.58      ! [B: int,C: int,A: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 8.57/4.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4043_mod__mult__self4,axiom,
% 8.57/4.58      ! [B: nat,C: nat,A: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 8.57/4.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4044_mod__mult__self4,axiom,
% 8.57/4.58      ! [B: code_integer,C: code_integer,A: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 8.57/4.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4045_mod__mult__self4,axiom,
% 8.57/4.58      ! [B: code_natural,C: code_natural,A: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 8.57/4.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4046_mod__div__trivial,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 8.57/4.58        = zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4047_mod__div__trivial,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 8.57/4.58        = zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4048_mod__div__trivial,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 8.57/4.58        = zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4049_mod__div__trivial,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural] :
% 8.57/4.58        ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 8.57/4.58        = zero_z2226904508553997617atural ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4050_bits__mod__div__trivial,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 8.57/4.58        = zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4051_bits__mod__div__trivial,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 8.57/4.58        = zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4052_bits__mod__div__trivial,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 8.57/4.58        = zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4053_bits__mod__div__trivial,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural] :
% 8.57/4.58        ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 8.57/4.58        = zero_z2226904508553997617atural ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4054_abs__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58        = ( numeral_numeral_int @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4055_abs__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.57/4.58        = ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4056_abs__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.57/4.58        = ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4057_power__int__mult__distrib__numeral1,axiom,
% 8.57/4.58      ! [W2: num,Y: rat,M: int] :
% 8.57/4.58        ( ( power_int_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Y ) @ M )
% 8.57/4.58        = ( times_times_rat @ ( power_int_rat @ ( numeral_numeral_rat @ W2 ) @ M ) @ ( power_int_rat @ Y @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4058_power__int__mult__distrib__numeral2,axiom,
% 8.57/4.58      ! [X2: rat,W2: num,M: int] :
% 8.57/4.58        ( ( power_int_rat @ ( times_times_rat @ X2 @ ( numeral_numeral_rat @ W2 ) ) @ M )
% 8.57/4.58        = ( times_times_rat @ ( power_int_rat @ X2 @ M ) @ ( power_int_rat @ ( numeral_numeral_rat @ W2 ) @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4059_mod__by__Suc__0,axiom,
% 8.57/4.58      ! [M: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 8.57/4.58        = zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4060_nat__neg__numeral,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.57/4.58        = zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4061_nat__power__eq__Suc__0__iff,axiom,
% 8.57/4.58      ! [X2: nat,M: nat] :
% 8.57/4.58        ( ( ( power_power_nat @ X2 @ M )
% 8.57/4.58          = ( suc @ zero_zero_nat ) )
% 8.57/4.58        = ( ( M = zero_zero_nat )
% 8.57/4.58          | ( X2
% 8.57/4.58            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4062_power__Suc__0,axiom,
% 8.57/4.58      ! [N: nat] :
% 8.57/4.58        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.58        = ( suc @ zero_zero_nat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4063_nat__zero__less__power__iff,axiom,
% 8.57/4.58      ! [X2: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X2 @ N ) )
% 8.57/4.58        = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 8.57/4.58          | ( N = zero_zero_nat ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4064_diff__nat__numeral,axiom,
% 8.57/4.58      ! [V: num,V2: num] :
% 8.57/4.58        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V2 ) )
% 8.57/4.58        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4065_nat__eq__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ( nat2 @ Y )
% 8.57/4.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4066_numeral__power__eq__nat__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: int] :
% 8.57/4.58        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 8.57/4.58          = ( nat2 @ Y ) )
% 8.57/4.58        = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4067_dbl__simps_I1_J,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4068_dbl__simps_I1_J,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4069_dbl__simps_I1_J,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4070_le__divide__eq__numeral1_I1_J,axiom,
% 8.57/4.58      ! [A: rat,B: rat,W2: num] :
% 8.57/4.58        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 8.57/4.58        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4071_divide__le__eq__numeral1_I1_J,axiom,
% 8.57/4.58      ! [B: rat,W2: num,A: rat] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 8.57/4.58        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4072_eq__divide__eq__numeral1_I1_J,axiom,
% 8.57/4.58      ! [A: rat,B: rat,W2: num] :
% 8.57/4.58        ( ( A
% 8.57/4.58          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 8.57/4.58        = ( ( ( ( numeral_numeral_rat @ W2 )
% 8.57/4.58             != zero_zero_rat )
% 8.57/4.58           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58              = B ) )
% 8.57/4.58          & ( ( ( numeral_numeral_rat @ W2 )
% 8.57/4.58              = zero_zero_rat )
% 8.57/4.58           => ( A = zero_zero_rat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4073_divide__eq__eq__numeral1_I1_J,axiom,
% 8.57/4.58      ! [B: rat,W2: num,A: rat] :
% 8.57/4.58        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58          = A )
% 8.57/4.58        = ( ( ( ( numeral_numeral_rat @ W2 )
% 8.57/4.58             != zero_zero_rat )
% 8.57/4.58           => ( B
% 8.57/4.58              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 8.57/4.58          & ( ( ( numeral_numeral_rat @ W2 )
% 8.57/4.58              = zero_zero_rat )
% 8.57/4.58           => ( A = zero_zero_rat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4074_divide__less__eq__numeral1_I1_J,axiom,
% 8.57/4.58      ! [B: rat,W2: num,A: rat] :
% 8.57/4.58        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 8.57/4.58        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4075_less__divide__eq__numeral1_I1_J,axiom,
% 8.57/4.58      ! [A: rat,B: rat,W2: num] :
% 8.57/4.58        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 8.57/4.58        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4076_mod__minus1__right,axiom,
% 8.57/4.58      ! [A: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.58        = zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4077_mod__minus1__right,axiom,
% 8.57/4.58      ! [A: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.57/4.58        = zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4078_of__int__numeral__le__iff,axiom,
% 8.57/4.58      ! [N: num,Z2: int] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4079_of__int__numeral__le__iff,axiom,
% 8.57/4.58      ! [N: num,Z2: int] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4080_of__int__numeral__le__iff,axiom,
% 8.57/4.58      ! [N: num,Z2: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4081_of__int__le__numeral__iff,axiom,
% 8.57/4.58      ! [Z2: int,N: num] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4082_of__int__le__numeral__iff,axiom,
% 8.57/4.58      ! [Z2: int,N: num] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4083_of__int__le__numeral__iff,axiom,
% 8.57/4.58      ! [Z2: int,N: num] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4084_of__int__numeral__less__iff,axiom,
% 8.57/4.58      ! [N: num,Z2: int] :
% 8.57/4.58        ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z2 ) )
% 8.57/4.58        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4085_of__int__numeral__less__iff,axiom,
% 8.57/4.58      ! [N: num,Z2: int] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ ( ring_18347121197199848620nteger @ Z2 ) )
% 8.57/4.58        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4086_of__int__numeral__less__iff,axiom,
% 8.57/4.58      ! [N: num,Z2: int] :
% 8.57/4.58        ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z2 ) )
% 8.57/4.58        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4087_of__int__less__numeral__iff,axiom,
% 8.57/4.58      ! [Z2: int,N: num] :
% 8.57/4.58        ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.58        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4088_of__int__less__numeral__iff,axiom,
% 8.57/4.58      ! [Z2: int,N: num] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z2 ) @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.58        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4089_of__int__less__numeral__iff,axiom,
% 8.57/4.58      ! [Z2: int,N: num] :
% 8.57/4.58        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N ) )
% 8.57/4.58        = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4090_numeral__le__floor,axiom,
% 8.57/4.58      ! [V: num,X2: rat] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4091_floor__less__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 8.57/4.58        = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4092_ceiling__le__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 8.57/4.58        = ( ord_less_eq_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4093_numeral__less__ceiling,axiom,
% 8.57/4.58      ! [V: num,X2: rat] :
% 8.57/4.58        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4094_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: nat] :
% 8.57/4.58        ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 8.57/4.58          = ( semiri1314217659103216013at_int @ Y ) )
% 8.57/4.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4095_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: nat] :
% 8.57/4.58        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 8.57/4.58          = ( semiri1316708129612266289at_nat @ Y ) )
% 8.57/4.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4096_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: nat] :
% 8.57/4.58        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N )
% 8.57/4.58          = ( semiri4939895301339042750nteger @ Y ) )
% 8.57/4.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4097_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: nat] :
% 8.57/4.58        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 8.57/4.58          = ( semiri681578069525770553at_rat @ Y ) )
% 8.57/4.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4098_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: nat] :
% 8.57/4.58        ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ X2 ) @ N )
% 8.57/4.58          = ( semiri3763490453095760265atural @ Y ) )
% 8.57/4.58        = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4099_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: nat,X2: num,N: nat] :
% 8.57/4.58        ( ( ( semiri1314217659103216013at_int @ Y )
% 8.57/4.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4100_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: nat,X2: num,N: nat] :
% 8.57/4.58        ( ( ( semiri1316708129612266289at_nat @ Y )
% 8.57/4.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4101_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: nat,X2: num,N: nat] :
% 8.57/4.58        ( ( ( semiri4939895301339042750nteger @ Y )
% 8.57/4.58          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4102_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: nat,X2: num,N: nat] :
% 8.57/4.58        ( ( ( semiri681578069525770553at_rat @ Y )
% 8.57/4.58          = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4103_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: nat,X2: num,N: nat] :
% 8.57/4.58        ( ( ( semiri3763490453095760265atural @ Y )
% 8.57/4.58          = ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ X2 ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4104_Suc__mod__mult__self1,axiom,
% 8.57/4.58      ! [M: nat,K: nat,N: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 8.57/4.58        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4105_Suc__mod__mult__self2,axiom,
% 8.57/4.58      ! [M: nat,N: nat,K: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 8.57/4.58        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4106_Suc__mod__mult__self3,axiom,
% 8.57/4.58      ! [K: nat,N: nat,M: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 8.57/4.58        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4107_Suc__mod__mult__self4,axiom,
% 8.57/4.58      ! [N: nat,K: nat,M: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 8.57/4.58        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4108_floor__neg__numeral,axiom,
% 8.57/4.58      ! [V: num] :
% 8.57/4.58        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4109_ceiling__add__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 8.57/4.58        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4110_floor__diff__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 8.57/4.58        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4111_ceiling__neg__numeral,axiom,
% 8.57/4.58      ! [V: num] :
% 8.57/4.58        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4112_Suc__times__numeral__mod__eq,axiom,
% 8.57/4.58      ! [K: num,N: nat] :
% 8.57/4.58        ( ( ( numeral_numeral_nat @ K )
% 8.57/4.58         != one_one_nat )
% 8.57/4.58       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 8.57/4.58          = one_one_nat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4113_ceiling__diff__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 8.57/4.58        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4114_of__int__eq__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ( ring_1_of_int_int @ Y )
% 8.57/4.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4115_of__int__eq__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ( ring_18347121197199848620nteger @ Y )
% 8.57/4.58          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4116_of__int__eq__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ( ring_1_of_int_rat @ Y )
% 8.57/4.58          = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4117_numeral__power__eq__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: int] :
% 8.57/4.58        ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 8.57/4.58          = ( ring_1_of_int_int @ Y ) )
% 8.57/4.58        = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4118_numeral__power__eq__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: int] :
% 8.57/4.58        ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N )
% 8.57/4.58          = ( ring_18347121197199848620nteger @ Y ) )
% 8.57/4.58        = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4119_numeral__power__eq__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: int] :
% 8.57/4.58        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 8.57/4.58          = ( ring_1_of_int_rat @ Y ) )
% 8.57/4.58        = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4120_mod__neg__neg__trivial,axiom,
% 8.57/4.58      ! [K: int,L: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 8.57/4.58       => ( ( ord_less_int @ L @ K )
% 8.57/4.58         => ( ( modulo_modulo_int @ K @ L )
% 8.57/4.58            = K ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4121_mod__pos__pos__trivial,axiom,
% 8.57/4.58      ! [K: int,L: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.58       => ( ( ord_less_int @ K @ L )
% 8.57/4.58         => ( ( modulo_modulo_int @ K @ L )
% 8.57/4.58            = K ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4122_le__divide__eq__numeral1_I2_J,axiom,
% 8.57/4.58      ! [A: rat,B: rat,W2: num] :
% 8.57/4.58        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 8.57/4.58        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4123_divide__le__eq__numeral1_I2_J,axiom,
% 8.57/4.58      ! [B: rat,W2: num,A: rat] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 8.57/4.58        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4124_eq__divide__eq__numeral1_I2_J,axiom,
% 8.57/4.58      ! [A: rat,B: rat,W2: num] :
% 8.57/4.58        ( ( A
% 8.57/4.58          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 8.57/4.58        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58             != zero_zero_rat )
% 8.57/4.58           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.57/4.58              = B ) )
% 8.57/4.58          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58              = zero_zero_rat )
% 8.57/4.58           => ( A = zero_zero_rat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4125_divide__eq__eq__numeral1_I2_J,axiom,
% 8.57/4.58      ! [B: rat,W2: num,A: rat] :
% 8.57/4.58        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.57/4.58          = A )
% 8.57/4.58        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58             != zero_zero_rat )
% 8.57/4.58           => ( B
% 8.57/4.58              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 8.57/4.58          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58              = zero_zero_rat )
% 8.57/4.58           => ( A = zero_zero_rat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4126_less__divide__eq__numeral1_I2_J,axiom,
% 8.57/4.58      ! [A: rat,B: rat,W2: num] :
% 8.57/4.58        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 8.57/4.58        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4127_divide__less__eq__numeral1_I2_J,axiom,
% 8.57/4.58      ! [B: rat,W2: num,A: rat] :
% 8.57/4.58        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 8.57/4.58        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4128_dbl__dec__simps_I1_J,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4129_dbl__dec__simps_I1_J,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4130_dbl__dec__simps_I1_J,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4131_dbl__inc__simps_I1_J,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4132_dbl__inc__simps_I1_J,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4133_dbl__inc__simps_I1_J,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4134_nat__numeral__diff__1,axiom,
% 8.57/4.58      ! [V: num] :
% 8.57/4.58        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 8.57/4.58        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4135_numeral__power__less__nat__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 8.57/4.58        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4136_nat__less__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 8.57/4.58        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4137_nat__le__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4138_numeral__power__le__nat__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4139_numeral__less__floor,axiom,
% 8.57/4.58      ! [V: num,X2: rat] :
% 8.57/4.58        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4140_floor__le__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 8.57/4.58        = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4141_ceiling__less__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 8.57/4.58        = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4142_numeral__le__ceiling,axiom,
% 8.57/4.58      ! [V: num,X2: rat] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4143_numeral__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 8.57/4.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4144_numeral__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 8.57/4.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4145_numeral__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 8.57/4.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4146_numeral__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4147_numeral__power__less__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I ) @ N ) @ ( semiri3763490453095760265atural @ X2 ) )
% 8.57/4.58        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4148_of__nat__less__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4149_of__nat__less__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4150_of__nat__less__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4151_of__nat__less__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4152_of__nat__less__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ X2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4153_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4154_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ X2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4155_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4156_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4157_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [X2: nat,I: num,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4158_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 8.57/4.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4159_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I ) @ N ) @ ( semiri3763490453095760265atural @ X2 ) )
% 8.57/4.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4160_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4161_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 8.57/4.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4162_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.57/4.58      ! [I: num,N: nat,X2: nat] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 8.57/4.58        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4163_neg__numeral__le__floor,axiom,
% 8.57/4.58      ! [V: num,X2: rat] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4164_floor__less__neg__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.57/4.58        = ( ord_less_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4165_ceiling__le__neg__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.57/4.58        = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4166_neg__numeral__less__ceiling,axiom,
% 8.57/4.58      ! [V: num,X2: rat] :
% 8.57/4.58        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4167_of__int__le__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4168_of__int__le__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4169_of__int__le__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4170_numeral__power__le__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4171_numeral__power__le__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4172_numeral__power__le__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4173_numeral__power__less__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 8.57/4.58        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4174_numeral__power__less__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 8.57/4.58        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4175_numeral__power__less__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 8.57/4.58        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4176_of__int__less__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 8.57/4.58        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4177_of__int__less__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 8.57/4.58        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4178_of__int__less__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 8.57/4.58        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4179_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ( ring_1_of_int_int @ Y )
% 8.57/4.58          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4180_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ( ring_18347121197199848620nteger @ Y )
% 8.57/4.58          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4181_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [Y: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ( ring_1_of_int_rat @ Y )
% 8.57/4.58          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 8.57/4.58        = ( Y
% 8.57/4.58          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4182_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: int] :
% 8.57/4.58        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 8.57/4.58          = ( ring_1_of_int_int @ Y ) )
% 8.57/4.58        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4183_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: int] :
% 8.57/4.58        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N )
% 8.57/4.58          = ( ring_18347121197199848620nteger @ Y ) )
% 8.57/4.58        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4184_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,Y: int] :
% 8.57/4.58        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N )
% 8.57/4.58          = ( ring_1_of_int_rat @ Y ) )
% 8.57/4.58        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 8.57/4.58          = Y ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4185_neg__numeral__less__floor,axiom,
% 8.57/4.58      ! [V: num,X2: rat] :
% 8.57/4.58        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4186_floor__le__neg__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.57/4.58        = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4187_ceiling__less__neg__numeral,axiom,
% 8.57/4.58      ! [X2: rat,V: num] :
% 8.57/4.58        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.57/4.58        = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4188_neg__numeral__le__ceiling,axiom,
% 8.57/4.58      ! [V: num,X2: rat] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 8.57/4.58        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4189_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4190_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4191_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 8.57/4.58        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4192_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4193_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4194_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 8.57/4.58        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4195_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 8.57/4.58        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4196_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 8.57/4.58        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4197_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 8.57/4.58      ! [X2: num,N: nat,A: int] :
% 8.57/4.58        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 8.57/4.58        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4198_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 8.57/4.58        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4199_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 8.57/4.58        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4200_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 8.57/4.58      ! [A: int,X2: num,N: nat] :
% 8.57/4.58        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 8.57/4.58        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4201_zmod__int,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 8.57/4.58        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4202_nat__numeral__as__int,axiom,
% 8.57/4.58      ( numeral_numeral_nat
% 8.57/4.58      = ( ^ [I2: num] : ( nat2 @ ( numeral_numeral_int @ I2 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4203_int__ops_I3_J,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 8.57/4.58        = ( numeral_numeral_int @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4204_of__nat__mod,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 8.57/4.58        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4205_of__nat__mod,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 8.57/4.58        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4206_of__nat__mod,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 8.57/4.58        = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4207_of__nat__mod,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( semiri3763490453095760265atural @ ( modulo_modulo_nat @ M @ N ) )
% 8.57/4.58        = ( modulo8411746178871703098atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4208_mod__add__eq,axiom,
% 8.57/4.58      ! [A: int,C: int,B: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 8.57/4.58        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4209_mod__add__eq,axiom,
% 8.57/4.58      ! [A: nat,C: nat,B: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 8.57/4.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4210_mod__add__eq,axiom,
% 8.57/4.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 8.57/4.58        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4211_mod__add__eq,axiom,
% 8.57/4.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 8.57/4.58        = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4212_mod__add__cong,axiom,
% 8.57/4.58      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 8.57/4.58        ( ( ( modulo_modulo_int @ A @ C )
% 8.57/4.58          = ( modulo_modulo_int @ A5 @ C ) )
% 8.57/4.58       => ( ( ( modulo_modulo_int @ B @ C )
% 8.57/4.58            = ( modulo_modulo_int @ B5 @ C ) )
% 8.57/4.58         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.57/4.58            = ( modulo_modulo_int @ ( plus_plus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4213_mod__add__cong,axiom,
% 8.57/4.58      ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ A @ C )
% 8.57/4.58          = ( modulo_modulo_nat @ A5 @ C ) )
% 8.57/4.58       => ( ( ( modulo_modulo_nat @ B @ C )
% 8.57/4.58            = ( modulo_modulo_nat @ B5 @ C ) )
% 8.57/4.58         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.57/4.58            = ( modulo_modulo_nat @ ( plus_plus_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4214_mod__add__cong,axiom,
% 8.57/4.58      ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 8.57/4.58        ( ( ( modulo364778990260209775nteger @ A @ C )
% 8.57/4.58          = ( modulo364778990260209775nteger @ A5 @ C ) )
% 8.57/4.58       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 8.57/4.58            = ( modulo364778990260209775nteger @ B5 @ C ) )
% 8.57/4.58         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.58            = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4215_mod__add__cong,axiom,
% 8.57/4.58      ! [A: code_natural,C: code_natural,A5: code_natural,B: code_natural,B5: code_natural] :
% 8.57/4.58        ( ( ( modulo8411746178871703098atural @ A @ C )
% 8.57/4.58          = ( modulo8411746178871703098atural @ A5 @ C ) )
% 8.57/4.58       => ( ( ( modulo8411746178871703098atural @ B @ C )
% 8.57/4.58            = ( modulo8411746178871703098atural @ B5 @ C ) )
% 8.57/4.58         => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 8.57/4.58            = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A5 @ B5 ) @ C ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4216_mod__add__left__eq,axiom,
% 8.57/4.58      ! [A: int,C: int,B: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 8.57/4.58        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4217_mod__add__left__eq,axiom,
% 8.57/4.58      ! [A: nat,C: nat,B: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 8.57/4.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4218_mod__add__left__eq,axiom,
% 8.57/4.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 8.57/4.58        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4219_mod__add__left__eq,axiom,
% 8.57/4.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ B ) @ C )
% 8.57/4.58        = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4220_mod__add__right__eq,axiom,
% 8.57/4.58      ! [A: int,B: int,C: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 8.57/4.58        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4221_mod__add__right__eq,axiom,
% 8.57/4.58      ! [A: nat,B: nat,C: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 8.57/4.58        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4222_mod__add__right__eq,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 8.57/4.58        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4223_mod__add__right__eq,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 8.57/4.58        = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4224_zero__neq__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( zero_zero_int
% 8.57/4.58       != ( numeral_numeral_int @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4225_zero__neq__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( zero_zero_nat
% 8.57/4.58       != ( numeral_numeral_nat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4226_zero__neq__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( zero_z3403309356797280102nteger
% 8.57/4.58       != ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4227_zero__neq__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( zero_zero_rat
% 8.57/4.58       != ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4228_zero__neq__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( zero_z2226904508553997617atural
% 8.57/4.58       != ( numera5444537566228673987atural @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4229_mod__less__eq__dividend,axiom,
% 8.57/4.58      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4230_neg__numeral__neq__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 8.57/4.58       != ( numeral_numeral_int @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4231_neg__numeral__neq__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 8.57/4.58       != ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4232_neg__numeral__neq__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 8.57/4.58       != ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4233_numeral__neq__neg__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( numeral_numeral_int @ M )
% 8.57/4.58       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4234_numeral__neq__neg__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( numera6620942414471956472nteger @ M )
% 8.57/4.58       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4235_numeral__neq__neg__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( numeral_numeral_rat @ M )
% 8.57/4.58       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4236_nat__mod__as__int,axiom,
% 8.57/4.58      ( modulo_modulo_nat
% 8.57/4.58      = ( ^ [A2: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4237_Ints__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( member_int @ ( numeral_numeral_int @ N ) @ ring_1_Ints_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4238_Ints__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( member_Code_integer @ ( numera6620942414471956472nteger @ N ) @ ring_11222124179247155820nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4239_Ints__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( member_rat @ ( numeral_numeral_rat @ N ) @ ring_1_Ints_rat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4240_nat__mod__distrib,axiom,
% 8.57/4.58      ! [X2: int,Y: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.58       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.58         => ( ( nat2 @ ( modulo_modulo_int @ X2 @ Y ) )
% 8.57/4.58            = ( modulo_modulo_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4241_mod__abs__eq__div__nat,axiom,
% 8.57/4.58      ! [K: int,L: int] :
% 8.57/4.58        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 8.57/4.58        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4242_of__int__neg__numeral,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4243_of__int__neg__numeral,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4244_of__int__neg__numeral,axiom,
% 8.57/4.58      ! [K: num] :
% 8.57/4.58        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4245_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.58       => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4246_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.58       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4247_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.58       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4248_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 8.57/4.58      ! [B: int,A: int] :
% 8.57/4.58        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.58       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4249_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 8.57/4.58      ! [B: nat,A: nat] :
% 8.57/4.58        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.58       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4250_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 8.57/4.58      ! [B: code_integer,A: code_integer] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.58       => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4251_mod__eqE,axiom,
% 8.57/4.58      ! [A: int,C: int,B: int] :
% 8.57/4.58        ( ( ( modulo_modulo_int @ A @ C )
% 8.57/4.58          = ( modulo_modulo_int @ B @ C ) )
% 8.57/4.58       => ~ ! [D5: int] :
% 8.57/4.58              ( B
% 8.57/4.58             != ( plus_plus_int @ A @ ( times_times_int @ C @ D5 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4252_mod__eqE,axiom,
% 8.57/4.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.57/4.58        ( ( ( modulo364778990260209775nteger @ A @ C )
% 8.57/4.58          = ( modulo364778990260209775nteger @ B @ C ) )
% 8.57/4.58       => ~ ! [D5: code_integer] :
% 8.57/4.58              ( B
% 8.57/4.58             != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D5 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4253_mod__eq__self__iff__div__eq__0,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58          = A )
% 8.57/4.58        = ( ( divide_divide_int @ A @ B )
% 8.57/4.58          = zero_zero_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4254_mod__eq__self__iff__div__eq__0,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ A @ B )
% 8.57/4.58          = A )
% 8.57/4.58        = ( ( divide_divide_nat @ A @ B )
% 8.57/4.58          = zero_zero_nat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4255_mod__eq__self__iff__div__eq__0,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( ( modulo364778990260209775nteger @ A @ B )
% 8.57/4.58          = A )
% 8.57/4.58        = ( ( divide6298287555418463151nteger @ A @ B )
% 8.57/4.58          = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4256_mod__eq__self__iff__div__eq__0,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural] :
% 8.57/4.58        ( ( ( modulo8411746178871703098atural @ A @ B )
% 8.57/4.58          = A )
% 8.57/4.58        = ( ( divide5121882707175180666atural @ A @ B )
% 8.57/4.58          = zero_z2226904508553997617atural ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4257_div__add1__eq,axiom,
% 8.57/4.58      ! [A: int,B: int,C: int] :
% 8.57/4.58        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.57/4.58        = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4258_div__add1__eq,axiom,
% 8.57/4.58      ! [A: nat,B: nat,C: nat] :
% 8.57/4.58        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.57/4.58        = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4259_div__add1__eq,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.58        ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4260_div__add1__eq,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.58        ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 8.57/4.58        = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4261_nth__rotate1,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_nat] :
% 8.57/4.58        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 8.57/4.58       => ( ( nth_nat @ ( rotate1_nat @ Xs ) @ N )
% 8.57/4.58          = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4262_nth__rotate1,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_int] :
% 8.57/4.58        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 8.57/4.58       => ( ( nth_int @ ( rotate1_int @ Xs ) @ N )
% 8.57/4.58          = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4263_nth__rotate1,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_o] :
% 8.57/4.58        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 8.57/4.58       => ( ( nth_o @ ( rotate1_o @ Xs ) @ N )
% 8.57/4.58          = ( nth_o @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4264_list__eq__iff__nth__eq,axiom,
% 8.57/4.58      ( ( ^ [Y3: list_nat,Z: list_nat] : ( Y3 = Z ) )
% 8.57/4.58      = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 8.57/4.58            ( ( ( size_size_list_nat @ Xs3 )
% 8.57/4.58              = ( size_size_list_nat @ Ys3 ) )
% 8.57/4.58            & ! [I2: nat] :
% 8.57/4.58                ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs3 ) )
% 8.57/4.58               => ( ( nth_nat @ Xs3 @ I2 )
% 8.57/4.58                  = ( nth_nat @ Ys3 @ I2 ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4265_list__eq__iff__nth__eq,axiom,
% 8.57/4.58      ( ( ^ [Y3: list_int,Z: list_int] : ( Y3 = Z ) )
% 8.57/4.58      = ( ^ [Xs3: list_int,Ys3: list_int] :
% 8.57/4.58            ( ( ( size_size_list_int @ Xs3 )
% 8.57/4.58              = ( size_size_list_int @ Ys3 ) )
% 8.57/4.58            & ! [I2: nat] :
% 8.57/4.58                ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs3 ) )
% 8.57/4.58               => ( ( nth_int @ Xs3 @ I2 )
% 8.57/4.58                  = ( nth_int @ Ys3 @ I2 ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4266_list__eq__iff__nth__eq,axiom,
% 8.57/4.58      ( ( ^ [Y3: list_o,Z: list_o] : ( Y3 = Z ) )
% 8.57/4.58      = ( ^ [Xs3: list_o,Ys3: list_o] :
% 8.57/4.58            ( ( ( size_size_list_o @ Xs3 )
% 8.57/4.58              = ( size_size_list_o @ Ys3 ) )
% 8.57/4.58            & ! [I2: nat] :
% 8.57/4.58                ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs3 ) )
% 8.57/4.58               => ( ( nth_o @ Xs3 @ I2 )
% 8.57/4.58                  = ( nth_o @ Ys3 @ I2 ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4267_Skolem__list__nth,axiom,
% 8.57/4.58      ! [K: nat,P: nat > nat > $o] :
% 8.57/4.58        ( ( ! [I2: nat] :
% 8.57/4.58              ( ( ord_less_nat @ I2 @ K )
% 8.57/4.58             => ? [X5: nat] : ( P @ I2 @ X5 ) ) )
% 8.57/4.58        = ( ? [Xs3: list_nat] :
% 8.57/4.58              ( ( ( size_size_list_nat @ Xs3 )
% 8.57/4.58                = K )
% 8.57/4.58              & ! [I2: nat] :
% 8.57/4.58                  ( ( ord_less_nat @ I2 @ K )
% 8.57/4.58                 => ( P @ I2 @ ( nth_nat @ Xs3 @ I2 ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4268_Skolem__list__nth,axiom,
% 8.57/4.58      ! [K: nat,P: nat > int > $o] :
% 8.57/4.58        ( ( ! [I2: nat] :
% 8.57/4.58              ( ( ord_less_nat @ I2 @ K )
% 8.57/4.58             => ? [X5: int] : ( P @ I2 @ X5 ) ) )
% 8.57/4.58        = ( ? [Xs3: list_int] :
% 8.57/4.58              ( ( ( size_size_list_int @ Xs3 )
% 8.57/4.58                = K )
% 8.57/4.58              & ! [I2: nat] :
% 8.57/4.58                  ( ( ord_less_nat @ I2 @ K )
% 8.57/4.58                 => ( P @ I2 @ ( nth_int @ Xs3 @ I2 ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4269_Skolem__list__nth,axiom,
% 8.57/4.58      ! [K: nat,P: nat > $o > $o] :
% 8.57/4.58        ( ( ! [I2: nat] :
% 8.57/4.58              ( ( ord_less_nat @ I2 @ K )
% 8.57/4.58             => ? [X5: $o] : ( P @ I2 @ X5 ) ) )
% 8.57/4.58        = ( ? [Xs3: list_o] :
% 8.57/4.58              ( ( ( size_size_list_o @ Xs3 )
% 8.57/4.58                = K )
% 8.57/4.58              & ! [I2: nat] :
% 8.57/4.58                  ( ( ord_less_nat @ I2 @ K )
% 8.57/4.58                 => ( P @ I2 @ ( nth_o @ Xs3 @ I2 ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4270_nth__equalityI,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_nat] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_nat @ Ys ) )
% 8.57/4.58       => ( ! [I3: nat] :
% 8.57/4.58              ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 8.57/4.58             => ( ( nth_nat @ Xs @ I3 )
% 8.57/4.58                = ( nth_nat @ Ys @ I3 ) ) )
% 8.57/4.58         => ( Xs = Ys ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4271_nth__equalityI,axiom,
% 8.57/4.58      ! [Xs: list_int,Ys: list_int] :
% 8.57/4.58        ( ( ( size_size_list_int @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ! [I3: nat] :
% 8.57/4.58              ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 8.57/4.58             => ( ( nth_int @ Xs @ I3 )
% 8.57/4.58                = ( nth_int @ Ys @ I3 ) ) )
% 8.57/4.58         => ( Xs = Ys ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4272_nth__equalityI,axiom,
% 8.57/4.58      ! [Xs: list_o,Ys: list_o] :
% 8.57/4.58        ( ( ( size_size_list_o @ Xs )
% 8.57/4.58          = ( size_size_list_o @ Ys ) )
% 8.57/4.58       => ( ! [I3: nat] :
% 8.57/4.58              ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 8.57/4.58             => ( ( nth_o @ Xs @ I3 )
% 8.57/4.58                = ( nth_o @ Ys @ I3 ) ) )
% 8.57/4.58         => ( Xs = Ys ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4273_obtain__list__from__elements,axiom,
% 8.57/4.58      ! [N: nat,P: nat > nat > $o] :
% 8.57/4.58        ( ! [I3: nat] :
% 8.57/4.58            ( ( ord_less_nat @ I3 @ N )
% 8.57/4.58           => ? [Li: nat] : ( P @ Li @ I3 ) )
% 8.57/4.58       => ~ ! [L3: list_nat] :
% 8.57/4.58              ( ( ( size_size_list_nat @ L3 )
% 8.57/4.58                = N )
% 8.57/4.58             => ~ ! [I4: nat] :
% 8.57/4.58                    ( ( ord_less_nat @ I4 @ N )
% 8.57/4.58                   => ( P @ ( nth_nat @ L3 @ I4 ) @ I4 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4274_obtain__list__from__elements,axiom,
% 8.57/4.58      ! [N: nat,P: int > nat > $o] :
% 8.57/4.58        ( ! [I3: nat] :
% 8.57/4.58            ( ( ord_less_nat @ I3 @ N )
% 8.57/4.58           => ? [Li: int] : ( P @ Li @ I3 ) )
% 8.57/4.58       => ~ ! [L3: list_int] :
% 8.57/4.58              ( ( ( size_size_list_int @ L3 )
% 8.57/4.58                = N )
% 8.57/4.58             => ~ ! [I4: nat] :
% 8.57/4.58                    ( ( ord_less_nat @ I4 @ N )
% 8.57/4.58                   => ( P @ ( nth_int @ L3 @ I4 ) @ I4 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4275_obtain__list__from__elements,axiom,
% 8.57/4.58      ! [N: nat,P: $o > nat > $o] :
% 8.57/4.58        ( ! [I3: nat] :
% 8.57/4.58            ( ( ord_less_nat @ I3 @ N )
% 8.57/4.58           => ? [Li: $o] : ( P @ Li @ I3 ) )
% 8.57/4.58       => ~ ! [L3: list_o] :
% 8.57/4.58              ( ( ( size_size_list_o @ L3 )
% 8.57/4.58                = N )
% 8.57/4.58             => ~ ! [I4: nat] :
% 8.57/4.58                    ( ( ord_less_nat @ I4 @ N )
% 8.57/4.58                   => ( P @ ( nth_o @ L3 @ I4 ) @ I4 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4276_mod__Suc,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 8.57/4.58            = N )
% 8.57/4.58         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 8.57/4.58            = zero_zero_nat ) )
% 8.57/4.58        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 8.57/4.58           != N )
% 8.57/4.58         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 8.57/4.58            = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4277_mod__less__divisor,axiom,
% 8.57/4.58      ! [N: nat,M: nat] :
% 8.57/4.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.58       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4278_gcd__nat__induct,axiom,
% 8.57/4.58      ! [P: nat > nat > $o,M: nat,N: nat] :
% 8.57/4.58        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 8.57/4.58       => ( ! [M4: nat,N2: nat] :
% 8.57/4.58              ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 8.57/4.58             => ( ( P @ N2 @ ( modulo_modulo_nat @ M4 @ N2 ) )
% 8.57/4.58               => ( P @ M4 @ N2 ) ) )
% 8.57/4.58         => ( P @ M @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4279_zero__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4280_zero__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( numera5444537566228673987atural @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4281_zero__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4282_zero__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4283_zero__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4284_not__numeral__le__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4285_not__numeral__le__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N ) @ zero_z2226904508553997617atural ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4286_not__numeral__le__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4287_not__numeral__le__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4288_not__numeral__le__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4289_mod__Suc__le__divisor,axiom,
% 8.57/4.58      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4290_zero__less__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4291_zero__less__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4292_zero__less__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4293_zero__less__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4294_zero__less__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( numera5444537566228673987atural @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4295_not__numeral__less__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4296_not__numeral__less__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4297_not__numeral__less__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4298_not__numeral__less__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4299_not__numeral__less__zero,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N ) @ zero_z2226904508553997617atural ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4300_one__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4301_one__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4302_one__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4303_one__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4304_one__le__numeral,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4305_nat__power__less__imp__less,axiom,
% 8.57/4.58      ! [I: nat,M: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_nat @ zero_zero_nat @ I )
% 8.57/4.58       => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 8.57/4.58         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4306_mod__eq__0D,axiom,
% 8.57/4.58      ! [M: nat,D: nat] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ M @ D )
% 8.57/4.58          = zero_zero_nat )
% 8.57/4.58       => ? [Q4: nat] :
% 8.57/4.58            ( M
% 8.57/4.58            = ( times_times_nat @ D @ Q4 ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4307_zmod__le__nonneg__dividend,axiom,
% 8.57/4.58      ! [M: int,K: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 8.57/4.58       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4308_Euclidean__Division_Opos__mod__bound,axiom,
% 8.57/4.58      ! [L: int,K: int] :
% 8.57/4.58        ( ( ord_less_int @ zero_zero_int @ L )
% 8.57/4.58       => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4309_neg__mod__bound,axiom,
% 8.57/4.58      ! [L: int,K: int] :
% 8.57/4.58        ( ( ord_less_int @ L @ zero_zero_int )
% 8.57/4.58       => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4310_not__numeral__less__one,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4311_not__numeral__less__one,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4312_not__numeral__less__one,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4313_not__numeral__less__one,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4314_not__numeral__less__one,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4315_le__mod__geq,axiom,
% 8.57/4.58      ! [N: nat,M: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.58       => ( ( modulo_modulo_nat @ M @ N )
% 8.57/4.58          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4316_not__numeral__le__neg__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4317_not__numeral__le__neg__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4318_not__numeral__le__neg__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4319_neg__numeral__le__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4320_neg__numeral__le__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4321_neg__numeral__le__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4322_zero__neq__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( zero_zero_int
% 8.57/4.58       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4323_zero__neq__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( zero_z3403309356797280102nteger
% 8.57/4.58       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4324_zero__neq__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( zero_zero_rat
% 8.57/4.58       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4325_one__plus__numeral__commute,axiom,
% 8.57/4.58      ! [X2: num] :
% 8.57/4.58        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 8.57/4.58        = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4326_one__plus__numeral__commute,axiom,
% 8.57/4.58      ! [X2: num] :
% 8.57/4.58        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 8.57/4.58        = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4327_one__plus__numeral__commute,axiom,
% 8.57/4.58      ! [X2: num] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X2 ) )
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X2 ) @ one_one_Code_integer ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4328_one__plus__numeral__commute,axiom,
% 8.57/4.58      ! [X2: num] :
% 8.57/4.58        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 8.57/4.58        = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4329_one__plus__numeral__commute,axiom,
% 8.57/4.58      ! [X2: num] :
% 8.57/4.58        ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X2 ) )
% 8.57/4.58        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X2 ) @ one_one_Code_natural ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4330_zmod__eq__0D,axiom,
% 8.57/4.58      ! [M: int,D: int] :
% 8.57/4.58        ( ( ( modulo_modulo_int @ M @ D )
% 8.57/4.58          = zero_zero_int )
% 8.57/4.58       => ? [Q4: int] :
% 8.57/4.58            ( M
% 8.57/4.58            = ( times_times_int @ D @ Q4 ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4331_zmod__eq__0__iff,axiom,
% 8.57/4.58      ! [M: int,D: int] :
% 8.57/4.58        ( ( ( modulo_modulo_int @ M @ D )
% 8.57/4.58          = zero_zero_int )
% 8.57/4.58        = ( ? [Q6: int] :
% 8.57/4.58              ( M
% 8.57/4.58              = ( times_times_int @ D @ Q6 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4332_zmod__zminus2__not__zero,axiom,
% 8.57/4.58      ! [K: int,L: int] :
% 8.57/4.58        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 8.57/4.58         != zero_zero_int )
% 8.57/4.58       => ( ( modulo_modulo_int @ K @ L )
% 8.57/4.58         != zero_zero_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4333_zmod__zminus1__not__zero,axiom,
% 8.57/4.58      ! [K: int,L: int] :
% 8.57/4.58        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 8.57/4.58         != zero_zero_int )
% 8.57/4.58       => ( ( modulo_modulo_int @ K @ L )
% 8.57/4.58         != zero_zero_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4334_neg__numeral__less__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4335_neg__numeral__less__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4336_neg__numeral__less__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4337_not__numeral__less__neg__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4338_not__numeral__less__neg__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4339_not__numeral__less__neg__numeral,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4340_nat__mod__eq__iff,axiom,
% 8.57/4.58      ! [X2: nat,N: nat,Y: nat] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ X2 @ N )
% 8.57/4.58          = ( modulo_modulo_nat @ Y @ N ) )
% 8.57/4.58        = ( ? [Q1: nat,Q22: nat] :
% 8.57/4.58              ( ( plus_plus_nat @ X2 @ ( times_times_nat @ N @ Q1 ) )
% 8.57/4.58              = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4341_numeral__neq__neg__one,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( numeral_numeral_int @ N )
% 8.57/4.58       != ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4342_numeral__neq__neg__one,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( numera6620942414471956472nteger @ N )
% 8.57/4.58       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4343_numeral__neq__neg__one,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( numeral_numeral_rat @ N )
% 8.57/4.58       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4344_one__neq__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( one_one_int
% 8.57/4.58       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4345_one__neq__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( one_one_Code_integer
% 8.57/4.58       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4346_one__neq__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( one_one_rat
% 8.57/4.58       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4347_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.57/4.58       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.57/4.58         => ( ( modulo364778990260209775nteger @ A @ B )
% 8.57/4.58            = A ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4348_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.57/4.58       => ( ( ord_less_nat @ A @ B )
% 8.57/4.58         => ( ( modulo_modulo_nat @ A @ B )
% 8.57/4.58            = A ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4349_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.58       => ( ( ord_less_int @ A @ B )
% 8.57/4.58         => ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58            = A ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4350_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 8.57/4.58      ! [B: code_integer,A: code_integer] :
% 8.57/4.58        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.57/4.58       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4351_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 8.57/4.58      ! [B: nat,A: nat] :
% 8.57/4.58        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.57/4.58       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4352_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 8.57/4.58      ! [B: int,A: int] :
% 8.57/4.58        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.58       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4353_div__mult1__eq,axiom,
% 8.57/4.58      ! [A: int,B: int,C: int] :
% 8.57/4.58        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 8.57/4.58        = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4354_div__mult1__eq,axiom,
% 8.57/4.58      ! [A: nat,B: nat,C: nat] :
% 8.57/4.58        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.57/4.58        = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4355_div__mult1__eq,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.58        ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4356_div__mult1__eq,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.58        ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 8.57/4.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4357_cancel__div__mod__rules_I2_J,axiom,
% 8.57/4.58      ! [B: int,A: int,C: int] :
% 8.57/4.58        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 8.57/4.58        = ( plus_plus_int @ A @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4358_cancel__div__mod__rules_I2_J,axiom,
% 8.57/4.58      ! [B: nat,A: nat,C: nat] :
% 8.57/4.58        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 8.57/4.58        = ( plus_plus_nat @ A @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4359_cancel__div__mod__rules_I2_J,axiom,
% 8.57/4.58      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4360_cancel__div__mod__rules_I2_J,axiom,
% 8.57/4.58      ! [B: code_natural,A: code_natural,C: code_natural] :
% 8.57/4.58        ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 8.57/4.58        = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4361_cancel__div__mod__rules_I1_J,axiom,
% 8.57/4.58      ! [A: int,B: int,C: int] :
% 8.57/4.58        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 8.57/4.58        = ( plus_plus_int @ A @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4362_cancel__div__mod__rules_I1_J,axiom,
% 8.57/4.58      ! [A: nat,B: nat,C: nat] :
% 8.57/4.58        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 8.57/4.58        = ( plus_plus_nat @ A @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4363_cancel__div__mod__rules_I1_J,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4364_cancel__div__mod__rules_I1_J,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 8.57/4.58        ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 8.57/4.58        = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4365_mod__div__decomp,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( A
% 8.57/4.58        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4366_mod__div__decomp,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( A
% 8.57/4.58        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4367_mod__div__decomp,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( A
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4368_mod__div__decomp,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural] :
% 8.57/4.58        ( A
% 8.57/4.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4369_div__mult__mod__eq,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4370_div__mult__mod__eq,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4371_div__mult__mod__eq,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4372_div__mult__mod__eq,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural] :
% 8.57/4.58        ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4373_mod__div__mult__eq,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4374_mod__div__mult__eq,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4375_mod__div__mult__eq,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4376_mod__div__mult__eq,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural] :
% 8.57/4.58        ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4377_mod__mult__div__eq,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4378_mod__mult__div__eq,axiom,
% 8.57/4.58      ! [A: nat,B: nat] :
% 8.57/4.58        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4379_mod__mult__div__eq,axiom,
% 8.57/4.58      ! [A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4380_mod__mult__div__eq,axiom,
% 8.57/4.58      ! [A: code_natural,B: code_natural] :
% 8.57/4.58        ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4381_mult__div__mod__eq,axiom,
% 8.57/4.58      ! [B: int,A: int] :
% 8.57/4.58        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4382_mult__div__mod__eq,axiom,
% 8.57/4.58      ! [B: nat,A: nat] :
% 8.57/4.58        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4383_mult__div__mod__eq,axiom,
% 8.57/4.58      ! [B: code_integer,A: code_integer] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4384_mult__div__mod__eq,axiom,
% 8.57/4.58      ! [B: code_natural,A: code_natural] :
% 8.57/4.58        ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 8.57/4.58        = A ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4385_mod__le__divisor,axiom,
% 8.57/4.58      ! [N: nat,M: nat] :
% 8.57/4.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.58       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4386_fact__mod,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.58       => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 8.57/4.58          = zero_zero_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4387_fact__mod,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.58       => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 8.57/4.58          = zero_z3403309356797280102nteger ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4388_fact__mod,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.58       => ( ( modulo8411746178871703098atural @ ( semiri2447717529341329178atural @ N ) @ ( semiri2447717529341329178atural @ M ) )
% 8.57/4.58          = zero_z2226904508553997617atural ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4389_fact__mod,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.58       => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 8.57/4.58          = zero_zero_nat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4390_neg__numeral__le__zero,axiom,
% 8.57/4.58      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4391_neg__numeral__le__zero,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4392_neg__numeral__le__zero,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4393_not__zero__le__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4394_not__zero__le__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4395_not__zero__le__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4396_power__gt__expt,axiom,
% 8.57/4.58      ! [N: nat,K: nat] :
% 8.57/4.58        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.58       => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4397_not__zero__less__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4398_not__zero__less__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4399_not__zero__less__neg__numeral,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4400_neg__numeral__less__zero,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4401_neg__numeral__less__zero,axiom,
% 8.57/4.58      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4402_neg__numeral__less__zero,axiom,
% 8.57/4.58      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4403_nat__one__le__power,axiom,
% 8.57/4.58      ! [I: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 8.57/4.58       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4404_not__one__le__neg__numeral,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4405_not__one__le__neg__numeral,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4406_not__one__le__neg__numeral,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4407_not__numeral__le__neg__one,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4408_not__numeral__le__neg__one,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4409_not__numeral__le__neg__one,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4410_neg__numeral__le__neg__one,axiom,
% 8.57/4.58      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4411_neg__numeral__le__neg__one,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4412_neg__numeral__le__neg__one,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4413_neg__one__le__numeral,axiom,
% 8.57/4.58      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4414_neg__one__le__numeral,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4415_neg__one__le__numeral,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4416_neg__numeral__le__one,axiom,
% 8.57/4.58      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4417_neg__numeral__le__one,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4418_neg__numeral__le__one,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4419_neg__mod__sign,axiom,
% 8.57/4.58      ! [L: int,K: int] :
% 8.57/4.58        ( ( ord_less_int @ L @ zero_zero_int )
% 8.57/4.58       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4420_Euclidean__Division_Opos__mod__sign,axiom,
% 8.57/4.58      ! [L: int,K: int] :
% 8.57/4.58        ( ( ord_less_int @ zero_zero_int @ L )
% 8.57/4.58       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4421_neg__mod__conj,axiom,
% 8.57/4.58      ! [B: int,A: int] :
% 8.57/4.58        ( ( ord_less_int @ B @ zero_zero_int )
% 8.57/4.58       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 8.57/4.58          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4422_pos__mod__conj,axiom,
% 8.57/4.58      ! [B: int,A: int] :
% 8.57/4.58        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.58       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 8.57/4.58          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4423_zmod__trivial__iff,axiom,
% 8.57/4.58      ! [I: int,K: int] :
% 8.57/4.58        ( ( ( modulo_modulo_int @ I @ K )
% 8.57/4.58          = I )
% 8.57/4.58        = ( ( K = zero_zero_int )
% 8.57/4.58          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 8.57/4.58            & ( ord_less_int @ I @ K ) )
% 8.57/4.58          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 8.57/4.58            & ( ord_less_int @ K @ I ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4424_eq__divide__eq__numeral_I1_J,axiom,
% 8.57/4.58      ! [W2: num,B: rat,C: rat] :
% 8.57/4.58        ( ( ( numeral_numeral_rat @ W2 )
% 8.57/4.58          = ( divide_divide_rat @ B @ C ) )
% 8.57/4.58        = ( ( ( C != zero_zero_rat )
% 8.57/4.58           => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C )
% 8.57/4.58              = B ) )
% 8.57/4.58          & ( ( C = zero_zero_rat )
% 8.57/4.58           => ( ( numeral_numeral_rat @ W2 )
% 8.57/4.58              = zero_zero_rat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4425_divide__eq__eq__numeral_I1_J,axiom,
% 8.57/4.58      ! [B: rat,C: rat,W2: num] :
% 8.57/4.58        ( ( ( divide_divide_rat @ B @ C )
% 8.57/4.58          = ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58        = ( ( ( C != zero_zero_rat )
% 8.57/4.58           => ( B
% 8.57/4.58              = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 8.57/4.58          & ( ( C = zero_zero_rat )
% 8.57/4.58           => ( ( numeral_numeral_rat @ W2 )
% 8.57/4.58              = zero_zero_rat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4426_nat__mod__eq__lemma,axiom,
% 8.57/4.58      ! [X2: nat,N: nat,Y: nat] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ X2 @ N )
% 8.57/4.58          = ( modulo_modulo_nat @ Y @ N ) )
% 8.57/4.58       => ( ( ord_less_eq_nat @ Y @ X2 )
% 8.57/4.58         => ? [Q4: nat] :
% 8.57/4.58              ( X2
% 8.57/4.58              = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q4 ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4427_mod__eq__nat2E,axiom,
% 8.57/4.58      ! [M: nat,Q2: nat,N: nat] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 8.57/4.58          = ( modulo_modulo_nat @ N @ Q2 ) )
% 8.57/4.58       => ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.58         => ~ ! [S2: nat] :
% 8.57/4.58                ( N
% 8.57/4.58               != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4428_mod__eq__nat1E,axiom,
% 8.57/4.58      ! [M: nat,Q2: nat,N: nat] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 8.57/4.58          = ( modulo_modulo_nat @ N @ Q2 ) )
% 8.57/4.58       => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.58         => ~ ! [S2: nat] :
% 8.57/4.58                ( M
% 8.57/4.58               != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4429_neg__numeral__less__one,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4430_neg__numeral__less__one,axiom,
% 8.57/4.58      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4431_neg__numeral__less__one,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4432_neg__one__less__numeral,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4433_neg__one__less__numeral,axiom,
% 8.57/4.58      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4434_neg__one__less__numeral,axiom,
% 8.57/4.58      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4435_not__numeral__less__neg__one,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4436_not__numeral__less__neg__one,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4437_not__numeral__less__neg__one,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4438_not__one__less__neg__numeral,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4439_not__one__less__neg__numeral,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4440_not__one__less__neg__numeral,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4441_not__neg__one__less__neg__numeral,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4442_not__neg__one__less__neg__numeral,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4443_not__neg__one__less__neg__numeral,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4444_div__less__mono,axiom,
% 8.57/4.58      ! [A4: nat,B4: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_nat @ A4 @ B4 )
% 8.57/4.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.58         => ( ( ( modulo_modulo_nat @ A4 @ N )
% 8.57/4.58              = zero_zero_nat )
% 8.57/4.58           => ( ( ( modulo_modulo_nat @ B4 @ N )
% 8.57/4.58                = zero_zero_nat )
% 8.57/4.58             => ( ord_less_nat @ ( divide_divide_nat @ A4 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4445_abs__mod__less,axiom,
% 8.57/4.58      ! [L: int,K: int] :
% 8.57/4.58        ( ( L != zero_zero_int )
% 8.57/4.58       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4446_zmod__zminus1__eq__if,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58            = zero_zero_int )
% 8.57/4.58         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 8.57/4.58            = zero_zero_int ) )
% 8.57/4.58        & ( ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58           != zero_zero_int )
% 8.57/4.58         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 8.57/4.58            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4447_zmod__zminus2__eq__if,axiom,
% 8.57/4.58      ! [A: int,B: int] :
% 8.57/4.58        ( ( ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58            = zero_zero_int )
% 8.57/4.58         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 8.57/4.58            = zero_zero_int ) )
% 8.57/4.58        & ( ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58           != zero_zero_int )
% 8.57/4.58         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 8.57/4.58            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4448_zdiv__mono__strict,axiom,
% 8.57/4.58      ! [A4: int,B4: int,N: int] :
% 8.57/4.58        ( ( ord_less_int @ A4 @ B4 )
% 8.57/4.58       => ( ( ord_less_int @ zero_zero_int @ N )
% 8.57/4.58         => ( ( ( modulo_modulo_int @ A4 @ N )
% 8.57/4.58              = zero_zero_int )
% 8.57/4.58           => ( ( ( modulo_modulo_int @ B4 @ N )
% 8.57/4.58                = zero_zero_int )
% 8.57/4.58             => ( ord_less_int @ ( divide_divide_int @ A4 @ N ) @ ( divide_divide_int @ B4 @ N ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4449_mod__mult2__eq,axiom,
% 8.57/4.58      ! [M: nat,N: nat,Q2: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 8.57/4.58        = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4450_div__mod__decomp,axiom,
% 8.57/4.58      ! [A4: nat,N: nat] :
% 8.57/4.58        ( A4
% 8.57/4.58        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A4 @ N ) @ N ) @ ( modulo_modulo_nat @ A4 @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4451_fact__le__power,axiom,
% 8.57/4.58      ! [N: nat] : ( ord_le3102999989581377725nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri4939895301339042750nteger @ ( power_power_nat @ N @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4452_fact__le__power,axiom,
% 8.57/4.58      ! [N: nat] : ( ord_le1926595141338095240atural @ ( semiri2447717529341329178atural @ N ) @ ( semiri3763490453095760265atural @ ( power_power_nat @ N @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4453_fact__le__power,axiom,
% 8.57/4.58      ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4454_fact__le__power,axiom,
% 8.57/4.58      ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4455_fact__le__power,axiom,
% 8.57/4.58      ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4456_div__mod__decomp__int,axiom,
% 8.57/4.58      ! [A4: int,N: int] :
% 8.57/4.58        ( A4
% 8.57/4.58        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A4 @ N ) @ N ) @ ( modulo_modulo_int @ A4 @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4457_fact__div__fact__le__pow,axiom,
% 8.57/4.58      ! [R: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ R @ N )
% 8.57/4.58       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4458_mod__mult2__eq_H,axiom,
% 8.57/4.58      ! [A: int,M: nat,N: nat] :
% 8.57/4.58        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.57/4.58        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4459_mod__mult2__eq_H,axiom,
% 8.57/4.58      ! [A: nat,M: nat,N: nat] :
% 8.57/4.58        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 8.57/4.58        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4460_mod__mult2__eq_H,axiom,
% 8.57/4.58      ! [A: code_integer,M: nat,N: nat] :
% 8.57/4.58        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 8.57/4.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4461_mod__mult2__eq_H,axiom,
% 8.57/4.58      ! [A: code_natural,M: nat,N: nat] :
% 8.57/4.58        ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) )
% 8.57/4.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4462_split__mod,axiom,
% 8.57/4.58      ! [P: nat > $o,M: nat,N: nat] :
% 8.57/4.58        ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 8.57/4.58        = ( ( ( N = zero_zero_nat )
% 8.57/4.58           => ( P @ M ) )
% 8.57/4.58          & ( ( N != zero_zero_nat )
% 8.57/4.58           => ! [I2: nat,J3: nat] :
% 8.57/4.58                ( ( ord_less_nat @ J3 @ N )
% 8.57/4.58               => ( ( M
% 8.57/4.58                    = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 8.57/4.58                 => ( P @ J3 ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4463_less__divide__eq__numeral_I1_J,axiom,
% 8.57/4.58      ! [W2: num,B: rat,C: rat] :
% 8.57/4.58        ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.58        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 8.57/4.58          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 8.57/4.58              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4464_divide__less__eq__numeral_I1_J,axiom,
% 8.57/4.58      ! [B: rat,C: rat,W2: num] :
% 8.57/4.58        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 8.57/4.58          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 8.57/4.58              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4465_field__char__0__class_Oof__nat__div,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 8.57/4.58        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4466_eq__divide__eq__numeral_I2_J,axiom,
% 8.57/4.58      ! [W2: num,B: rat,C: rat] :
% 8.57/4.58        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58          = ( divide_divide_rat @ B @ C ) )
% 8.57/4.58        = ( ( ( C != zero_zero_rat )
% 8.57/4.58           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C )
% 8.57/4.58              = B ) )
% 8.57/4.58          & ( ( C = zero_zero_rat )
% 8.57/4.58           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58              = zero_zero_rat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4467_divide__eq__eq__numeral_I2_J,axiom,
% 8.57/4.58      ! [B: rat,C: rat,W2: num] :
% 8.57/4.58        ( ( ( divide_divide_rat @ B @ C )
% 8.57/4.58          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.57/4.58        = ( ( ( C != zero_zero_rat )
% 8.57/4.58           => ( B
% 8.57/4.58              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 8.57/4.58          & ( ( C = zero_zero_rat )
% 8.57/4.58           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58              = zero_zero_rat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4468_mod__pos__neg__trivial,axiom,
% 8.57/4.58      ! [K: int,L: int] :
% 8.57/4.58        ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.58       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 8.57/4.58         => ( ( modulo_modulo_int @ K @ L )
% 8.57/4.58            = ( plus_plus_int @ K @ L ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4469_mod__pos__geq,axiom,
% 8.57/4.58      ! [L: int,K: int] :
% 8.57/4.58        ( ( ord_less_int @ zero_zero_int @ L )
% 8.57/4.58       => ( ( ord_less_eq_int @ L @ K )
% 8.57/4.58         => ( ( modulo_modulo_int @ K @ L )
% 8.57/4.58            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4470_array__of__list__make,axiom,
% 8.57/4.58      ( array_of_list_nat
% 8.57/4.58      = ( ^ [Xs3: list_nat] : ( array_make_nat @ ( size_size_list_nat @ Xs3 ) @ ( nth_nat @ Xs3 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4471_array__of__list__make,axiom,
% 8.57/4.58      ( array_of_list_int
% 8.57/4.58      = ( ^ [Xs3: list_int] : ( array_make_int @ ( size_size_list_int @ Xs3 ) @ ( nth_int @ Xs3 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4472_array__of__list__make,axiom,
% 8.57/4.58      ( array_of_list_o
% 8.57/4.58      = ( ^ [Xs3: list_o] : ( array_make_o @ ( size_size_list_o @ Xs3 ) @ ( nth_o @ Xs3 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4473_nat__power__eq,axiom,
% 8.57/4.58      ! [Z2: int,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.58       => ( ( nat2 @ ( power_power_int @ Z2 @ N ) )
% 8.57/4.58          = ( power_power_nat @ ( nat2 @ Z2 ) @ N ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4474_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 8.57/4.58      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.57/4.58        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.57/4.58       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.57/4.58          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4475_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 8.57/4.58      ! [C: nat,A: nat,B: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.57/4.58       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 8.57/4.58          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4476_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 8.57/4.58      ! [C: int,A: int,B: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.58       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 8.57/4.58          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4477_fold__atLeastAtMost__nat_Osimps,axiom,
% 8.57/4.58      ( set_fo2584398358068434914at_nat
% 8.57/4.58      = ( ^ [F3: nat > nat > nat,A2: nat,B2: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B2 @ A2 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A2 @ one_one_nat ) @ B2 @ ( F3 @ A2 @ Acc ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4478_fold__atLeastAtMost__nat_Oelims,axiom,
% 8.57/4.58      ! [X2: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 8.57/4.58        ( ( ( set_fo2584398358068434914at_nat @ X2 @ Xa @ Xb @ Xc )
% 8.57/4.58          = Y )
% 8.57/4.58       => ( ( ( ord_less_nat @ Xb @ Xa )
% 8.57/4.58           => ( Y = Xc ) )
% 8.57/4.58          & ( ~ ( ord_less_nat @ Xb @ Xa )
% 8.57/4.58           => ( Y
% 8.57/4.58              = ( set_fo2584398358068434914at_nat @ X2 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X2 @ Xa @ Xc ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4479_divide__le__eq__numeral_I1_J,axiom,
% 8.57/4.58      ! [B: rat,C: rat,W2: num] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 8.57/4.58        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 8.57/4.58          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 8.57/4.58              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4480_le__divide__eq__numeral_I1_J,axiom,
% 8.57/4.58      ! [W2: num,B: rat,C: rat] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.58        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 8.57/4.58          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 8.57/4.58              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4481_Suc__times__mod__eq,axiom,
% 8.57/4.58      ! [M: nat,N: nat] :
% 8.57/4.58        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.57/4.58       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 8.57/4.58          = one_one_nat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4482_divide__less__eq__numeral_I2_J,axiom,
% 8.57/4.58      ! [B: rat,C: rat,W2: num] :
% 8.57/4.58        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.57/4.58        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 8.57/4.58          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 8.57/4.58              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4483_less__divide__eq__numeral_I2_J,axiom,
% 8.57/4.58      ! [W2: num,B: rat,C: rat] :
% 8.57/4.58        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 8.57/4.58        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 8.57/4.58          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 8.57/4.58              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4484_int__mod__pos__eq,axiom,
% 8.57/4.58      ! [A: int,B: int,Q2: int,R: int] :
% 8.57/4.58        ( ( A
% 8.57/4.58          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.57/4.58       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 8.57/4.58         => ( ( ord_less_int @ R @ B )
% 8.57/4.58           => ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58              = R ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4485_int__mod__neg__eq,axiom,
% 8.57/4.58      ! [A: int,B: int,Q2: int,R: int] :
% 8.57/4.58        ( ( A
% 8.57/4.58          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.57/4.58       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 8.57/4.58         => ( ( ord_less_int @ B @ R )
% 8.57/4.58           => ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58              = R ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4486_split__zmod,axiom,
% 8.57/4.58      ! [P: int > $o,N: int,K: int] :
% 8.57/4.58        ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 8.57/4.58        = ( ( ( K = zero_zero_int )
% 8.57/4.58           => ( P @ N ) )
% 8.57/4.58          & ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.58           => ! [I2: int,J3: int] :
% 8.57/4.58                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 8.57/4.58                  & ( ord_less_int @ J3 @ K )
% 8.57/4.58                  & ( N
% 8.57/4.58                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 8.57/4.58               => ( P @ J3 ) ) )
% 8.57/4.58          & ( ( ord_less_int @ K @ zero_zero_int )
% 8.57/4.58           => ! [I2: int,J3: int] :
% 8.57/4.58                ( ( ( ord_less_int @ K @ J3 )
% 8.57/4.58                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 8.57/4.58                  & ( N
% 8.57/4.58                    = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 8.57/4.58               => ( P @ J3 ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4487_minus__mod__int__eq,axiom,
% 8.57/4.58      ! [L: int,K: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 8.57/4.58       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 8.57/4.58          = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4488_zmod__minus1,axiom,
% 8.57/4.58      ! [B: int] :
% 8.57/4.58        ( ( ord_less_int @ zero_zero_int @ B )
% 8.57/4.58       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 8.57/4.58          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4489_zmod__zmult2__eq,axiom,
% 8.57/4.58      ! [C: int,A: int,B: int] :
% 8.57/4.58        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.57/4.58       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 8.57/4.58          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4490_zdiv__zminus1__eq__if,axiom,
% 8.57/4.58      ! [B: int,A: int] :
% 8.57/4.58        ( ( B != zero_zero_int )
% 8.57/4.58       => ( ( ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58              = zero_zero_int )
% 8.57/4.58           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 8.57/4.58              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 8.57/4.58          & ( ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58             != zero_zero_int )
% 8.57/4.58           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 8.57/4.58              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4491_zdiv__zminus2__eq__if,axiom,
% 8.57/4.58      ! [B: int,A: int] :
% 8.57/4.58        ( ( B != zero_zero_int )
% 8.57/4.58       => ( ( ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58              = zero_zero_int )
% 8.57/4.58           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 8.57/4.58              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 8.57/4.58          & ( ( ( modulo_modulo_int @ A @ B )
% 8.57/4.58             != zero_zero_int )
% 8.57/4.58           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 8.57/4.58              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4492_divide__le__eq__numeral_I2_J,axiom,
% 8.57/4.58      ! [B: rat,C: rat,W2: num] :
% 8.57/4.58        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.57/4.58        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 8.57/4.58          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.57/4.58           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 8.57/4.58              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.57/4.58               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4493_sorted__in__between,axiom,
% 8.57/4.58      ! [I: nat,J: nat,L: list_o,X2: $o] :
% 8.57/4.58        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 8.57/4.58       => ( ( ord_less_nat @ I @ J )
% 8.57/4.58         => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 8.57/4.58           => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 8.57/4.58             => ( ( ord_less_eq_o @ ( nth_o @ L @ I ) @ X2 )
% 8.57/4.58               => ( ( ord_less_o @ X2 @ ( nth_o @ L @ J ) )
% 8.57/4.58                 => ~ ! [K3: nat] :
% 8.57/4.58                        ( ( ord_less_eq_nat @ I @ K3 )
% 8.57/4.58                       => ( ( ord_less_nat @ K3 @ J )
% 8.57/4.58                         => ( ( ord_less_eq_o @ ( nth_o @ L @ K3 ) @ X2 )
% 8.57/4.58                           => ~ ( ord_less_o @ X2 @ ( nth_o @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4494_sorted__in__between,axiom,
% 8.57/4.58      ! [I: nat,J: nat,L: list_Code_integer,X2: code_integer] :
% 8.57/4.58        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 8.57/4.58       => ( ( ord_less_nat @ I @ J )
% 8.57/4.58         => ( ( ord_less_nat @ J @ ( size_s3445333598471063425nteger @ L ) )
% 8.57/4.58           => ( ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ L )
% 8.57/4.58             => ( ( ord_le3102999989581377725nteger @ ( nth_Code_integer @ L @ I ) @ X2 )
% 8.57/4.58               => ( ( ord_le6747313008572928689nteger @ X2 @ ( nth_Code_integer @ L @ J ) )
% 8.57/4.58                 => ~ ! [K3: nat] :
% 8.57/4.58                        ( ( ord_less_eq_nat @ I @ K3 )
% 8.57/4.58                       => ( ( ord_less_nat @ K3 @ J )
% 8.57/4.58                         => ( ( ord_le3102999989581377725nteger @ ( nth_Code_integer @ L @ K3 ) @ X2 )
% 8.57/4.58                           => ~ ( ord_le6747313008572928689nteger @ X2 @ ( nth_Code_integer @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4495_sorted__in__between,axiom,
% 8.57/4.58      ! [I: nat,J: nat,L: list_rat,X2: rat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 8.57/4.58       => ( ( ord_less_nat @ I @ J )
% 8.57/4.58         => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 8.57/4.58           => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 8.57/4.58             => ( ( ord_less_eq_rat @ ( nth_rat @ L @ I ) @ X2 )
% 8.57/4.58               => ( ( ord_less_rat @ X2 @ ( nth_rat @ L @ J ) )
% 8.57/4.58                 => ~ ! [K3: nat] :
% 8.57/4.58                        ( ( ord_less_eq_nat @ I @ K3 )
% 8.57/4.58                       => ( ( ord_less_nat @ K3 @ J )
% 8.57/4.58                         => ( ( ord_less_eq_rat @ ( nth_rat @ L @ K3 ) @ X2 )
% 8.57/4.58                           => ~ ( ord_less_rat @ X2 @ ( nth_rat @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4496_sorted__in__between,axiom,
% 8.57/4.58      ! [I: nat,J: nat,L: list_num,X2: num] :
% 8.57/4.58        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 8.57/4.58       => ( ( ord_less_nat @ I @ J )
% 8.57/4.58         => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 8.57/4.58           => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 8.57/4.58             => ( ( ord_less_eq_num @ ( nth_num @ L @ I ) @ X2 )
% 8.57/4.58               => ( ( ord_less_num @ X2 @ ( nth_num @ L @ J ) )
% 8.57/4.58                 => ~ ! [K3: nat] :
% 8.57/4.58                        ( ( ord_less_eq_nat @ I @ K3 )
% 8.57/4.58                       => ( ( ord_less_nat @ K3 @ J )
% 8.57/4.58                         => ( ( ord_less_eq_num @ ( nth_num @ L @ K3 ) @ X2 )
% 8.57/4.58                           => ~ ( ord_less_num @ X2 @ ( nth_num @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4497_sorted__in__between,axiom,
% 8.57/4.58      ! [I: nat,J: nat,L: list_nat,X2: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 8.57/4.58       => ( ( ord_less_nat @ I @ J )
% 8.57/4.58         => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 8.57/4.58           => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 8.57/4.58             => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I ) @ X2 )
% 8.57/4.58               => ( ( ord_less_nat @ X2 @ ( nth_nat @ L @ J ) )
% 8.57/4.58                 => ~ ! [K3: nat] :
% 8.57/4.58                        ( ( ord_less_eq_nat @ I @ K3 )
% 8.57/4.58                       => ( ( ord_less_nat @ K3 @ J )
% 8.57/4.58                         => ( ( ord_less_eq_nat @ ( nth_nat @ L @ K3 ) @ X2 )
% 8.57/4.58                           => ~ ( ord_less_nat @ X2 @ ( nth_nat @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4498_sorted__in__between,axiom,
% 8.57/4.58      ! [I: nat,J: nat,L: list_int,X2: int] :
% 8.57/4.58        ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 8.57/4.58       => ( ( ord_less_nat @ I @ J )
% 8.57/4.58         => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 8.57/4.58           => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 8.57/4.58             => ( ( ord_less_eq_int @ ( nth_int @ L @ I ) @ X2 )
% 8.57/4.58               => ( ( ord_less_int @ X2 @ ( nth_int @ L @ J ) )
% 8.57/4.58                 => ~ ! [K3: nat] :
% 8.57/4.58                        ( ( ord_less_eq_nat @ I @ K3 )
% 8.57/4.58                       => ( ( ord_less_nat @ K3 @ J )
% 8.57/4.58                         => ( ( ord_less_eq_int @ ( nth_int @ L @ K3 ) @ X2 )
% 8.57/4.58                           => ~ ( ord_less_int @ X2 @ ( nth_int @ L @ ( plus_plus_nat @ K3 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4499_diff__numeral__special_I6_J,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.58        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4500_diff__numeral__special_I6_J,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.57/4.58        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4501_diff__numeral__special_I6_J,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.57/4.58        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4502_diff__numeral__special_I5_J,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4503_diff__numeral__special_I5_J,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4504_diff__numeral__special_I5_J,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4505_add__neg__numeral__special_I5_J,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4506_add__neg__numeral__special_I5_J,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4507_add__neg__numeral__special_I5_J,axiom,
% 8.57/4.58      ! [N: num] :
% 8.57/4.58        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4508_add__neg__numeral__special_I6_J,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4509_add__neg__numeral__special_I6_J,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.57/4.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4510_add__neg__numeral__special_I6_J,axiom,
% 8.57/4.58      ! [M: num] :
% 8.57/4.58        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.57/4.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4511_nth__rotate,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_nat,M: nat] :
% 8.57/4.58        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 8.57/4.58       => ( ( nth_nat @ ( rotate_nat @ M @ Xs ) @ N )
% 8.57/4.58          = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( plus_plus_nat @ M @ N ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4512_nth__rotate,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_int,M: nat] :
% 8.57/4.58        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 8.57/4.58       => ( ( nth_int @ ( rotate_int @ M @ Xs ) @ N )
% 8.57/4.58          = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( plus_plus_nat @ M @ N ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4513_nth__rotate,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_o,M: nat] :
% 8.57/4.58        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 8.57/4.58       => ( ( nth_o @ ( rotate_o @ M @ Xs ) @ N )
% 8.57/4.58          = ( nth_o @ Xs @ ( modulo_modulo_nat @ ( plus_plus_nat @ M @ N ) @ ( size_size_list_o @ Xs ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4514_nth__Cons__pos,axiom,
% 8.57/4.58      ! [N: nat,X2: int,Xs: list_int] :
% 8.57/4.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.58       => ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ N )
% 8.57/4.58          = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4515_nth__Cons__pos,axiom,
% 8.57/4.58      ! [N: nat,X2: nat,Xs: list_nat] :
% 8.57/4.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.58       => ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ N )
% 8.57/4.58          = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4516_nth__Cons__pos,axiom,
% 8.57/4.58      ! [N: nat,X2: char,Xs: list_char] :
% 8.57/4.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.58       => ( ( nth_char @ ( cons_char @ X2 @ Xs ) @ N )
% 8.57/4.58          = ( nth_char @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4517_length__rotate,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_nat] :
% 8.57/4.58        ( ( size_size_list_nat @ ( rotate_nat @ N @ Xs ) )
% 8.57/4.58        = ( size_size_list_nat @ Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4518_length__rotate,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_int] :
% 8.57/4.58        ( ( size_size_list_int @ ( rotate_int @ N @ Xs ) )
% 8.57/4.58        = ( size_size_list_int @ Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4519_length__rotate,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_o] :
% 8.57/4.58        ( ( size_size_list_o @ ( rotate_o @ N @ Xs ) )
% 8.57/4.58        = ( size_size_list_o @ Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4520_nth__Cons__0,axiom,
% 8.57/4.58      ! [X2: int,Xs: list_int] :
% 8.57/4.58        ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ zero_zero_nat )
% 8.57/4.58        = X2 ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4521_nth__Cons__0,axiom,
% 8.57/4.58      ! [X2: nat,Xs: list_nat] :
% 8.57/4.58        ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ zero_zero_nat )
% 8.57/4.58        = X2 ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4522_nth__Cons__0,axiom,
% 8.57/4.58      ! [X2: char,Xs: list_char] :
% 8.57/4.58        ( ( nth_char @ ( cons_char @ X2 @ Xs ) @ zero_zero_nat )
% 8.57/4.58        = X2 ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4523_rotate__length01,axiom,
% 8.57/4.58      ! [Xs: list_nat,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 8.57/4.58       => ( ( rotate_nat @ N @ Xs )
% 8.57/4.58          = Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4524_rotate__length01,axiom,
% 8.57/4.58      ! [Xs: list_int,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 8.57/4.58       => ( ( rotate_int @ N @ Xs )
% 8.57/4.58          = Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4525_rotate__length01,axiom,
% 8.57/4.58      ! [Xs: list_o,N: nat] :
% 8.57/4.58        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 8.57/4.58       => ( ( rotate_o @ N @ Xs )
% 8.57/4.58          = Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4526_rotate__id,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_nat] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Xs ) )
% 8.57/4.58          = zero_zero_nat )
% 8.57/4.58       => ( ( rotate_nat @ N @ Xs )
% 8.57/4.58          = Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4527_rotate__id,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_int] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ N @ ( size_size_list_int @ Xs ) )
% 8.57/4.58          = zero_zero_nat )
% 8.57/4.58       => ( ( rotate_int @ N @ Xs )
% 8.57/4.58          = Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4528_rotate__id,axiom,
% 8.57/4.58      ! [N: nat,Xs: list_o] :
% 8.57/4.58        ( ( ( modulo_modulo_nat @ N @ ( size_size_list_o @ Xs ) )
% 8.57/4.58          = zero_zero_nat )
% 8.57/4.58       => ( ( rotate_o @ N @ Xs )
% 8.57/4.58          = Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4529_nth__Cons__numeral,axiom,
% 8.57/4.58      ! [X2: int,Xs: list_int,V: num] :
% 8.57/4.58        ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ ( numeral_numeral_nat @ V ) )
% 8.57/4.58        = ( nth_int @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4530_nth__Cons__numeral,axiom,
% 8.57/4.58      ! [X2: nat,Xs: list_nat,V: num] :
% 8.57/4.58        ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ ( numeral_numeral_nat @ V ) )
% 8.57/4.58        = ( nth_nat @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4531_nth__Cons__numeral,axiom,
% 8.57/4.58      ! [X2: char,Xs: list_char,V: num] :
% 8.57/4.58        ( ( nth_char @ ( cons_char @ X2 @ Xs ) @ ( numeral_numeral_nat @ V ) )
% 8.57/4.58        = ( nth_char @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4532_mult__inc,axiom,
% 8.57/4.58      ! [X2: num,Y: num] :
% 8.57/4.58        ( ( times_times_num @ X2 @ ( inc @ Y ) )
% 8.57/4.58        = ( plus_plus_num @ ( times_times_num @ X2 @ Y ) @ X2 ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4533_sorted2,axiom,
% 8.57/4.58      ! [X2: rat,Y: rat,Zs: list_rat] :
% 8.57/4.58        ( ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ X2 @ ( cons_rat @ Y @ Zs ) ) )
% 8.57/4.58        = ( ( ord_less_eq_rat @ X2 @ Y )
% 8.57/4.58          & ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ Y @ Zs ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4534_sorted2,axiom,
% 8.57/4.58      ! [X2: num,Y: num,Zs: list_num] :
% 8.57/4.58        ( ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ X2 @ ( cons_num @ Y @ Zs ) ) )
% 8.57/4.58        = ( ( ord_less_eq_num @ X2 @ Y )
% 8.57/4.58          & ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ Y @ Zs ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4535_sorted2,axiom,
% 8.57/4.58      ! [X2: nat,Y: nat,Zs: list_nat] :
% 8.57/4.58        ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X2 @ ( cons_nat @ Y @ Zs ) ) )
% 8.57/4.58        = ( ( ord_less_eq_nat @ X2 @ Y )
% 8.57/4.58          & ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ Y @ Zs ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4536_sorted2,axiom,
% 8.57/4.58      ! [X2: int,Y: int,Zs: list_int] :
% 8.57/4.58        ( ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X2 @ ( cons_int @ Y @ Zs ) ) )
% 8.57/4.58        = ( ( ord_less_eq_int @ X2 @ Y )
% 8.57/4.58          & ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ Y @ Zs ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4537_add__inc,axiom,
% 8.57/4.58      ! [X2: num,Y: num] :
% 8.57/4.58        ( ( plus_plus_num @ X2 @ ( inc @ Y ) )
% 8.57/4.58        = ( inc @ ( plus_plus_num @ X2 @ Y ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4538_list__tail__coinc,axiom,
% 8.57/4.58      ! [N1: int,R1: list_int,N22: int,R22: list_int] :
% 8.57/4.58        ( ( ( cons_int @ N1 @ R1 )
% 8.57/4.58          = ( cons_int @ N22 @ R22 ) )
% 8.57/4.58       => ( ( N1 = N22 )
% 8.57/4.58          & ( R1 = R22 ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4539_list__tail__coinc,axiom,
% 8.57/4.58      ! [N1: nat,R1: list_nat,N22: nat,R22: list_nat] :
% 8.57/4.58        ( ( ( cons_nat @ N1 @ R1 )
% 8.57/4.58          = ( cons_nat @ N22 @ R22 ) )
% 8.57/4.58       => ( ( N1 = N22 )
% 8.57/4.58          & ( R1 = R22 ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4540_list__tail__coinc,axiom,
% 8.57/4.58      ! [N1: char,R1: list_char,N22: char,R22: list_char] :
% 8.57/4.58        ( ( ( cons_char @ N1 @ R1 )
% 8.57/4.58          = ( cons_char @ N22 @ R22 ) )
% 8.57/4.58       => ( ( N1 = N22 )
% 8.57/4.58          & ( R1 = R22 ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4541_sorted__wrt__true,axiom,
% 8.57/4.58      ! [Xs: list_nat] :
% 8.57/4.58        ( sorted_wrt_nat
% 8.57/4.58        @ ^ [Uu: nat,Uv: nat] : $true
% 8.57/4.58        @ Xs ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4542_sorted__wrt__true,axiom,
% 8.57/4.58      ! [Xs: list_int] :
% 8.57/4.58        ( sorted_wrt_int
% 8.57/4.58        @ ^ [Uu: int,Uv: int] : $true
% 8.57/4.58        @ Xs ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4543_sorted1,axiom,
% 8.57/4.58      ! [X2: rat] : ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ X2 @ nil_rat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4544_sorted1,axiom,
% 8.57/4.58      ! [X2: num] : ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ X2 @ nil_num ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4545_sorted1,axiom,
% 8.57/4.58      ! [X2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X2 @ nil_nat ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4546_sorted1,axiom,
% 8.57/4.58      ! [X2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X2 @ nil_int ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4547_mergesort__by__rel__merge__induct,axiom,
% 8.57/4.58      ! [P: list_int > list_int > $o,R3: int > int > $o,Xs: list_int,Ys: list_int] :
% 8.57/4.58        ( ! [Xs2: list_int] : ( P @ Xs2 @ nil_int )
% 8.57/4.58       => ( ! [X_12: list_int] : ( P @ nil_int @ X_12 )
% 8.57/4.58         => ( ! [X3: int,Xs2: list_int,Y2: int,Ys4: list_int] :
% 8.57/4.58                ( ( R3 @ X3 @ Y2 )
% 8.57/4.58               => ( ( P @ Xs2 @ ( cons_int @ Y2 @ Ys4 ) )
% 8.57/4.58                 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58           => ( ! [X3: int,Xs2: list_int,Y2: int,Ys4: list_int] :
% 8.57/4.58                  ( ~ ( R3 @ X3 @ Y2 )
% 8.57/4.58                 => ( ( P @ ( cons_int @ X3 @ Xs2 ) @ Ys4 )
% 8.57/4.58                   => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4548_mergesort__by__rel__merge__induct,axiom,
% 8.57/4.58      ! [P: list_nat > list_int > $o,R3: nat > int > $o,Xs: list_nat,Ys: list_int] :
% 8.57/4.58        ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_int )
% 8.57/4.58       => ( ! [X_12: list_int] : ( P @ nil_nat @ X_12 )
% 8.57/4.58         => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int] :
% 8.57/4.58                ( ( R3 @ X3 @ Y2 )
% 8.57/4.58               => ( ( P @ Xs2 @ ( cons_int @ Y2 @ Ys4 ) )
% 8.57/4.58                 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58           => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int] :
% 8.57/4.58                  ( ~ ( R3 @ X3 @ Y2 )
% 8.57/4.58                 => ( ( P @ ( cons_nat @ X3 @ Xs2 ) @ Ys4 )
% 8.57/4.58                   => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4549_mergesort__by__rel__merge__induct,axiom,
% 8.57/4.58      ! [P: list_char > list_int > $o,R3: char > int > $o,Xs: list_char,Ys: list_int] :
% 8.57/4.58        ( ! [Xs2: list_char] : ( P @ Xs2 @ nil_int )
% 8.57/4.58       => ( ! [X_12: list_int] : ( P @ nil_char @ X_12 )
% 8.57/4.58         => ( ! [X3: char,Xs2: list_char,Y2: int,Ys4: list_int] :
% 8.57/4.58                ( ( R3 @ X3 @ Y2 )
% 8.57/4.58               => ( ( P @ Xs2 @ ( cons_int @ Y2 @ Ys4 ) )
% 8.57/4.58                 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58           => ( ! [X3: char,Xs2: list_char,Y2: int,Ys4: list_int] :
% 8.57/4.58                  ( ~ ( R3 @ X3 @ Y2 )
% 8.57/4.58                 => ( ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys4 )
% 8.57/4.58                   => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4550_mergesort__by__rel__merge__induct,axiom,
% 8.57/4.58      ! [P: list_int > list_nat > $o,R3: int > nat > $o,Xs: list_int,Ys: list_nat] :
% 8.57/4.58        ( ! [Xs2: list_int] : ( P @ Xs2 @ nil_nat )
% 8.57/4.58       => ( ! [X_12: list_nat] : ( P @ nil_int @ X_12 )
% 8.57/4.58         => ( ! [X3: int,Xs2: list_int,Y2: nat,Ys4: list_nat] :
% 8.57/4.58                ( ( R3 @ X3 @ Y2 )
% 8.57/4.58               => ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys4 ) )
% 8.57/4.58                 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58           => ( ! [X3: int,Xs2: list_int,Y2: nat,Ys4: list_nat] :
% 8.57/4.58                  ( ~ ( R3 @ X3 @ Y2 )
% 8.57/4.58                 => ( ( P @ ( cons_int @ X3 @ Xs2 ) @ Ys4 )
% 8.57/4.58                   => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4551_mergesort__by__rel__merge__induct,axiom,
% 8.57/4.58      ! [P: list_nat > list_nat > $o,R3: nat > nat > $o,Xs: list_nat,Ys: list_nat] :
% 8.57/4.58        ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_nat )
% 8.57/4.58       => ( ! [X_12: list_nat] : ( P @ nil_nat @ X_12 )
% 8.57/4.58         => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys4: list_nat] :
% 8.57/4.58                ( ( R3 @ X3 @ Y2 )
% 8.57/4.58               => ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys4 ) )
% 8.57/4.58                 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58           => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys4: list_nat] :
% 8.57/4.58                  ( ~ ( R3 @ X3 @ Y2 )
% 8.57/4.58                 => ( ( P @ ( cons_nat @ X3 @ Xs2 ) @ Ys4 )
% 8.57/4.58                   => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4552_mergesort__by__rel__merge__induct,axiom,
% 8.57/4.58      ! [P: list_char > list_nat > $o,R3: char > nat > $o,Xs: list_char,Ys: list_nat] :
% 8.57/4.58        ( ! [Xs2: list_char] : ( P @ Xs2 @ nil_nat )
% 8.57/4.58       => ( ! [X_12: list_nat] : ( P @ nil_char @ X_12 )
% 8.57/4.58         => ( ! [X3: char,Xs2: list_char,Y2: nat,Ys4: list_nat] :
% 8.57/4.58                ( ( R3 @ X3 @ Y2 )
% 8.57/4.58               => ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys4 ) )
% 8.57/4.58                 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58           => ( ! [X3: char,Xs2: list_char,Y2: nat,Ys4: list_nat] :
% 8.57/4.58                  ( ~ ( R3 @ X3 @ Y2 )
% 8.57/4.58                 => ( ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys4 )
% 8.57/4.58                   => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4553_mergesort__by__rel__merge__induct,axiom,
% 8.57/4.58      ! [P: list_int > list_char > $o,R3: int > char > $o,Xs: list_int,Ys: list_char] :
% 8.57/4.58        ( ! [Xs2: list_int] : ( P @ Xs2 @ nil_char )
% 8.57/4.58       => ( ! [X_12: list_char] : ( P @ nil_int @ X_12 )
% 8.57/4.58         => ( ! [X3: int,Xs2: list_int,Y2: char,Ys4: list_char] :
% 8.57/4.58                ( ( R3 @ X3 @ Y2 )
% 8.57/4.58               => ( ( P @ Xs2 @ ( cons_char @ Y2 @ Ys4 ) )
% 8.57/4.58                 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58           => ( ! [X3: int,Xs2: list_int,Y2: char,Ys4: list_char] :
% 8.57/4.58                  ( ~ ( R3 @ X3 @ Y2 )
% 8.57/4.58                 => ( ( P @ ( cons_int @ X3 @ Xs2 ) @ Ys4 )
% 8.57/4.58                   => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4554_mergesort__by__rel__merge__induct,axiom,
% 8.57/4.58      ! [P: list_nat > list_char > $o,R3: nat > char > $o,Xs: list_nat,Ys: list_char] :
% 8.57/4.58        ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_char )
% 8.57/4.58       => ( ! [X_12: list_char] : ( P @ nil_nat @ X_12 )
% 8.57/4.58         => ( ! [X3: nat,Xs2: list_nat,Y2: char,Ys4: list_char] :
% 8.57/4.58                ( ( R3 @ X3 @ Y2 )
% 8.57/4.58               => ( ( P @ Xs2 @ ( cons_char @ Y2 @ Ys4 ) )
% 8.57/4.58                 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58           => ( ! [X3: nat,Xs2: list_nat,Y2: char,Ys4: list_char] :
% 8.57/4.58                  ( ~ ( R3 @ X3 @ Y2 )
% 8.57/4.58                 => ( ( P @ ( cons_nat @ X3 @ Xs2 ) @ Ys4 )
% 8.57/4.58                   => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4555_mergesort__by__rel__merge__induct,axiom,
% 8.57/4.58      ! [P: list_char > list_char > $o,R3: char > char > $o,Xs: list_char,Ys: list_char] :
% 8.57/4.58        ( ! [Xs2: list_char] : ( P @ Xs2 @ nil_char )
% 8.57/4.58       => ( ! [X_12: list_char] : ( P @ nil_char @ X_12 )
% 8.57/4.58         => ( ! [X3: char,Xs2: list_char,Y2: char,Ys4: list_char] :
% 8.57/4.58                ( ( R3 @ X3 @ Y2 )
% 8.57/4.58               => ( ( P @ Xs2 @ ( cons_char @ Y2 @ Ys4 ) )
% 8.57/4.58                 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58           => ( ! [X3: char,Xs2: list_char,Y2: char,Ys4: list_char] :
% 8.57/4.58                  ( ~ ( R3 @ X3 @ Y2 )
% 8.57/4.58                 => ( ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys4 )
% 8.57/4.58                   => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y2 @ Ys4 ) ) ) )
% 8.57/4.58             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4556_list__induct__first2,axiom,
% 8.57/4.58      ! [P: list_int > $o,Xs: list_int] :
% 8.57/4.58        ( ( P @ nil_int )
% 8.57/4.58       => ( ! [X3: int] : ( P @ ( cons_int @ X3 @ nil_int ) )
% 8.57/4.58         => ( ! [X1: int,X23: int,Xs2: list_int] :
% 8.57/4.58                ( ( P @ Xs2 )
% 8.57/4.58               => ( P @ ( cons_int @ X1 @ ( cons_int @ X23 @ Xs2 ) ) ) )
% 8.57/4.58           => ( P @ Xs ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4557_list__induct__first2,axiom,
% 8.57/4.58      ! [P: list_nat > $o,Xs: list_nat] :
% 8.57/4.58        ( ( P @ nil_nat )
% 8.57/4.58       => ( ! [X3: nat] : ( P @ ( cons_nat @ X3 @ nil_nat ) )
% 8.57/4.58         => ( ! [X1: nat,X23: nat,Xs2: list_nat] :
% 8.57/4.58                ( ( P @ Xs2 )
% 8.57/4.58               => ( P @ ( cons_nat @ X1 @ ( cons_nat @ X23 @ Xs2 ) ) ) )
% 8.57/4.58           => ( P @ Xs ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4558_list__induct__first2,axiom,
% 8.57/4.58      ! [P: list_char > $o,Xs: list_char] :
% 8.57/4.58        ( ( P @ nil_char )
% 8.57/4.58       => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 8.57/4.58         => ( ! [X1: char,X23: char,Xs2: list_char] :
% 8.57/4.58                ( ( P @ Xs2 )
% 8.57/4.58               => ( P @ ( cons_char @ X1 @ ( cons_char @ X23 @ Xs2 ) ) ) )
% 8.57/4.58           => ( P @ Xs ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4559_list__2pre__induct,axiom,
% 8.57/4.58      ! [P: list_int > list_int > $o,W1: list_int,W22: list_int] :
% 8.57/4.58        ( ( P @ nil_int @ nil_int )
% 8.57/4.58       => ( ! [E3: int,W12: list_int,W23: list_int] :
% 8.57/4.58              ( ( P @ W12 @ W23 )
% 8.57/4.58             => ( P @ ( cons_int @ E3 @ W12 ) @ W23 ) )
% 8.57/4.58         => ( ! [E3: int,W13: list_int,W24: list_int] :
% 8.57/4.58                ( ( P @ W13 @ W24 )
% 8.57/4.58               => ( P @ W13 @ ( cons_int @ E3 @ W24 ) ) )
% 8.57/4.58           => ( P @ W1 @ W22 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4560_list__2pre__induct,axiom,
% 8.57/4.58      ! [P: list_int > list_nat > $o,W1: list_int,W22: list_nat] :
% 8.57/4.58        ( ( P @ nil_int @ nil_nat )
% 8.57/4.58       => ( ! [E3: int,W12: list_int,W23: list_nat] :
% 8.57/4.58              ( ( P @ W12 @ W23 )
% 8.57/4.58             => ( P @ ( cons_int @ E3 @ W12 ) @ W23 ) )
% 8.57/4.58         => ( ! [E3: nat,W13: list_int,W24: list_nat] :
% 8.57/4.58                ( ( P @ W13 @ W24 )
% 8.57/4.58               => ( P @ W13 @ ( cons_nat @ E3 @ W24 ) ) )
% 8.57/4.58           => ( P @ W1 @ W22 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4561_list__2pre__induct,axiom,
% 8.57/4.58      ! [P: list_int > list_char > $o,W1: list_int,W22: list_char] :
% 8.57/4.58        ( ( P @ nil_int @ nil_char )
% 8.57/4.58       => ( ! [E3: int,W12: list_int,W23: list_char] :
% 8.57/4.58              ( ( P @ W12 @ W23 )
% 8.57/4.58             => ( P @ ( cons_int @ E3 @ W12 ) @ W23 ) )
% 8.57/4.58         => ( ! [E3: char,W13: list_int,W24: list_char] :
% 8.57/4.58                ( ( P @ W13 @ W24 )
% 8.57/4.58               => ( P @ W13 @ ( cons_char @ E3 @ W24 ) ) )
% 8.57/4.58           => ( P @ W1 @ W22 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4562_list__2pre__induct,axiom,
% 8.57/4.58      ! [P: list_nat > list_int > $o,W1: list_nat,W22: list_int] :
% 8.57/4.58        ( ( P @ nil_nat @ nil_int )
% 8.57/4.58       => ( ! [E3: nat,W12: list_nat,W23: list_int] :
% 8.57/4.58              ( ( P @ W12 @ W23 )
% 8.57/4.58             => ( P @ ( cons_nat @ E3 @ W12 ) @ W23 ) )
% 8.57/4.58         => ( ! [E3: int,W13: list_nat,W24: list_int] :
% 8.57/4.58                ( ( P @ W13 @ W24 )
% 8.57/4.58               => ( P @ W13 @ ( cons_int @ E3 @ W24 ) ) )
% 8.57/4.58           => ( P @ W1 @ W22 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4563_list__2pre__induct,axiom,
% 8.57/4.58      ! [P: list_nat > list_nat > $o,W1: list_nat,W22: list_nat] :
% 8.57/4.58        ( ( P @ nil_nat @ nil_nat )
% 8.57/4.58       => ( ! [E3: nat,W12: list_nat,W23: list_nat] :
% 8.57/4.58              ( ( P @ W12 @ W23 )
% 8.57/4.58             => ( P @ ( cons_nat @ E3 @ W12 ) @ W23 ) )
% 8.57/4.58         => ( ! [E3: nat,W13: list_nat,W24: list_nat] :
% 8.57/4.58                ( ( P @ W13 @ W24 )
% 8.57/4.58               => ( P @ W13 @ ( cons_nat @ E3 @ W24 ) ) )
% 8.57/4.58           => ( P @ W1 @ W22 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4564_list__2pre__induct,axiom,
% 8.57/4.58      ! [P: list_nat > list_char > $o,W1: list_nat,W22: list_char] :
% 8.57/4.58        ( ( P @ nil_nat @ nil_char )
% 8.57/4.58       => ( ! [E3: nat,W12: list_nat,W23: list_char] :
% 8.57/4.58              ( ( P @ W12 @ W23 )
% 8.57/4.58             => ( P @ ( cons_nat @ E3 @ W12 ) @ W23 ) )
% 8.57/4.58         => ( ! [E3: char,W13: list_nat,W24: list_char] :
% 8.57/4.58                ( ( P @ W13 @ W24 )
% 8.57/4.58               => ( P @ W13 @ ( cons_char @ E3 @ W24 ) ) )
% 8.57/4.58           => ( P @ W1 @ W22 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4565_list__2pre__induct,axiom,
% 8.57/4.58      ! [P: list_char > list_int > $o,W1: list_char,W22: list_int] :
% 8.57/4.58        ( ( P @ nil_char @ nil_int )
% 8.57/4.58       => ( ! [E3: char,W12: list_char,W23: list_int] :
% 8.57/4.58              ( ( P @ W12 @ W23 )
% 8.57/4.58             => ( P @ ( cons_char @ E3 @ W12 ) @ W23 ) )
% 8.57/4.58         => ( ! [E3: int,W13: list_char,W24: list_int] :
% 8.57/4.58                ( ( P @ W13 @ W24 )
% 8.57/4.58               => ( P @ W13 @ ( cons_int @ E3 @ W24 ) ) )
% 8.57/4.58           => ( P @ W1 @ W22 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4566_list__2pre__induct,axiom,
% 8.57/4.58      ! [P: list_char > list_nat > $o,W1: list_char,W22: list_nat] :
% 8.57/4.58        ( ( P @ nil_char @ nil_nat )
% 8.57/4.58       => ( ! [E3: char,W12: list_char,W23: list_nat] :
% 8.57/4.58              ( ( P @ W12 @ W23 )
% 8.57/4.58             => ( P @ ( cons_char @ E3 @ W12 ) @ W23 ) )
% 8.57/4.58         => ( ! [E3: nat,W13: list_char,W24: list_nat] :
% 8.57/4.58                ( ( P @ W13 @ W24 )
% 8.57/4.58               => ( P @ W13 @ ( cons_nat @ E3 @ W24 ) ) )
% 8.57/4.58           => ( P @ W1 @ W22 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4567_list__2pre__induct,axiom,
% 8.57/4.58      ! [P: list_char > list_char > $o,W1: list_char,W22: list_char] :
% 8.57/4.58        ( ( P @ nil_char @ nil_char )
% 8.57/4.58       => ( ! [E3: char,W12: list_char,W23: list_char] :
% 8.57/4.58              ( ( P @ W12 @ W23 )
% 8.57/4.58             => ( P @ ( cons_char @ E3 @ W12 ) @ W23 ) )
% 8.57/4.58         => ( ! [E3: char,W13: list_char,W24: list_char] :
% 8.57/4.58                ( ( P @ W13 @ W24 )
% 8.57/4.58               => ( P @ W13 @ ( cons_char @ E3 @ W24 ) ) )
% 8.57/4.58           => ( P @ W1 @ W22 ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4568_neq__NilE,axiom,
% 8.57/4.58      ! [L: list_int] :
% 8.57/4.58        ( ( L != nil_int )
% 8.57/4.58       => ~ ! [X3: int,Xs2: list_int] :
% 8.57/4.58              ( L
% 8.57/4.58             != ( cons_int @ X3 @ Xs2 ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4569_neq__NilE,axiom,
% 8.57/4.58      ! [L: list_nat] :
% 8.57/4.58        ( ( L != nil_nat )
% 8.57/4.58       => ~ ! [X3: nat,Xs2: list_nat] :
% 8.57/4.58              ( L
% 8.57/4.58             != ( cons_nat @ X3 @ Xs2 ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4570_neq__NilE,axiom,
% 8.57/4.58      ! [L: list_char] :
% 8.57/4.58        ( ( L != nil_char )
% 8.57/4.58       => ~ ! [X3: char,Xs2: list_char] :
% 8.57/4.58              ( L
% 8.57/4.58             != ( cons_char @ X3 @ Xs2 ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4571_strict__sorted__imp__sorted,axiom,
% 8.57/4.58      ! [Xs: list_Code_integer] :
% 8.57/4.58        ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ Xs )
% 8.57/4.58       => ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4572_strict__sorted__imp__sorted,axiom,
% 8.57/4.58      ! [Xs: list_rat] :
% 8.57/4.58        ( ( sorted_wrt_rat @ ord_less_rat @ Xs )
% 8.57/4.58       => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4573_strict__sorted__imp__sorted,axiom,
% 8.57/4.58      ! [Xs: list_num] :
% 8.57/4.58        ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 8.57/4.58       => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4574_strict__sorted__imp__sorted,axiom,
% 8.57/4.58      ! [Xs: list_nat] :
% 8.57/4.58        ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 8.57/4.58       => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4575_strict__sorted__imp__sorted,axiom,
% 8.57/4.58      ! [Xs: list_int] :
% 8.57/4.58        ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 8.57/4.58       => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4576_sorted0,axiom,
% 8.57/4.58      sorted_wrt_rat @ ord_less_eq_rat @ nil_rat ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4577_sorted0,axiom,
% 8.57/4.58      sorted_wrt_num @ ord_less_eq_num @ nil_num ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4578_sorted0,axiom,
% 8.57/4.58      sorted_wrt_nat @ ord_less_eq_nat @ nil_nat ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4579_sorted0,axiom,
% 8.57/4.58      sorted_wrt_int @ ord_less_eq_int @ nil_int ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4580_sorted__wrt__less__idx,axiom,
% 8.57/4.58      ! [Ns: list_nat,I: nat] :
% 8.57/4.58        ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 8.57/4.58       => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 8.57/4.58         => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4581_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_char,Ws: list_char,P: list_nat > list_int > list_char > list_char > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_char @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_char @ Zs )
% 8.57/4.58              = ( size_size_list_char @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_char @ nil_char )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: char,Zs2: list_char,W3: char,Ws2: list_char] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_char @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_char @ Zs2 )
% 8.57/4.58                          = ( size_size_list_char @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_char @ Z4 @ Zs2 ) @ ( cons_char @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4582_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_char,Ws: list_nat,P: list_nat > list_int > list_char > list_nat > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_char @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_char @ Zs )
% 8.57/4.58              = ( size_size_list_nat @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_char @ nil_nat )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: char,Zs2: list_char,W3: nat,Ws2: list_nat] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_char @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_char @ Zs2 )
% 8.57/4.58                          = ( size_size_list_nat @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_char @ Z4 @ Zs2 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4583_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_char,Ws: list_int,P: list_nat > list_int > list_char > list_int > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_char @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_char @ Zs )
% 8.57/4.58              = ( size_size_list_int @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_char @ nil_int )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: char,Zs2: list_char,W3: int,Ws2: list_int] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_char @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_char @ Zs2 )
% 8.57/4.58                          = ( size_size_list_int @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_char @ Z4 @ Zs2 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4584_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_char,Ws: list_o,P: list_nat > list_int > list_char > list_o > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_char @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_char @ Zs )
% 8.57/4.58              = ( size_size_list_o @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_char @ nil_o )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: char,Zs2: list_char,W3: $o,Ws2: list_o] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_char @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_char @ Zs2 )
% 8.57/4.58                          = ( size_size_list_o @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_char @ Z4 @ Zs2 ) @ ( cons_o @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4585_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_nat,Ws: list_char,P: list_nat > list_int > list_nat > list_char > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_nat @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_nat @ Zs )
% 8.57/4.58              = ( size_size_list_char @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_nat @ nil_char )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: nat,Zs2: list_nat,W3: char,Ws2: list_char] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_nat @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_nat @ Zs2 )
% 8.57/4.58                          = ( size_size_list_char @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_nat @ Z4 @ Zs2 ) @ ( cons_char @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4586_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_nat,Ws: list_nat,P: list_nat > list_int > list_nat > list_nat > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_nat @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_nat @ Zs )
% 8.57/4.58              = ( size_size_list_nat @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_nat @ nil_nat )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: nat,Zs2: list_nat,W3: nat,Ws2: list_nat] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_nat @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_nat @ Zs2 )
% 8.57/4.58                          = ( size_size_list_nat @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_nat @ Z4 @ Zs2 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4587_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_nat,Ws: list_int,P: list_nat > list_int > list_nat > list_int > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_nat @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_nat @ Zs )
% 8.57/4.58              = ( size_size_list_int @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_nat @ nil_int )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: nat,Zs2: list_nat,W3: int,Ws2: list_int] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_nat @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_nat @ Zs2 )
% 8.57/4.58                          = ( size_size_list_int @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_nat @ Z4 @ Zs2 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4588_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_nat,Ws: list_o,P: list_nat > list_int > list_nat > list_o > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_nat @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_nat @ Zs )
% 8.57/4.58              = ( size_size_list_o @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_nat @ nil_o )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: nat,Zs2: list_nat,W3: $o,Ws2: list_o] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_nat @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_nat @ Zs2 )
% 8.57/4.58                          = ( size_size_list_o @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_nat @ Z4 @ Zs2 ) @ ( cons_o @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4589_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_int,Ws: list_char,P: list_nat > list_int > list_int > list_char > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_int @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_int @ Zs )
% 8.57/4.58              = ( size_size_list_char @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_int @ nil_char )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: int,Zs2: list_int,W3: char,Ws2: list_char] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_int @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_int @ Zs2 )
% 8.57/4.58                          = ( size_size_list_char @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_int @ Z4 @ Zs2 ) @ ( cons_char @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4590_list__induct4,axiom,
% 8.57/4.58      ! [Xs: list_nat,Ys: list_int,Zs: list_int,Ws: list_nat,P: list_nat > list_int > list_int > list_nat > $o] :
% 8.57/4.58        ( ( ( size_size_list_nat @ Xs )
% 8.57/4.58          = ( size_size_list_int @ Ys ) )
% 8.57/4.58       => ( ( ( size_size_list_int @ Ys )
% 8.57/4.58            = ( size_size_list_int @ Zs ) )
% 8.57/4.58         => ( ( ( size_size_list_int @ Zs )
% 8.57/4.58              = ( size_size_list_nat @ Ws ) )
% 8.57/4.58           => ( ( P @ nil_nat @ nil_int @ nil_int @ nil_nat )
% 8.57/4.58             => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys4: list_int,Z4: int,Zs2: list_int,W3: nat,Ws2: list_nat] :
% 8.57/4.58                    ( ( ( size_size_list_nat @ Xs2 )
% 8.57/4.58                      = ( size_size_list_int @ Ys4 ) )
% 8.57/4.58                   => ( ( ( size_size_list_int @ Ys4 )
% 8.57/4.58                        = ( size_size_list_int @ Zs2 ) )
% 8.57/4.58                     => ( ( ( size_size_list_int @ Zs2 )
% 8.57/4.58                          = ( size_size_list_nat @ Ws2 ) )
% 8.57/4.58                       => ( ( P @ Xs2 @ Ys4 @ Zs2 @ Ws2 )
% 8.57/4.58                         => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys4 ) @ ( cons_int @ Z4 @ Zs2 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 8.57/4.58               => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4591_upto__aux__rec,axiom,
% 8.57/4.58      ( upto_aux
% 8.57/4.58      = ( ^ [I2: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I2 ) @ Js @ ( upto_aux @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4592_upto__rec__numeral_I4_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 8.57/4.58        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58            = nil_int ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4593_upto__rec__numeral_I3_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.58         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.58            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 8.57/4.58        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.58         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.58            = nil_int ) ) ) ).
% 8.57/4.58  
% 8.57/4.58  thf(fact_4594_upto__rec__numeral_I2_J,axiom,
% 8.57/4.58      ! [M: num,N: num] :
% 8.57/4.58        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 8.57/4.58        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.58         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.59            = nil_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4595_Suc__numeral,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( suc @ ( numeral_numeral_nat @ N ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4596_nth__upto,axiom,
% 8.57/4.59      ! [I: int,K: nat,J: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 8.57/4.59       => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 8.57/4.59          = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4597_length__upto,axiom,
% 8.57/4.59      ! [I: int,J: int] :
% 8.57/4.59        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 8.57/4.59        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4598_upto__rec__numeral_I1_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.59         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.59            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 8.57/4.59        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.59         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.59            = nil_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4599_num_Osize_I4_J,axiom,
% 8.57/4.59      ( ( size_size_num @ one )
% 8.57/4.59      = zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4600_sorted__upto,axiom,
% 8.57/4.59      ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4601_add__One__commute,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( plus_plus_num @ one @ N )
% 8.57/4.59        = ( plus_plus_num @ N @ one ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4602_num__induct,axiom,
% 8.57/4.59      ! [P: num > $o,X2: num] :
% 8.57/4.59        ( ( P @ one )
% 8.57/4.59       => ( ! [X3: num] :
% 8.57/4.59              ( ( P @ X3 )
% 8.57/4.59             => ( P @ ( inc @ X3 ) ) )
% 8.57/4.59         => ( P @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4603_le__num__One__iff,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( ord_less_eq_num @ X2 @ one )
% 8.57/4.59        = ( X2 = one ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4604_numerals_I1_J,axiom,
% 8.57/4.59      ( ( numeral_numeral_nat @ one )
% 8.57/4.59      = one_one_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4605_add__One,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( plus_plus_num @ X2 @ one )
% 8.57/4.59        = ( inc @ X2 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4606_numeral__1__eq__Suc__0,axiom,
% 8.57/4.59      ( ( numeral_numeral_nat @ one )
% 8.57/4.59      = ( suc @ zero_zero_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4607_upto__rec1,axiom,
% 8.57/4.59      ! [I: int,J: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ I @ J )
% 8.57/4.59       => ( ( upto @ I @ J )
% 8.57/4.59          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4608_upto_Osimps,axiom,
% 8.57/4.59      ( upto
% 8.57/4.59      = ( ^ [I2: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I2 @ J3 ) @ ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4609_upto_Oelims,axiom,
% 8.57/4.59      ! [X2: int,Xa: int,Y: list_int] :
% 8.57/4.59        ( ( ( upto @ X2 @ Xa )
% 8.57/4.59          = Y )
% 8.57/4.59       => ( ( ( ord_less_eq_int @ X2 @ Xa )
% 8.57/4.59           => ( Y
% 8.57/4.59              = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa ) ) ) )
% 8.57/4.59          & ( ~ ( ord_less_eq_int @ X2 @ Xa )
% 8.57/4.59           => ( Y = nil_int ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4610_Suc__nat__number__of__add,axiom,
% 8.57/4.59      ! [V: num,N: nat] :
% 8.57/4.59        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 8.57/4.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4611_neg__zmod__mult__2,axiom,
% 8.57/4.59      ! [A: int,B: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.59       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.57/4.59          = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4612_verit__eq__simplify_I8_J,axiom,
% 8.57/4.59      ! [X22: num,Y22: num] :
% 8.57/4.59        ( ( ( bit0 @ X22 )
% 8.57/4.59          = ( bit0 @ Y22 ) )
% 8.57/4.59        = ( X22 = Y22 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4613_semiring__norm_I6_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 8.57/4.59        = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4614_semiring__norm_I2_J,axiom,
% 8.57/4.59      ( ( plus_plus_num @ one @ one )
% 8.57/4.59      = ( bit0 @ one ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4615_num__double,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( times_times_num @ ( bit0 @ one ) @ N )
% 8.57/4.59        = ( bit0 @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4616_add__2__eq__Suc_H,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59        = ( suc @ ( suc @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4617_add__2__eq__Suc,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.57/4.59        = ( suc @ ( suc @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4618_Suc__1,axiom,
% 8.57/4.59      ( ( suc @ one_one_nat )
% 8.57/4.59      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4619_add__self__div__2,axiom,
% 8.57/4.59      ! [M: nat] :
% 8.57/4.59        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59        = M ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4620_not__mod2__eq__Suc__0__eq__0,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59         != ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59          = zero_zero_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4621_add__self__mod__2,axiom,
% 8.57/4.59      ! [M: nat] :
% 8.57/4.59        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59        = zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4622_half__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 8.57/4.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4623_half__negative__int__iff,axiom,
% 8.57/4.59      ! [K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 8.57/4.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4624_mod2__gr__0,axiom,
% 8.57/4.59      ! [M: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.57/4.59        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59          = one_one_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4625_verit__eq__simplify_I10_J,axiom,
% 8.57/4.59      ! [X22: num] :
% 8.57/4.59        ( one
% 8.57/4.59       != ( bit0 @ X22 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4626_inc_Osimps_I1_J,axiom,
% 8.57/4.59      ( ( inc @ one )
% 8.57/4.59      = ( bit0 @ one ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4627_num_Osize_I5_J,axiom,
% 8.57/4.59      ! [X22: num] :
% 8.57/4.59        ( ( size_size_num @ ( bit0 @ X22 ) )
% 8.57/4.59        = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4628_numeral__2__eq__2,axiom,
% 8.57/4.59      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 8.57/4.59      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4629_nat__1__add__1,axiom,
% 8.57/4.59      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 8.57/4.59      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4630_power2__nat__le__imp__le,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 8.57/4.59       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4631_power2__nat__le__eq__le,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.57/4.59        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4632_self__le__ge2__pow,axiom,
% 8.57/4.59      ! [K: nat,M: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.57/4.59       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4633_less__2__cases__iff,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59        = ( ( N = zero_zero_nat )
% 8.57/4.59          | ( N
% 8.57/4.59            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4634_less__2__cases,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59       => ( ( N = zero_zero_nat )
% 8.57/4.59          | ( N
% 8.57/4.59            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4635_nat__induct2,axiom,
% 8.57/4.59      ! [P: nat > $o,N: nat] :
% 8.57/4.59        ( ( P @ zero_zero_nat )
% 8.57/4.59       => ( ( P @ one_one_nat )
% 8.57/4.59         => ( ! [N2: nat] :
% 8.57/4.59                ( ( P @ N2 )
% 8.57/4.59               => ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.57/4.59           => ( P @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4636_nat__2,axiom,
% 8.57/4.59      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.57/4.59      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4637_diff__le__diff__pow,axiom,
% 8.57/4.59      ! [K: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.57/4.59       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4638_not__exp__less__eq__0__int,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4639_nat__bit__induct,axiom,
% 8.57/4.59      ! [P: nat > $o,N: nat] :
% 8.57/4.59        ( ( P @ zero_zero_nat )
% 8.57/4.59       => ( ! [N2: nat] :
% 8.57/4.59              ( ( P @ N2 )
% 8.57/4.59             => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 8.57/4.59               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 8.57/4.59         => ( ! [N2: nat] :
% 8.57/4.59                ( ( P @ N2 )
% 8.57/4.59               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 8.57/4.59           => ( P @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4640_div__2__gt__zero,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.59       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4641_Suc__n__div__2__gt__zero,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4642_minus__1__div__exp__eq__int,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.57/4.59        = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4643_ex__power__ivl2,axiom,
% 8.57/4.59      ! [B: nat,K: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.57/4.59       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.57/4.59         => ? [N2: nat] :
% 8.57/4.59              ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 8.57/4.59              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4644_ex__power__ivl1,axiom,
% 8.57/4.59      ! [B: nat,K: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.57/4.59       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 8.57/4.59         => ? [N2: nat] :
% 8.57/4.59              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 8.57/4.59              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4645_int__bit__induct,axiom,
% 8.57/4.59      ! [P: int > $o,K: int] :
% 8.57/4.59        ( ( P @ zero_zero_int )
% 8.57/4.59       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.59         => ( ! [K3: int] :
% 8.57/4.59                ( ( P @ K3 )
% 8.57/4.59               => ( ( K3 != zero_zero_int )
% 8.57/4.59                 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 8.57/4.59           => ( ! [K3: int] :
% 8.57/4.59                  ( ( P @ K3 )
% 8.57/4.59                 => ( ( K3
% 8.57/4.59                     != ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.59                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 8.57/4.59             => ( P @ K ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4646_pos__zdiv__mult__2,axiom,
% 8.57/4.59      ! [A: int,B: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.59       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.57/4.59          = ( divide_divide_int @ B @ A ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4647_neg__zdiv__mult__2,axiom,
% 8.57/4.59      ! [A: int,B: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.57/4.59       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.57/4.59          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4648_pos__zmod__mult__2,axiom,
% 8.57/4.59      ! [A: int,B: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.57/4.59       => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.57/4.59          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4649_unset__bit__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 8.57/4.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4650_set__bit__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 8.57/4.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4651_flip__bit__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 8.57/4.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4652_unset__bit__negative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 8.57/4.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4653_set__bit__negative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 8.57/4.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4654_flip__bit__negative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 8.57/4.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4655_signed__take__bit__add,axiom,
% 8.57/4.59      ! [N: nat,K: int,L: int] :
% 8.57/4.59        ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 8.57/4.59        = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4656_unset__bit__nat__def,axiom,
% 8.57/4.59      ( bit_se4205575877204974255it_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M2 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4657_unset__bit__less__eq,axiom,
% 8.57/4.59      ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4658_set__bit__greater__eq,axiom,
% 8.57/4.59      ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4659_signed__take__bit__int__greater__eq__self__iff,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 8.57/4.59        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4660_signed__take__bit__int__less__self__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 8.57/4.59        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4661_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 8.57/4.59      ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4662_signed__take__bit__int__less__eq__self__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 8.57/4.59        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4663_signed__take__bit__int__less__eq,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 8.57/4.59       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4664_signed__take__bit__int__eq__self__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 8.57/4.59          = K )
% 8.57/4.59        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 8.57/4.59          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4665_signed__take__bit__int__eq__self,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 8.57/4.59       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.57/4.59         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 8.57/4.59            = K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4666_signed__take__bit__int__greater__eq,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 8.57/4.59       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4667_binomial__code,axiom,
% 8.57/4.59      ( binomial
% 8.57/4.59      = ( ^ [N3: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N3 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N3 @ ( minus_minus_nat @ N3 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N3 @ K2 ) @ one_one_nat ) @ N3 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4668_signed__take__bit__Suc__minus__bit1,axiom,
% 8.57/4.59      ! [N: nat,K: num] :
% 8.57/4.59        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.57/4.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4669_concat__bit__Suc,axiom,
% 8.57/4.59      ! [N: nat,K: int,L: int] :
% 8.57/4.59        ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 8.57/4.59        = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4670_verit__eq__simplify_I9_J,axiom,
% 8.57/4.59      ! [X32: num,Y32: num] :
% 8.57/4.59        ( ( ( bit1 @ X32 )
% 8.57/4.59          = ( bit1 @ Y32 ) )
% 8.57/4.59        = ( X32 = Y32 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4671_nat__dvd__1__iff__1,axiom,
% 8.57/4.59      ! [M: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 8.57/4.59        = ( M = one_one_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4672_int__dvd__int__iff,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.57/4.59        = ( dvd_dvd_nat @ M @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4673_dvd__1__iff__1,axiom,
% 8.57/4.59      ! [M: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( M
% 8.57/4.59          = ( suc @ zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4674_dvd__1__left,axiom,
% 8.57/4.59      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4675_nat__mult__dvd__cancel__disj,axiom,
% 8.57/4.59      ! [K: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.59        = ( ( K = zero_zero_nat )
% 8.57/4.59          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4676_zdvd1__eq,axiom,
% 8.57/4.59      ! [X2: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ X2 @ one_one_int )
% 8.57/4.59        = ( ( abs_abs_int @ X2 )
% 8.57/4.59          = one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4677_binomial__n__n,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( binomial @ N @ N )
% 8.57/4.59        = one_one_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4678_concat__bit__0,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 8.57/4.59        = L ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4679_concat__bit__of__zero__2,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 8.57/4.59        = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4680_binomial__1,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = N ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4681_binomial__0__Suc,axiom,
% 8.57/4.59      ! [K: nat] :
% 8.57/4.59        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 8.57/4.59        = zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4682_binomial__eq__0__iff,axiom,
% 8.57/4.59      ! [N: nat,K: nat] :
% 8.57/4.59        ( ( ( binomial @ N @ K )
% 8.57/4.59          = zero_zero_nat )
% 8.57/4.59        = ( ord_less_nat @ N @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4683_binomial__Suc__Suc,axiom,
% 8.57/4.59      ! [N: nat,K: nat] :
% 8.57/4.59        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 8.57/4.59        = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4684_semiring__norm_I7_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.57/4.59        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4685_semiring__norm_I9_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.57/4.59        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4686_binomial__n__0,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( binomial @ N @ zero_zero_nat )
% 8.57/4.59        = one_one_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4687_dvd__nat__abs__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( dvd_dvd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 8.57/4.59        = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4688_nat__abs__dvd__iff,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 8.57/4.59        = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4689_concat__bit__nonnegative__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int,L: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 8.57/4.59        = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4690_concat__bit__negative__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int,L: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 8.57/4.59        = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4691_zero__less__binomial__iff,axiom,
% 8.57/4.59      ! [N: nat,K: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 8.57/4.59        = ( ord_less_eq_nat @ K @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4692_semiring__norm_I3_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 8.57/4.59        = ( bit1 @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4693_semiring__norm_I4_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 8.57/4.59        = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4694_semiring__norm_I5_J,axiom,
% 8.57/4.59      ! [M: num] :
% 8.57/4.59        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 8.57/4.59        = ( bit1 @ M ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4695_semiring__norm_I8_J,axiom,
% 8.57/4.59      ! [M: num] :
% 8.57/4.59        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 8.57/4.59        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4696_semiring__norm_I10_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.57/4.59        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4697_semiring__norm_I16_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.57/4.59        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4698_odd__Suc__minus__one,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.57/4.59       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 8.57/4.59          = N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4699_even__diff__nat,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.59        = ( ( ord_less_nat @ M @ N )
% 8.57/4.59          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4700_Suc__mod__eq__add3__mod__numeral,axiom,
% 8.57/4.59      ! [M: nat,V: num] :
% 8.57/4.59        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 8.57/4.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4701_mod__Suc__eq__mod__add3,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 8.57/4.59        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4702_Suc__div__eq__add3__div__numeral,axiom,
% 8.57/4.59      ! [M: nat,V: num] :
% 8.57/4.59        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 8.57/4.59        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4703_div__Suc__eq__div__add3,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 8.57/4.59        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4704_odd__two__times__div__two__nat,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.57/4.59       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.57/4.59          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4705_zmod__numeral__Bit1,axiom,
% 8.57/4.59      ! [V: num,W2: num] :
% 8.57/4.59        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 8.57/4.59        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W2 ) ) ) @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4706_signed__take__bit__Suc__bit1,axiom,
% 8.57/4.59      ! [N: nat,K: num] :
% 8.57/4.59        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 8.57/4.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4707_take__bit__nat__less__eq__self,axiom,
% 8.57/4.59      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4708_take__bit__tightened__less__eq__nat,axiom,
% 8.57/4.59      ! [M: nat,N: nat,Q2: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4709_choose__one,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( binomial @ N @ one_one_nat )
% 8.57/4.59        = N ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4710_verit__eq__simplify_I14_J,axiom,
% 8.57/4.59      ! [X22: num,X32: num] :
% 8.57/4.59        ( ( bit0 @ X22 )
% 8.57/4.59       != ( bit1 @ X32 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4711_verit__eq__simplify_I12_J,axiom,
% 8.57/4.59      ! [X32: num] :
% 8.57/4.59        ( one
% 8.57/4.59       != ( bit1 @ X32 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4712_gcd__nat_Oextremum,axiom,
% 8.57/4.59      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4713_gcd__nat_Oextremum__strict,axiom,
% 8.57/4.59      ! [A: nat] :
% 8.57/4.59        ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.57/4.59          & ( zero_zero_nat != A ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4714_gcd__nat_Oextremum__unique,axiom,
% 8.57/4.59      ! [A: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.57/4.59        = ( A = zero_zero_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4715_gcd__nat_Onot__eq__extremum,axiom,
% 8.57/4.59      ! [A: nat] :
% 8.57/4.59        ( ( A != zero_zero_nat )
% 8.57/4.59        = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 8.57/4.59          & ( A != zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4716_gcd__nat_Oextremum__uniqueI,axiom,
% 8.57/4.59      ! [A: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.57/4.59       => ( A = zero_zero_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4717_dvd__diff__nat,axiom,
% 8.57/4.59      ! [K: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ K @ M )
% 8.57/4.59       => ( ( dvd_dvd_nat @ K @ N )
% 8.57/4.59         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4718_uminus__dvd__conv_I2_J,axiom,
% 8.57/4.59      ( dvd_dvd_int
% 8.57/4.59      = ( ^ [D4: int,T2: int] : ( dvd_dvd_int @ D4 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4719_uminus__dvd__conv_I1_J,axiom,
% 8.57/4.59      ( dvd_dvd_int
% 8.57/4.59      = ( ^ [D4: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D4 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4720_zdvd__zdiffD,axiom,
% 8.57/4.59      ! [K: int,M: int,N: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 8.57/4.59       => ( ( dvd_dvd_int @ K @ N )
% 8.57/4.59         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4721_zdvd__antisym__abs,axiom,
% 8.57/4.59      ! [A: int,B: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ A @ B )
% 8.57/4.59       => ( ( dvd_dvd_int @ B @ A )
% 8.57/4.59         => ( ( abs_abs_int @ A )
% 8.57/4.59            = ( abs_abs_int @ B ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4722_take__bit__nat__eq,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.59       => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 8.57/4.59          = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4723_nat__take__bit__eq,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.59       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 8.57/4.59          = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4724_concat__bit__assoc,axiom,
% 8.57/4.59      ! [N: nat,K: int,M: nat,L: int,R: int] :
% 8.57/4.59        ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R ) )
% 8.57/4.59        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4725_binomial__eq__0,axiom,
% 8.57/4.59      ! [N: nat,K: nat] :
% 8.57/4.59        ( ( ord_less_nat @ N @ K )
% 8.57/4.59       => ( ( binomial @ N @ K )
% 8.57/4.59          = zero_zero_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4726_binomial__symmetric,axiom,
% 8.57/4.59      ! [K: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.59       => ( ( binomial @ N @ K )
% 8.57/4.59          = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4727_take__bit__tightened__less__eq__int,axiom,
% 8.57/4.59      ! [M: nat,N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4728_take__bit__int__less__eq__self__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 8.57/4.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4729_take__bit__nonnegative,axiom,
% 8.57/4.59      ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4730_not__take__bit__negative,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4731_take__bit__int__greater__self__iff,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 8.57/4.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4732_choose__mult__lemma,axiom,
% 8.57/4.59      ! [M: nat,R: nat,K: nat] :
% 8.57/4.59        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 8.57/4.59        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4733_num_Oexhaust,axiom,
% 8.57/4.59      ! [Y: num] :
% 8.57/4.59        ( ( Y != one )
% 8.57/4.59       => ( ! [X23: num] :
% 8.57/4.59              ( Y
% 8.57/4.59             != ( bit0 @ X23 ) )
% 8.57/4.59         => ~ ! [X33: num] :
% 8.57/4.59                ( Y
% 8.57/4.59               != ( bit1 @ X33 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4734_binomial__le__pow,axiom,
% 8.57/4.59      ! [R: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ R @ N )
% 8.57/4.59       => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4735_dvd__pos__nat,axiom,
% 8.57/4.59      ! [N: nat,M: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59       => ( ( dvd_dvd_nat @ M @ N )
% 8.57/4.59         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4736_nat__dvd__not__less,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.59       => ( ( ord_less_nat @ M @ N )
% 8.57/4.59         => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4737_dvd__minus__self,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 8.57/4.59        = ( ( ord_less_nat @ N @ M )
% 8.57/4.59          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4738_zdvd__antisym__nonneg,axiom,
% 8.57/4.59      ! [M: int,N: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 8.57/4.59       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 8.57/4.59         => ( ( dvd_dvd_int @ M @ N )
% 8.57/4.59           => ( ( dvd_dvd_int @ N @ M )
% 8.57/4.59             => ( M = N ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4739_zdvd__not__zless,axiom,
% 8.57/4.59      ! [M: int,N: int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ M )
% 8.57/4.59       => ( ( ord_less_int @ M @ N )
% 8.57/4.59         => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4740_less__eq__dvd__minus,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59       => ( ( dvd_dvd_nat @ M @ N )
% 8.57/4.59          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4741_dvd__diffD1,axiom,
% 8.57/4.59      ! [K: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.59       => ( ( dvd_dvd_nat @ K @ M )
% 8.57/4.59         => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.59           => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4742_dvd__diffD,axiom,
% 8.57/4.59      ! [K: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 8.57/4.59       => ( ( dvd_dvd_nat @ K @ N )
% 8.57/4.59         => ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.59           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4743_zdvd__mult__cancel,axiom,
% 8.57/4.59      ! [K: int,M: int,N: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 8.57/4.59       => ( ( K != zero_zero_int )
% 8.57/4.59         => ( dvd_dvd_int @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4744_zdvd__mono,axiom,
% 8.57/4.59      ! [K: int,M: int,T: int] :
% 8.57/4.59        ( ( K != zero_zero_int )
% 8.57/4.59       => ( ( dvd_dvd_int @ M @ T )
% 8.57/4.59          = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4745_bezout__add__nat,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59      ? [D5: nat,X3: nat,Y2: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ D5 @ A )
% 8.57/4.59        & ( dvd_dvd_nat @ D5 @ B )
% 8.57/4.59        & ( ( ( times_times_nat @ A @ X3 )
% 8.57/4.59            = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D5 ) )
% 8.57/4.59          | ( ( times_times_nat @ B @ X3 )
% 8.57/4.59            = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D5 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4746_bezout__lemma__nat,axiom,
% 8.57/4.59      ! [D: nat,A: nat,B: nat,X2: nat,Y: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ D @ A )
% 8.57/4.59       => ( ( dvd_dvd_nat @ D @ B )
% 8.57/4.59         => ( ( ( ( times_times_nat @ A @ X2 )
% 8.57/4.59                = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 8.57/4.59              | ( ( times_times_nat @ B @ X2 )
% 8.57/4.59                = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 8.57/4.59           => ? [X3: nat,Y2: nat] :
% 8.57/4.59                ( ( dvd_dvd_nat @ D @ A )
% 8.57/4.59                & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 8.57/4.59                & ( ( ( times_times_nat @ A @ X3 )
% 8.57/4.59                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y2 ) @ D ) )
% 8.57/4.59                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 8.57/4.59                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4747_bezout1__nat,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59      ? [D5: nat,X3: nat,Y2: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ D5 @ A )
% 8.57/4.59        & ( dvd_dvd_nat @ D5 @ B )
% 8.57/4.59        & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y2 ) )
% 8.57/4.59            = D5 )
% 8.57/4.59          | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y2 ) )
% 8.57/4.59            = D5 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4748_zdvd__reduce,axiom,
% 8.57/4.59      ! [K: int,N: int,M: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 8.57/4.59        = ( dvd_dvd_int @ K @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4749_zdvd__period,axiom,
% 8.57/4.59      ! [A: int,D: int,X2: int,T: int,C: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ A @ D )
% 8.57/4.59       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X2 @ T ) )
% 8.57/4.59          = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X2 @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4750_inc_Osimps_I3_J,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( inc @ ( bit1 @ X2 ) )
% 8.57/4.59        = ( bit0 @ ( inc @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4751_inc_Osimps_I2_J,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( inc @ ( bit0 @ X2 ) )
% 8.57/4.59        = ( bit1 @ X2 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4752_nat__dvd__iff,axiom,
% 8.57/4.59      ! [Z2: int,M: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ ( nat2 @ Z2 ) @ M )
% 8.57/4.59        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.59           => ( dvd_dvd_int @ Z2 @ ( semiri1314217659103216013at_int @ M ) ) )
% 8.57/4.59          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 8.57/4.59           => ( M = zero_zero_nat ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4753_zero__less__binomial,axiom,
% 8.57/4.59      ! [K: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.59       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4754_Suc__times__binomial__add,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 8.57/4.59        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4755_choose__mult,axiom,
% 8.57/4.59      ! [K: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ K @ M )
% 8.57/4.59       => ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59         => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 8.57/4.59            = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4756_binomial__absorb__comp,axiom,
% 8.57/4.59      ! [N: nat,K: nat] :
% 8.57/4.59        ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 8.57/4.59        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4757_take__bit__decr__eq,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.57/4.59         != zero_zero_int )
% 8.57/4.59       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 8.57/4.59          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4758_eval__nat__numeral_I3_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 8.57/4.59        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4759_dvd__imp__le,axiom,
% 8.57/4.59      ! [K: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ K @ N )
% 8.57/4.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59         => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4760_dvd__mult__cancel,axiom,
% 8.57/4.59      ! [K: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.59       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.59         => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4761_nat__mult__dvd__cancel1,axiom,
% 8.57/4.59      ! [K: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.57/4.59          = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4762_bezout__add__strong__nat,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( A != zero_zero_nat )
% 8.57/4.59       => ? [D5: nat,X3: nat,Y2: nat] :
% 8.57/4.59            ( ( dvd_dvd_nat @ D5 @ A )
% 8.57/4.59            & ( dvd_dvd_nat @ D5 @ B )
% 8.57/4.59            & ( ( times_times_nat @ A @ X3 )
% 8.57/4.59              = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D5 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4763_zdvd__imp__le,axiom,
% 8.57/4.59      ! [Z2: int,N: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ Z2 @ N )
% 8.57/4.59       => ( ( ord_less_int @ zero_zero_int @ N )
% 8.57/4.59         => ( ord_less_eq_int @ Z2 @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4764_mod__greater__zero__iff__not__dvd,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 8.57/4.59        = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4765_dvd__imp__le__int,axiom,
% 8.57/4.59      ! [I: int,D: int] :
% 8.57/4.59        ( ( I != zero_zero_int )
% 8.57/4.59       => ( ( dvd_dvd_int @ D @ I )
% 8.57/4.59         => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4766_mod__eq__dvd__iff__nat,axiom,
% 8.57/4.59      ! [N: nat,M: nat,Q2: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.59       => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 8.57/4.59            = ( modulo_modulo_nat @ N @ Q2 ) )
% 8.57/4.59          = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4767_dvd__fact,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 8.57/4.59       => ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4768_even__nat__iff,axiom,
% 8.57/4.59      ! [K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.59       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 8.57/4.59          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4769_gcd__nat_Oordering__top__axioms,axiom,
% 8.57/4.59      ( ordering_top_nat @ dvd_dvd_nat
% 8.57/4.59      @ ^ [M2: nat,N3: nat] :
% 8.57/4.59          ( ( dvd_dvd_nat @ M2 @ N3 )
% 8.57/4.59          & ( M2 != N3 ) )
% 8.57/4.59      @ zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4770_binomial__absorption,axiom,
% 8.57/4.59      ! [K: nat,N: nat] :
% 8.57/4.59        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 8.57/4.59        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4771_odd__mod__4__div__2,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.57/4.59          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.57/4.59       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4772_numeral__3__eq__3,axiom,
% 8.57/4.59      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 8.57/4.59      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4773_Suc3__eq__add__3,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( suc @ ( suc @ ( suc @ N ) ) )
% 8.57/4.59        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4774_binomial__fact__lemma,axiom,
% 8.57/4.59      ! [K: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.59       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 8.57/4.59          = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4775_dvd__mult__cancel2,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 8.57/4.59          = ( N = one_one_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4776_dvd__mult__cancel1,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 8.57/4.59          = ( N = one_one_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4777_even__even__mod__4__iff,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.57/4.59        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4778_dvd__minus__add,axiom,
% 8.57/4.59      ! [Q2: nat,N: nat,R: nat,M: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ Q2 @ N )
% 8.57/4.59       => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 8.57/4.59         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 8.57/4.59            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4779_mod__nat__eqI,axiom,
% 8.57/4.59      ! [R: nat,N: nat,M: nat] :
% 8.57/4.59        ( ( ord_less_nat @ R @ N )
% 8.57/4.59       => ( ( ord_less_eq_nat @ R @ M )
% 8.57/4.59         => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 8.57/4.59           => ( ( modulo_modulo_nat @ M @ N )
% 8.57/4.59              = R ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4780_zdvd__mult__cancel1,axiom,
% 8.57/4.59      ! [M: int,N: int] :
% 8.57/4.59        ( ( M != zero_zero_int )
% 8.57/4.59       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 8.57/4.59          = ( ( abs_abs_int @ N )
% 8.57/4.59            = one_one_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4781_mod__int__pos__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 8.57/4.59        = ( ( dvd_dvd_int @ L @ K )
% 8.57/4.59          | ( ( L = zero_zero_int )
% 8.57/4.59            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 8.57/4.59          | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4782_power__dvd__imp__le,axiom,
% 8.57/4.59      ! [I: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 8.57/4.59       => ( ( ord_less_nat @ one_one_nat @ I )
% 8.57/4.59         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4783_take__bit__Suc__minus__bit1,axiom,
% 8.57/4.59      ! [N: nat,K: num] :
% 8.57/4.59        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.57/4.59        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4784_num_Osize_I6_J,axiom,
% 8.57/4.59      ! [X32: num] :
% 8.57/4.59        ( ( size_size_num @ ( bit1 @ X32 ) )
% 8.57/4.59        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4785_choose__reduce__nat,axiom,
% 8.57/4.59      ! [N: nat,K: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.59         => ( ( binomial @ N @ K )
% 8.57/4.59            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4786_times__binomial__minus1__eq,axiom,
% 8.57/4.59      ! [K: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.57/4.59       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 8.57/4.59          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4787_binomial__le__pow2,axiom,
% 8.57/4.59      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4788_odd__pos,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.57/4.59       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4789_binomial__altdef__nat,axiom,
% 8.57/4.59      ! [K: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ K @ N )
% 8.57/4.59       => ( ( binomial @ N @ K )
% 8.57/4.59          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4790_Suc__mod__eq__add3__mod,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 8.57/4.59        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4791_Suc__div__eq__add3__div,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 8.57/4.59        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4792_even__diff__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 8.57/4.59        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4793_even__add__abs__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 8.57/4.59        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4794_even__abs__add__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 8.57/4.59        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4795_dvd__power__iff__le,axiom,
% 8.57/4.59      ! [K: nat,M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.57/4.59       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 8.57/4.59          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4796_take__bit__nat__less__self__iff,axiom,
% 8.57/4.59      ! [N: nat,M: nat] :
% 8.57/4.59        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 8.57/4.59        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4797_binomial__addition__formula,axiom,
% 8.57/4.59      ! [N: nat,K: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59       => ( ( binomial @ N @ ( suc @ K ) )
% 8.57/4.59          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4798_take__bit__int__less__self__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 8.57/4.59        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4799_take__bit__int__greater__eq__self__iff,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 8.57/4.59        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4800_choose__two,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4801_take__bit__int__eq__self__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.57/4.59          = K )
% 8.57/4.59        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.59          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4802_take__bit__int__eq__self,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.59       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.57/4.59         => ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.57/4.59            = K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4803_signed__take__bit__eq__take__bit__shift,axiom,
% 8.57/4.59      ( bit_ri631733984087533419it_int
% 8.57/4.59      = ( ^ [N3: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4804_take__bit__incr__eq,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.57/4.59         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 8.57/4.59       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 8.57/4.59          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4805_take__bit__int__less__eq,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 8.57/4.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4806_take__bit__int__greater__eq,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( ord_less_int @ K @ zero_zero_int )
% 8.57/4.59       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4807_even__mod__4__div__2,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.57/4.59          = ( suc @ zero_zero_nat ) )
% 8.57/4.59       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4808_take__bit__minus__small__eq,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ K )
% 8.57/4.59       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.57/4.59         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 8.57/4.59            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4809_signed__take__bit__numeral__minus__bit1,axiom,
% 8.57/4.59      ! [L: num,K: num] :
% 8.57/4.59        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.57/4.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4810_signed__take__bit__numeral__bit1,axiom,
% 8.57/4.59      ! [L: num,K: num] :
% 8.57/4.59        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 8.57/4.59        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4811_take__bit__numeral__minus__bit1,axiom,
% 8.57/4.59      ! [L: num,K: num] :
% 8.57/4.59        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.57/4.59        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4812_num_Osize__gen_I3_J,axiom,
% 8.57/4.59      ! [X32: num] :
% 8.57/4.59        ( ( size_num @ ( bit1 @ X32 ) )
% 8.57/4.59        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4813_num_Osize__gen_I2_J,axiom,
% 8.57/4.59      ! [X22: num] :
% 8.57/4.59        ( ( size_num @ ( bit0 @ X22 ) )
% 8.57/4.59        = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4814_nat__of__bool,axiom,
% 8.57/4.59      ! [P: $o] :
% 8.57/4.59        ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 8.57/4.59        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4815_Suc__0__mod__eq,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.59        = ( zero_n2687167440665602831ol_nat
% 8.57/4.59          @ ( N
% 8.57/4.59           != ( suc @ zero_zero_nat ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4816_pred__numeral__simps_I1_J,axiom,
% 8.57/4.59      ( ( pred_numeral @ one )
% 8.57/4.59      = zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4817_eq__numeral__Suc,axiom,
% 8.57/4.59      ! [K: num,N: nat] :
% 8.57/4.59        ( ( ( numeral_numeral_nat @ K )
% 8.57/4.59          = ( suc @ N ) )
% 8.57/4.59        = ( ( pred_numeral @ K )
% 8.57/4.59          = N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4818_Suc__eq__numeral,axiom,
% 8.57/4.59      ! [N: nat,K: num] :
% 8.57/4.59        ( ( ( suc @ N )
% 8.57/4.59          = ( numeral_numeral_nat @ K ) )
% 8.57/4.59        = ( N
% 8.57/4.59          = ( pred_numeral @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4819_pred__numeral__inc,axiom,
% 8.57/4.59      ! [K: num] :
% 8.57/4.59        ( ( pred_numeral @ ( inc @ K ) )
% 8.57/4.59        = ( numeral_numeral_nat @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4820_less__numeral__Suc,axiom,
% 8.57/4.59      ! [K: num,N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.57/4.59        = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4821_less__Suc__numeral,axiom,
% 8.57/4.59      ! [N: nat,K: num] :
% 8.57/4.59        ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.57/4.59        = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4822_pred__numeral__simps_I3_J,axiom,
% 8.57/4.59      ! [K: num] :
% 8.57/4.59        ( ( pred_numeral @ ( bit1 @ K ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4823_le__numeral__Suc,axiom,
% 8.57/4.59      ! [K: num,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.57/4.59        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4824_le__Suc__numeral,axiom,
% 8.57/4.59      ! [N: nat,K: num] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.57/4.59        = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4825_diff__numeral__Suc,axiom,
% 8.57/4.59      ! [K: num,N: nat] :
% 8.57/4.59        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.57/4.59        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4826_diff__Suc__numeral,axiom,
% 8.57/4.59      ! [N: nat,K: num] :
% 8.57/4.59        ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.57/4.59        = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4827_take__bit__of__Suc__0,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4828_dvd__antisym,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ M @ N )
% 8.57/4.59       => ( ( dvd_dvd_nat @ N @ M )
% 8.57/4.59         => ( M = N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4829_gcd__nat_Onot__eq__order__implies__strict,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( A != B )
% 8.57/4.59       => ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59         => ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59            & ( A != B ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4830_gcd__nat_Ostrict__implies__not__eq,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59          & ( A != B ) )
% 8.57/4.59       => ( A != B ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4831_gcd__nat_Ostrict__implies__order,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59          & ( A != B ) )
% 8.57/4.59       => ( dvd_dvd_nat @ A @ B ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4832_gcd__nat_Ostrict__iff__order,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59          & ( A != B ) )
% 8.57/4.59        = ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59          & ( A != B ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4833_gcd__nat_Oorder__iff__strict,axiom,
% 8.57/4.59      ( dvd_dvd_nat
% 8.57/4.59      = ( ^ [A2: nat,B2: nat] :
% 8.57/4.59            ( ( ( dvd_dvd_nat @ A2 @ B2 )
% 8.57/4.59              & ( A2 != B2 ) )
% 8.57/4.59            | ( A2 = B2 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4834_gcd__nat_Ostrict__iff__not,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59          & ( A != B ) )
% 8.57/4.59        = ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4835_gcd__nat_Ostrict__trans2,axiom,
% 8.57/4.59      ! [A: nat,B: nat,C: nat] :
% 8.57/4.59        ( ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59          & ( A != B ) )
% 8.57/4.59       => ( ( dvd_dvd_nat @ B @ C )
% 8.57/4.59         => ( ( dvd_dvd_nat @ A @ C )
% 8.57/4.59            & ( A != C ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4836_gcd__nat_Ostrict__trans1,axiom,
% 8.57/4.59      ! [A: nat,B: nat,C: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59       => ( ( ( dvd_dvd_nat @ B @ C )
% 8.57/4.59            & ( B != C ) )
% 8.57/4.59         => ( ( dvd_dvd_nat @ A @ C )
% 8.57/4.59            & ( A != C ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4837_gcd__nat_Ostrict__trans,axiom,
% 8.57/4.59      ! [A: nat,B: nat,C: nat] :
% 8.57/4.59        ( ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59          & ( A != B ) )
% 8.57/4.59       => ( ( ( dvd_dvd_nat @ B @ C )
% 8.57/4.59            & ( B != C ) )
% 8.57/4.59         => ( ( dvd_dvd_nat @ A @ C )
% 8.57/4.59            & ( A != C ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4838_gcd__nat_Oantisym,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59       => ( ( dvd_dvd_nat @ B @ A )
% 8.57/4.59         => ( A = B ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4839_gcd__nat_Oirrefl,axiom,
% 8.57/4.59      ! [A: nat] :
% 8.57/4.59        ~ ( ( dvd_dvd_nat @ A @ A )
% 8.57/4.59          & ( A != A ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4840_gcd__nat_Oeq__iff,axiom,
% 8.57/4.59      ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.57/4.59      = ( ^ [A2: nat,B2: nat] :
% 8.57/4.59            ( ( dvd_dvd_nat @ A2 @ B2 )
% 8.57/4.59            & ( dvd_dvd_nat @ B2 @ A2 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4841_gcd__nat_Otrans,axiom,
% 8.57/4.59      ! [A: nat,B: nat,C: nat] :
% 8.57/4.59        ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59       => ( ( dvd_dvd_nat @ B @ C )
% 8.57/4.59         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4842_gcd__nat_Orefl,axiom,
% 8.57/4.59      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4843_gcd__nat_Oasym,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( ( dvd_dvd_nat @ A @ B )
% 8.57/4.59          & ( A != B ) )
% 8.57/4.59       => ~ ( ( dvd_dvd_nat @ B @ A )
% 8.57/4.59            & ( B != A ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4844_numeral__eq__Suc,axiom,
% 8.57/4.59      ( numeral_numeral_nat
% 8.57/4.59      = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4845_pred__numeral__def,axiom,
% 8.57/4.59      ( pred_numeral
% 8.57/4.59      = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4846_num_Osize__gen_I1_J,axiom,
% 8.57/4.59      ( ( size_num @ one )
% 8.57/4.59      = zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4847_set__decode__0,axiom,
% 8.57/4.59      ! [X2: nat] :
% 8.57/4.59        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X2 ) )
% 8.57/4.59        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4848_set__decode__def,axiom,
% 8.57/4.59      ( nat_set_decode
% 8.57/4.59      = ( ^ [X: nat] :
% 8.57/4.59            ( collect_nat
% 8.57/4.59            @ ^ [N3: nat] :
% 8.57/4.59                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4849_and__int__unfold,axiom,
% 8.57/4.59      ( bit_se725231765392027082nd_int
% 8.57/4.59      = ( ^ [K2: int,L2: int] :
% 8.57/4.59            ( if_int
% 8.57/4.59            @ ( ( K2 = zero_zero_int )
% 8.57/4.59              | ( L2 = zero_zero_int ) )
% 8.57/4.59            @ zero_zero_int
% 8.57/4.59            @ ( if_int
% 8.57/4.59              @ ( K2
% 8.57/4.59                = ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.59              @ L2
% 8.57/4.59              @ ( if_int
% 8.57/4.59                @ ( L2
% 8.57/4.59                  = ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.59                @ K2
% 8.57/4.59                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4850_take__bit__eq__mask__iff__exp__dvd,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.57/4.59          = ( bit_se2000444600071755411sk_int @ N ) )
% 8.57/4.59        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4851_modulo__int__def,axiom,
% 8.57/4.59      ( modulo_modulo_int
% 8.57/4.59      = ( ^ [K2: int,L2: int] :
% 8.57/4.59            ( if_int @ ( L2 = zero_zero_int ) @ K2
% 8.57/4.59            @ ( if_int
% 8.57/4.59              @ ( ( sgn_sgn_int @ K2 )
% 8.57/4.59                = ( sgn_sgn_int @ L2 ) )
% 8.57/4.59              @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 8.57/4.59              @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 8.57/4.59                @ ( minus_minus_int
% 8.57/4.59                  @ ( times_times_int @ ( abs_abs_int @ L2 )
% 8.57/4.59                    @ ( zero_n2684676970156552555ol_int
% 8.57/4.59                      @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) )
% 8.57/4.59                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4852_mask__nat__positive__iff,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 8.57/4.59        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4853_and__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 8.57/4.59        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.59          | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4854_and__negative__int__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 8.57/4.59        = ( ( ord_less_int @ K @ zero_zero_int )
% 8.57/4.59          & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4855_sgn__mult__dvd__iff,axiom,
% 8.57/4.59      ! [R: int,L: int,K: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R ) @ L ) @ K )
% 8.57/4.59        = ( ( dvd_dvd_int @ L @ K )
% 8.57/4.59          & ( ( R = zero_zero_int )
% 8.57/4.59           => ( K = zero_zero_int ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4856_mult__sgn__dvd__iff,axiom,
% 8.57/4.59      ! [L: int,R: int,K: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R ) ) @ K )
% 8.57/4.59        = ( ( dvd_dvd_int @ L @ K )
% 8.57/4.59          & ( ( R = zero_zero_int )
% 8.57/4.59           => ( K = zero_zero_int ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4857_dvd__sgn__mult__iff,axiom,
% 8.57/4.59      ! [L: int,R: int,K: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R ) @ K ) )
% 8.57/4.59        = ( ( dvd_dvd_int @ L @ K )
% 8.57/4.59          | ( R = zero_zero_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4858_dvd__mult__sgn__iff,axiom,
% 8.57/4.59      ! [L: int,K: int,R: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R ) ) )
% 8.57/4.59        = ( ( dvd_dvd_int @ L @ K )
% 8.57/4.59          | ( R = zero_zero_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4859_and__minus__numerals_I2_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.57/4.59        = one_one_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4860_and__minus__numerals_I6_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 8.57/4.59        = one_one_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4861_and__minus__numerals_I5_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 8.57/4.59        = zero_zero_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4862_and__minus__numerals_I1_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.57/4.59        = zero_zero_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4863_less__eq__mask,axiom,
% 8.57/4.59      ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4864_subset__decode__imp__le,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 8.57/4.59       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4865_AND__upper2_H,axiom,
% 8.57/4.59      ! [Y: int,Z2: int,X2: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.59       => ( ( ord_less_eq_int @ Y @ Z2 )
% 8.57/4.59         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Z2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4866_AND__upper1_H,axiom,
% 8.57/4.59      ! [Y: int,Z2: int,Ya: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.59       => ( ( ord_less_eq_int @ Y @ Z2 )
% 8.57/4.59         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4867_AND__upper2,axiom,
% 8.57/4.59      ! [Y: int,X2: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.59       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Y ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4868_AND__upper1,axiom,
% 8.57/4.59      ! [X2: int,Y: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.59       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ X2 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4869_AND__lower,axiom,
% 8.57/4.59      ! [X2: int,Y: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.59       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4870_int__sgnE,axiom,
% 8.57/4.59      ! [K: int] :
% 8.57/4.59        ~ ! [N2: nat,L3: int] :
% 8.57/4.59            ( K
% 8.57/4.59           != ( times_times_int @ ( sgn_sgn_int @ L3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4871_mask__nonnegative__int,axiom,
% 8.57/4.59      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4872_not__mask__negative__int,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4873_AND__upper2_H_H,axiom,
% 8.57/4.59      ! [Y: int,Z2: int,X2: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.59       => ( ( ord_less_int @ Y @ Z2 )
% 8.57/4.59         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Z2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4874_AND__upper1_H_H,axiom,
% 8.57/4.59      ! [Y: int,Z2: int,Ya: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.59       => ( ( ord_less_int @ Y @ Z2 )
% 8.57/4.59         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4875_and__less__eq,axiom,
% 8.57/4.59      ! [L: int,K: int] :
% 8.57/4.59        ( ( ord_less_int @ L @ zero_zero_int )
% 8.57/4.59       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4876_sgn__mod,axiom,
% 8.57/4.59      ! [L: int,K: int] :
% 8.57/4.59        ( ( L != zero_zero_int )
% 8.57/4.59       => ( ~ ( dvd_dvd_int @ L @ K )
% 8.57/4.59         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 8.57/4.59            = ( sgn_sgn_int @ L ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4877_less__mask,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.59       => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4878_zsgn__def,axiom,
% 8.57/4.59      ( sgn_sgn_int
% 8.57/4.59      = ( ^ [I2: int] : ( if_int @ ( I2 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4879_div__sgn__abs__cancel,axiom,
% 8.57/4.59      ! [V: int,K: int,L: int] :
% 8.57/4.59        ( ( V != zero_zero_int )
% 8.57/4.59       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 8.57/4.59          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4880_take__bit__eq__mask__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.57/4.59          = ( bit_se2000444600071755411sk_int @ N ) )
% 8.57/4.59        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 8.57/4.59          = zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4881_div__noneq__sgn__abs,axiom,
% 8.57/4.59      ! [L: int,K: int] :
% 8.57/4.59        ( ( L != zero_zero_int )
% 8.57/4.59       => ( ( ( sgn_sgn_int @ K )
% 8.57/4.59           != ( sgn_sgn_int @ L ) )
% 8.57/4.59         => ( ( divide_divide_int @ K @ L )
% 8.57/4.59            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 8.57/4.59              @ ( zero_n2684676970156552555ol_int
% 8.57/4.59                @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4882_and__int__rec,axiom,
% 8.57/4.59      ( bit_se725231765392027082nd_int
% 8.57/4.59      = ( ^ [K2: int,L2: int] :
% 8.57/4.59            ( plus_plus_int
% 8.57/4.59            @ ( zero_n2684676970156552555ol_int
% 8.57/4.59              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.57/4.59                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 8.57/4.59            @ ( 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 ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4883_mask__half__int,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.57/4.59        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4884_mask__nat__def,axiom,
% 8.57/4.59      ( bit_se2002935070580805687sk_nat
% 8.57/4.59      = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4885_mask__int__def,axiom,
% 8.57/4.59      ( bit_se2000444600071755411sk_int
% 8.57/4.59      = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4886_divide__int__unfold,axiom,
% 8.57/4.59      ! [L: int,K: int,N: nat,M: nat] :
% 8.57/4.59        ( ( ( ( ( sgn_sgn_int @ L )
% 8.57/4.59              = zero_zero_int )
% 8.57/4.59            | ( ( sgn_sgn_int @ K )
% 8.57/4.59              = zero_zero_int )
% 8.57/4.59            | ( N = zero_zero_nat ) )
% 8.57/4.59         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.57/4.59            = zero_zero_int ) )
% 8.57/4.59        & ( ~ ( ( ( sgn_sgn_int @ L )
% 8.57/4.59                = zero_zero_int )
% 8.57/4.59              | ( ( sgn_sgn_int @ K )
% 8.57/4.59                = zero_zero_int )
% 8.57/4.59              | ( N = zero_zero_nat ) )
% 8.57/4.59         => ( ( ( ( sgn_sgn_int @ K )
% 8.57/4.59                = ( sgn_sgn_int @ L ) )
% 8.57/4.59             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.57/4.59                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 8.57/4.59            & ( ( ( sgn_sgn_int @ K )
% 8.57/4.59               != ( sgn_sgn_int @ L ) )
% 8.57/4.59             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.57/4.59                = ( uminus_uminus_int
% 8.57/4.59                  @ ( semiri1314217659103216013at_int
% 8.57/4.59                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 8.57/4.59                      @ ( zero_n2687167440665602831ol_nat
% 8.57/4.59                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4887_modulo__int__unfold,axiom,
% 8.57/4.59      ! [L: int,K: int,N: nat,M: nat] :
% 8.57/4.59        ( ( ( ( ( sgn_sgn_int @ L )
% 8.57/4.59              = zero_zero_int )
% 8.57/4.59            | ( ( sgn_sgn_int @ K )
% 8.57/4.59              = zero_zero_int )
% 8.57/4.59            | ( N = zero_zero_nat ) )
% 8.57/4.59         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.57/4.59            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 8.57/4.59        & ( ~ ( ( ( sgn_sgn_int @ L )
% 8.57/4.59                = zero_zero_int )
% 8.57/4.59              | ( ( sgn_sgn_int @ K )
% 8.57/4.59                = zero_zero_int )
% 8.57/4.59              | ( N = zero_zero_nat ) )
% 8.57/4.59         => ( ( ( ( sgn_sgn_int @ K )
% 8.57/4.59                = ( sgn_sgn_int @ L ) )
% 8.57/4.59             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.57/4.59                = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 8.57/4.59            & ( ( ( sgn_sgn_int @ K )
% 8.57/4.59               != ( sgn_sgn_int @ L ) )
% 8.57/4.59             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.57/4.59                = ( times_times_int @ ( sgn_sgn_int @ L )
% 8.57/4.59                  @ ( minus_minus_int
% 8.57/4.59                    @ ( semiri1314217659103216013at_int
% 8.57/4.59                      @ ( times_times_nat @ N
% 8.57/4.59                        @ ( zero_n2687167440665602831ol_nat
% 8.57/4.59                          @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 8.57/4.59                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4888_divide__int__def,axiom,
% 8.57/4.59      ( divide_divide_int
% 8.57/4.59      = ( ^ [K2: int,L2: int] :
% 8.57/4.59            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 8.57/4.59            @ ( if_int
% 8.57/4.59              @ ( ( sgn_sgn_int @ K2 )
% 8.57/4.59                = ( sgn_sgn_int @ L2 ) )
% 8.57/4.59              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 8.57/4.59              @ ( uminus_uminus_int
% 8.57/4.59                @ ( semiri1314217659103216013at_int
% 8.57/4.59                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 8.57/4.59                    @ ( zero_n2687167440665602831ol_nat
% 8.57/4.59                      @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4889_take__bit__Suc__from__most,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 8.57/4.59        = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4890_Suc__0__xor__eq,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.59        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.57/4.59          @ ( zero_n2687167440665602831ol_nat
% 8.57/4.59            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4891_xor__Suc__0__eq,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.57/4.59          @ ( zero_n2687167440665602831ol_nat
% 8.57/4.59            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4892_horner__sum__of__bool__2__less,axiom,
% 8.57/4.59      ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4893_xor__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 8.57/4.59        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.59          = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4894_push__bit__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 8.57/4.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4895_xor__negative__int__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 8.57/4.59        = ( ( ord_less_int @ K @ zero_zero_int )
% 8.57/4.59         != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4896_push__bit__negative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 8.57/4.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4897_concat__bit__of__zero__1,axiom,
% 8.57/4.59      ! [N: nat,L: int] :
% 8.57/4.59        ( ( bit_concat_bit @ N @ zero_zero_int @ L )
% 8.57/4.59        = ( bit_se545348938243370406it_int @ N @ L ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4898_signed__take__bit__nonnegative__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 8.57/4.59        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4899_signed__take__bit__negative__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 8.57/4.59        = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4900_and__nat__numerals_I1_J,axiom,
% 8.57/4.59      ! [Y: num] :
% 8.57/4.59        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.57/4.59        = zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4901_and__nat__numerals_I3_J,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4902_push__bit__of__Suc__0,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4903_xor__nat__numerals_I4_J,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4904_xor__nat__numerals_I3_J,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4905_xor__nat__numerals_I2_J,axiom,
% 8.57/4.59      ! [Y: num] :
% 8.57/4.59        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4906_xor__nat__numerals_I1_J,axiom,
% 8.57/4.59      ! [Y: num] :
% 8.57/4.59        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4907_and__nat__numerals_I4_J,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = one_one_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4908_and__nat__numerals_I2_J,axiom,
% 8.57/4.59      ! [Y: num] :
% 8.57/4.59        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.57/4.59        = one_one_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4909_and__Suc__0__eq,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4910_Suc__0__and__eq,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.59        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4911_flip__bit__nat__def,axiom,
% 8.57/4.59      ( bit_se2161824704523386999it_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] : ( bit_se6528837805403552850or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4912_xor__nat__def,axiom,
% 8.57/4.59      ( bit_se6528837805403552850or_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4913_bit__push__bit__iff__int,axiom,
% 8.57/4.59      ! [M: nat,K: int,N: nat] :
% 8.57/4.59        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 8.57/4.59        = ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4914_flip__bit__int__def,axiom,
% 8.57/4.59      ( bit_se2159334234014336723it_int
% 8.57/4.59      = ( ^ [N3: nat,K2: int] : ( bit_se6526347334894502574or_int @ K2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4915_XOR__lower,axiom,
% 8.57/4.59      ! [X2: int,Y: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.59       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.59         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4916_bit__not__int__iff_H,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 8.57/4.59        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4917_and__nat__def,axiom,
% 8.57/4.59      ( bit_se727722235901077358nd_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4918_concat__bit__eq,axiom,
% 8.57/4.59      ( bit_concat_bit
% 8.57/4.59      = ( ^ [N3: nat,K2: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N3 @ K2 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4919_bit__imp__take__bit__positive,axiom,
% 8.57/4.59      ! [N: nat,M: nat,K: int] :
% 8.57/4.59        ( ( ord_less_nat @ N @ M )
% 8.57/4.59       => ( ( bit_se1146084159140164899it_int @ K @ N )
% 8.57/4.59         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4920_bit__concat__bit__iff,axiom,
% 8.57/4.59      ! [M: nat,K: int,L: int,N: nat] :
% 8.57/4.59        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 8.57/4.59        = ( ( ( ord_less_nat @ N @ M )
% 8.57/4.59            & ( bit_se1146084159140164899it_int @ K @ N ) )
% 8.57/4.59          | ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59            & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4921_int__bit__bound,axiom,
% 8.57/4.59      ! [K: int] :
% 8.57/4.59        ~ ! [N2: nat] :
% 8.57/4.59            ( ! [M6: nat] :
% 8.57/4.59                ( ( ord_less_eq_nat @ N2 @ M6 )
% 8.57/4.59               => ( ( bit_se1146084159140164899it_int @ K @ M6 )
% 8.57/4.59                  = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 8.57/4.59           => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 8.57/4.59               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 8.57/4.59                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4922_push__bit__minus__one,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.59        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4923_XOR__upper,axiom,
% 8.57/4.59      ! [X2: int,N: nat,Y: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.59       => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.57/4.59         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.57/4.59           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4924_and__nat__unfold,axiom,
% 8.57/4.59      ( bit_se727722235901077358nd_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] :
% 8.57/4.59            ( if_nat
% 8.57/4.59            @ ( ( M2 = zero_zero_nat )
% 8.57/4.59              | ( N3 = zero_zero_nat ) )
% 8.57/4.59            @ zero_zero_nat
% 8.57/4.59            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4925_and__nat__rec,axiom,
% 8.57/4.59      ( bit_se727722235901077358nd_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] :
% 8.57/4.59            ( plus_plus_nat
% 8.57/4.59            @ ( zero_n2687167440665602831ol_nat
% 8.57/4.59              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 8.57/4.59                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 8.57/4.59            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4926_xor__nat__unfold,axiom,
% 8.57/4.59      ( bit_se6528837805403552850or_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4927_xor__int__rec,axiom,
% 8.57/4.59      ( bit_se6526347334894502574or_int
% 8.57/4.59      = ( ^ [K2: int,L2: int] :
% 8.57/4.59            ( plus_plus_int
% 8.57/4.59            @ ( zero_n2684676970156552555ol_int
% 8.57/4.59              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 8.57/4.59               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 8.57/4.59            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4928_xor__nat__rec,axiom,
% 8.57/4.59      ( bit_se6528837805403552850or_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] :
% 8.57/4.59            ( plus_plus_nat
% 8.57/4.59            @ ( zero_n2687167440665602831ol_nat
% 8.57/4.59              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.57/4.59               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 8.57/4.59            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4929_set__bit__eq,axiom,
% 8.57/4.59      ( bit_se7879613467334960850it_int
% 8.57/4.59      = ( ^ [N3: nat,K2: int] :
% 8.57/4.59            ( plus_plus_int @ K2
% 8.57/4.59            @ ( times_times_int
% 8.57/4.59              @ ( zero_n2684676970156552555ol_int
% 8.57/4.59                @ ~ ( bit_se1146084159140164899it_int @ K2 @ N3 ) )
% 8.57/4.59              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4930_xor__int__unfold,axiom,
% 8.57/4.59      ( bit_se6526347334894502574or_int
% 8.57/4.59      = ( ^ [K2: int,L2: int] :
% 8.57/4.59            ( if_int
% 8.57/4.59            @ ( K2
% 8.57/4.59              = ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.59            @ ( bit_ri7919022796975470100ot_int @ L2 )
% 8.57/4.59            @ ( if_int
% 8.57/4.59              @ ( L2
% 8.57/4.59                = ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.59              @ ( bit_ri7919022796975470100ot_int @ K2 )
% 8.57/4.59              @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4931_mask__eq__sum__exp__nat,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59          @ ( collect_nat
% 8.57/4.59            @ ^ [Q6: nat] : ( ord_less_nat @ Q6 @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4932_not__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 8.57/4.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4933_not__negative__int__iff,axiom,
% 8.57/4.59      ! [K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 8.57/4.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4934_bit__Suc__0__iff,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.59        = ( N = zero_zero_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4935_not__bit__Suc__0__Suc,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4936_bit__push__bit__iff__nat,axiom,
% 8.57/4.59      ! [M: nat,Q2: nat,N: nat] :
% 8.57/4.59        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 8.57/4.59        = ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59          & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4937_not__bit__Suc__0__numeral,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4938_not__int__def,axiom,
% 8.57/4.59      ( bit_ri7919022796975470100ot_int
% 8.57/4.59      = ( ^ [K2: int] : ( minus_minus_int @ ( uminus_uminus_int @ K2 ) @ one_one_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4939_and__not__numerals_I1_J,axiom,
% 8.57/4.59      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.57/4.59      = zero_zero_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4940_unset__bit__int__def,axiom,
% 8.57/4.59      ( bit_se4203085406695923979it_int
% 8.57/4.59      = ( ^ [N3: nat,K2: int] : ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4941_and__not__numerals_I2_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.57/4.59        = one_one_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4942_and__not__numerals_I4_J,axiom,
% 8.57/4.59      ! [M: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.57/4.59        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4943_bit__nat__iff,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 8.57/4.59        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.59          & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4944_bit__minus__int__iff,axiom,
% 8.57/4.59      ! [K: int,N: nat] :
% 8.57/4.59        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 8.57/4.59        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4945_and__not__numerals_I7_J,axiom,
% 8.57/4.59      ! [M: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.57/4.59        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4946_and__not__numerals_I3_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.57/4.59        = zero_zero_int ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4947_and__not__numerals_I8_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.57/4.59        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4948_not__int__rec,axiom,
% 8.57/4.59      ( bit_ri7919022796975470100ot_int
% 8.57/4.59      = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4949_atMost__atLeast0,axiom,
% 8.57/4.59      ( set_ord_atMost_nat
% 8.57/4.59      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4950_all__nat__less,axiom,
% 8.57/4.59      ! [N: nat,P: nat > $o] :
% 8.57/4.59        ( ( ! [M2: nat] :
% 8.57/4.59              ( ( ord_less_eq_nat @ M2 @ N )
% 8.57/4.59             => ( P @ M2 ) ) )
% 8.57/4.59        = ( ! [X: nat] :
% 8.57/4.59              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.57/4.59             => ( P @ X ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4951_ex__nat__less,axiom,
% 8.57/4.59      ! [N: nat,P: nat > $o] :
% 8.57/4.59        ( ( ? [M2: nat] :
% 8.57/4.59              ( ( ord_less_eq_nat @ M2 @ N )
% 8.57/4.59              & ( P @ M2 ) ) )
% 8.57/4.59        = ( ? [X: nat] :
% 8.57/4.59              ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.57/4.59              & ( P @ X ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4952_sum__choose__upper,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [K2: nat] : ( binomial @ K2 @ M )
% 8.57/4.59          @ ( set_ord_atMost_nat @ N ) )
% 8.57/4.59        = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4953_sum__choose__lower,axiom,
% 8.57/4.59      ! [R: nat,N: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R @ K2 ) @ K2 )
% 8.57/4.59          @ ( set_ord_atMost_nat @ N ) )
% 8.57/4.59        = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4954_choose__rising__sum_I1_J,axiom,
% 8.57/4.59      ! [N: nat,M: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 8.57/4.59          @ ( set_ord_atMost_nat @ M ) )
% 8.57/4.59        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4955_choose__rising__sum_I2_J,axiom,
% 8.57/4.59      ! [N: nat,M: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 8.57/4.59          @ ( set_ord_atMost_nat @ M ) )
% 8.57/4.59        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4956_sum__choose__diagonal,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59       => ( ( groups3542108847815614940at_nat
% 8.57/4.59            @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 8.57/4.59            @ ( set_ord_atMost_nat @ M ) )
% 8.57/4.59          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4957_vandermonde,axiom,
% 8.57/4.59      ! [M: nat,N: nat,R: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K2 ) ) )
% 8.57/4.59          @ ( set_ord_atMost_nat @ R ) )
% 8.57/4.59        = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4958_choose__row__sum,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 8.57/4.59        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4959_binomial,axiom,
% 8.57/4.59      ! [A: nat,B: nat,N: nat] :
% 8.57/4.59        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 8.57/4.59        = ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 8.57/4.59          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4960_choose__square__sum,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.57/4.59          @ ( set_ord_atMost_nat @ N ) )
% 8.57/4.59        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4961_gauss__sum__nat,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [X: nat] : X
% 8.57/4.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.57/4.59        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4962_binomial__r__part__sum,axiom,
% 8.57/4.59      ! [M: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 8.57/4.59        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4963_choose__linear__sum,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [I2: nat] : ( times_times_nat @ I2 @ ( binomial @ N @ I2 ) )
% 8.57/4.59          @ ( set_ord_atMost_nat @ N ) )
% 8.57/4.59        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4964_arith__series__nat,axiom,
% 8.57/4.59      ! [A: nat,D: nat,N: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I2 @ D ) )
% 8.57/4.59          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.57/4.59        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4965_Sum__Icc__nat,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [X: nat] : X
% 8.57/4.59          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.57/4.59        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4966_Sum__Icc__int,axiom,
% 8.57/4.59      ! [M: int,N: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ M @ N )
% 8.57/4.59       => ( ( groups4538972089207619220nt_int
% 8.57/4.59            @ ^ [X: int] : X
% 8.57/4.59            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 8.57/4.59          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4967_Sum__Ico__nat,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [X: nat] : X
% 8.57/4.59          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 8.57/4.59        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4968_sum__power2,axiom,
% 8.57/4.59      ! [K: nat] :
% 8.57/4.59        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 8.57/4.59        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4969_prod__Suc__Suc__fact,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.57/4.59        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4970_prod__Suc__fact,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.57/4.59        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4971_all__nat__less__eq,axiom,
% 8.57/4.59      ! [N: nat,P: nat > $o] :
% 8.57/4.59        ( ( ! [M2: nat] :
% 8.57/4.59              ( ( ord_less_nat @ M2 @ N )
% 8.57/4.59             => ( P @ M2 ) ) )
% 8.57/4.59        = ( ! [X: nat] :
% 8.57/4.59              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.57/4.59             => ( P @ X ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4972_ex__nat__less__eq,axiom,
% 8.57/4.59      ! [N: nat,P: nat > $o] :
% 8.57/4.59        ( ( ? [M2: nat] :
% 8.57/4.59              ( ( ord_less_nat @ M2 @ N )
% 8.57/4.59              & ( P @ M2 ) ) )
% 8.57/4.59        = ( ? [X: nat] :
% 8.57/4.59              ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.57/4.59              & ( P @ X ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4973_atLeastLessThanSuc__atLeastAtMost,axiom,
% 8.57/4.59      ! [L: nat,U: nat] :
% 8.57/4.59        ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 8.57/4.59        = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4974_bset_I1_J,axiom,
% 8.57/4.59      ! [D3: int,B4: set_int,P: int > $o,Q: int > $o] :
% 8.57/4.59        ( ! [X3: int] :
% 8.57/4.59            ( ! [Xa2: int] :
% 8.57/4.59                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb2: int] :
% 8.57/4.59                    ( ( member_int @ Xb2 @ B4 )
% 8.57/4.59                   => ( X3
% 8.57/4.59                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59           => ( ( P @ X3 )
% 8.57/4.59             => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59       => ( ! [X3: int] :
% 8.57/4.59              ( ! [Xa2: int] :
% 8.57/4.59                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb2: int] :
% 8.57/4.59                      ( ( member_int @ Xb2 @ B4 )
% 8.57/4.59                     => ( X3
% 8.57/4.59                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59             => ( ( Q @ X3 )
% 8.57/4.59               => ( Q @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( ( P @ X4 )
% 8.57/4.59                  & ( Q @ X4 ) )
% 8.57/4.59               => ( ( P @ ( minus_minus_int @ X4 @ D3 ) )
% 8.57/4.59                  & ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4975_bset_I2_J,axiom,
% 8.57/4.59      ! [D3: int,B4: set_int,P: int > $o,Q: int > $o] :
% 8.57/4.59        ( ! [X3: int] :
% 8.57/4.59            ( ! [Xa2: int] :
% 8.57/4.59                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb2: int] :
% 8.57/4.59                    ( ( member_int @ Xb2 @ B4 )
% 8.57/4.59                   => ( X3
% 8.57/4.59                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59           => ( ( P @ X3 )
% 8.57/4.59             => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59       => ( ! [X3: int] :
% 8.57/4.59              ( ! [Xa2: int] :
% 8.57/4.59                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb2: int] :
% 8.57/4.59                      ( ( member_int @ Xb2 @ B4 )
% 8.57/4.59                     => ( X3
% 8.57/4.59                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59             => ( ( Q @ X3 )
% 8.57/4.59               => ( Q @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( ( P @ X4 )
% 8.57/4.59                  | ( Q @ X4 ) )
% 8.57/4.59               => ( ( P @ ( minus_minus_int @ X4 @ D3 ) )
% 8.57/4.59                  | ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4976_aset_I1_J,axiom,
% 8.57/4.59      ! [D3: int,A4: set_int,P: int > $o,Q: int > $o] :
% 8.57/4.59        ( ! [X3: int] :
% 8.57/4.59            ( ! [Xa2: int] :
% 8.57/4.59                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb2: int] :
% 8.57/4.59                    ( ( member_int @ Xb2 @ A4 )
% 8.57/4.59                   => ( X3
% 8.57/4.59                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59           => ( ( P @ X3 )
% 8.57/4.59             => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59       => ( ! [X3: int] :
% 8.57/4.59              ( ! [Xa2: int] :
% 8.57/4.59                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb2: int] :
% 8.57/4.59                      ( ( member_int @ Xb2 @ A4 )
% 8.57/4.59                     => ( X3
% 8.57/4.59                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59             => ( ( Q @ X3 )
% 8.57/4.59               => ( Q @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( ( P @ X4 )
% 8.57/4.59                  & ( Q @ X4 ) )
% 8.57/4.59               => ( ( P @ ( plus_plus_int @ X4 @ D3 ) )
% 8.57/4.59                  & ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4977_aset_I2_J,axiom,
% 8.57/4.59      ! [D3: int,A4: set_int,P: int > $o,Q: int > $o] :
% 8.57/4.59        ( ! [X3: int] :
% 8.57/4.59            ( ! [Xa2: int] :
% 8.57/4.59                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb2: int] :
% 8.57/4.59                    ( ( member_int @ Xb2 @ A4 )
% 8.57/4.59                   => ( X3
% 8.57/4.59                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59           => ( ( P @ X3 )
% 8.57/4.59             => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59       => ( ! [X3: int] :
% 8.57/4.59              ( ! [Xa2: int] :
% 8.57/4.59                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb2: int] :
% 8.57/4.59                      ( ( member_int @ Xb2 @ A4 )
% 8.57/4.59                     => ( X3
% 8.57/4.59                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59             => ( ( Q @ X3 )
% 8.57/4.59               => ( Q @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( ( P @ X4 )
% 8.57/4.59                  | ( Q @ X4 ) )
% 8.57/4.59               => ( ( P @ ( plus_plus_int @ X4 @ D3 ) )
% 8.57/4.59                  | ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4978_bset_I9_J,axiom,
% 8.57/4.59      ! [D: int,D3: int,B4: set_int,T: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ D @ D3 )
% 8.57/4.59       => ! [X4: int] :
% 8.57/4.59            ( ! [Xa3: int] :
% 8.57/4.59                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb3: int] :
% 8.57/4.59                    ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                   => ( X4
% 8.57/4.59                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59           => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 8.57/4.59             => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4979_bset_I10_J,axiom,
% 8.57/4.59      ! [D: int,D3: int,B4: set_int,T: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ D @ D3 )
% 8.57/4.59       => ! [X4: int] :
% 8.57/4.59            ( ! [Xa3: int] :
% 8.57/4.59                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb3: int] :
% 8.57/4.59                    ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                   => ( X4
% 8.57/4.59                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59           => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 8.57/4.59             => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4980_aset_I9_J,axiom,
% 8.57/4.59      ! [D: int,D3: int,A4: set_int,T: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ D @ D3 )
% 8.57/4.59       => ! [X4: int] :
% 8.57/4.59            ( ! [Xa3: int] :
% 8.57/4.59                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb3: int] :
% 8.57/4.59                    ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                   => ( X4
% 8.57/4.59                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59           => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 8.57/4.59             => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4981_aset_I10_J,axiom,
% 8.57/4.59      ! [D: int,D3: int,A4: set_int,T: int] :
% 8.57/4.59        ( ( dvd_dvd_int @ D @ D3 )
% 8.57/4.59       => ! [X4: int] :
% 8.57/4.59            ( ! [Xa3: int] :
% 8.57/4.59                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb3: int] :
% 8.57/4.59                    ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                   => ( X4
% 8.57/4.59                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59           => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 8.57/4.59             => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4982_periodic__finite__ex,axiom,
% 8.57/4.59      ! [D: int,P: int > $o] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D )
% 8.57/4.59       => ( ! [X3: int,K3: int] :
% 8.57/4.59              ( ( P @ X3 )
% 8.57/4.59              = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D ) ) ) )
% 8.57/4.59         => ( ( ? [X5: int] : ( P @ X5 ) )
% 8.57/4.59            = ( ? [X: int] :
% 8.57/4.59                  ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 8.57/4.59                  & ( P @ X ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4983_bset_I3_J,axiom,
% 8.57/4.59      ! [D3: int,T: int,B4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( X4 = T )
% 8.57/4.59               => ( ( minus_minus_int @ X4 @ D3 )
% 8.57/4.59                  = T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4984_bset_I4_J,axiom,
% 8.57/4.59      ! [D3: int,T: int,B4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ( member_int @ T @ B4 )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( X4 != T )
% 8.57/4.59               => ( ( minus_minus_int @ X4 @ D3 )
% 8.57/4.59                 != T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4985_bset_I5_J,axiom,
% 8.57/4.59      ! [D3: int,B4: set_int,T: int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ! [X4: int] :
% 8.57/4.59            ( ! [Xa3: int] :
% 8.57/4.59                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb3: int] :
% 8.57/4.59                    ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                   => ( X4
% 8.57/4.59                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59           => ( ( ord_less_int @ X4 @ T )
% 8.57/4.59             => ( ord_less_int @ ( minus_minus_int @ X4 @ D3 ) @ T ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4986_bset_I7_J,axiom,
% 8.57/4.59      ! [D3: int,T: int,B4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ( member_int @ T @ B4 )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( ord_less_int @ T @ X4 )
% 8.57/4.59               => ( ord_less_int @ T @ ( minus_minus_int @ X4 @ D3 ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4987_aset_I3_J,axiom,
% 8.57/4.59      ! [D3: int,T: int,A4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( X4 = T )
% 8.57/4.59               => ( ( plus_plus_int @ X4 @ D3 )
% 8.57/4.59                  = T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4988_aset_I4_J,axiom,
% 8.57/4.59      ! [D3: int,T: int,A4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ( member_int @ T @ A4 )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( X4 != T )
% 8.57/4.59               => ( ( plus_plus_int @ X4 @ D3 )
% 8.57/4.59                 != T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4989_aset_I5_J,axiom,
% 8.57/4.59      ! [D3: int,T: int,A4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ( member_int @ T @ A4 )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( ord_less_int @ X4 @ T )
% 8.57/4.59               => ( ord_less_int @ ( plus_plus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4990_aset_I7_J,axiom,
% 8.57/4.59      ! [D3: int,A4: set_int,T: int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ! [X4: int] :
% 8.57/4.59            ( ! [Xa3: int] :
% 8.57/4.59                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb3: int] :
% 8.57/4.59                    ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                   => ( X4
% 8.57/4.59                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59           => ( ( ord_less_int @ T @ X4 )
% 8.57/4.59             => ( ord_less_int @ T @ ( plus_plus_int @ X4 @ D3 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4991_fact__eq__fact__times,axiom,
% 8.57/4.59      ! [N: nat,M: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.59       => ( ( semiri1408675320244567234ct_nat @ M )
% 8.57/4.59          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 8.57/4.59            @ ( groups708209901874060359at_nat
% 8.57/4.59              @ ^ [X: nat] : X
% 8.57/4.59              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4992_bset_I6_J,axiom,
% 8.57/4.59      ! [D3: int,B4: set_int,T: int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ! [X4: int] :
% 8.57/4.59            ( ! [Xa3: int] :
% 8.57/4.59                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb3: int] :
% 8.57/4.59                    ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                   => ( X4
% 8.57/4.59                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59           => ( ( ord_less_eq_int @ X4 @ T )
% 8.57/4.59             => ( ord_less_eq_int @ ( minus_minus_int @ X4 @ D3 ) @ T ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4993_bset_I8_J,axiom,
% 8.57/4.59      ! [D3: int,T: int,B4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ B4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( ord_less_eq_int @ T @ X4 )
% 8.57/4.59               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X4 @ D3 ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4994_aset_I6_J,axiom,
% 8.57/4.59      ! [D3: int,T: int,A4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 8.57/4.59         => ! [X4: int] :
% 8.57/4.59              ( ! [Xa3: int] :
% 8.57/4.59                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                 => ! [Xb3: int] :
% 8.57/4.59                      ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                     => ( X4
% 8.57/4.59                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59             => ( ( ord_less_eq_int @ X4 @ T )
% 8.57/4.59               => ( ord_less_eq_int @ ( plus_plus_int @ X4 @ D3 ) @ T ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4995_aset_I8_J,axiom,
% 8.57/4.59      ! [D3: int,A4: set_int,T: int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ! [X4: int] :
% 8.57/4.59            ( ! [Xa3: int] :
% 8.57/4.59                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59               => ! [Xb3: int] :
% 8.57/4.59                    ( ( member_int @ Xb3 @ A4 )
% 8.57/4.59                   => ( X4
% 8.57/4.59                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 8.57/4.59           => ( ( ord_less_eq_int @ T @ X4 )
% 8.57/4.59             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X4 @ D3 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4996_cppi,axiom,
% 8.57/4.59      ! [D3: int,P: int > $o,P2: int > $o,A4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ? [Z5: int] :
% 8.57/4.59            ! [X3: int] :
% 8.57/4.59              ( ( ord_less_int @ Z5 @ X3 )
% 8.57/4.59             => ( ( P @ X3 )
% 8.57/4.59                = ( P2 @ X3 ) ) )
% 8.57/4.59         => ( ! [X3: int] :
% 8.57/4.59                ( ! [Xa2: int] :
% 8.57/4.59                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                   => ! [Xb2: int] :
% 8.57/4.59                        ( ( member_int @ Xb2 @ A4 )
% 8.57/4.59                       => ( X3
% 8.57/4.59                         != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59               => ( ( P @ X3 )
% 8.57/4.59                 => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59           => ( ! [X3: int,K3: int] :
% 8.57/4.59                  ( ( P2 @ X3 )
% 8.57/4.59                  = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 8.57/4.59             => ( ( ? [X5: int] : ( P @ X5 ) )
% 8.57/4.59                = ( ? [X: int] :
% 8.57/4.59                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                      & ( P2 @ X ) )
% 8.57/4.59                  | ? [X: int] :
% 8.57/4.59                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                      & ? [Y4: int] :
% 8.57/4.59                          ( ( member_int @ Y4 @ A4 )
% 8.57/4.59                          & ( P @ ( minus_minus_int @ Y4 @ X ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4997_cpmi,axiom,
% 8.57/4.59      ! [D3: int,P: int > $o,P2: int > $o,B4: set_int] :
% 8.57/4.59        ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.57/4.59       => ( ? [Z5: int] :
% 8.57/4.59            ! [X3: int] :
% 8.57/4.59              ( ( ord_less_int @ X3 @ Z5 )
% 8.57/4.59             => ( ( P @ X3 )
% 8.57/4.59                = ( P2 @ X3 ) ) )
% 8.57/4.59         => ( ! [X3: int] :
% 8.57/4.59                ( ! [Xa2: int] :
% 8.57/4.59                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                   => ! [Xb2: int] :
% 8.57/4.59                        ( ( member_int @ Xb2 @ B4 )
% 8.57/4.59                       => ( X3
% 8.57/4.59                         != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 8.57/4.59               => ( ( P @ X3 )
% 8.57/4.59                 => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 8.57/4.59           => ( ! [X3: int,K3: int] :
% 8.57/4.59                  ( ( P2 @ X3 )
% 8.57/4.59                  = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D3 ) ) ) )
% 8.57/4.59             => ( ( ? [X5: int] : ( P @ X5 ) )
% 8.57/4.59                = ( ? [X: int] :
% 8.57/4.59                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                      & ( P2 @ X ) )
% 8.57/4.59                  | ? [X: int] :
% 8.57/4.59                      ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.57/4.59                      & ? [Y4: int] :
% 8.57/4.59                          ( ( member_int @ Y4 @ B4 )
% 8.57/4.59                          & ( P @ ( plus_plus_int @ Y4 @ X ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4998_fact__div__fact,axiom,
% 8.57/4.59      ! [N: nat,M: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ N @ M )
% 8.57/4.59       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 8.57/4.59          = ( groups708209901874060359at_nat
% 8.57/4.59            @ ^ [X: nat] : X
% 8.57/4.59            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_4999_integer__of__int__code,axiom,
% 8.57/4.59      ( code_integer_of_int
% 8.57/4.59      = ( ^ [K2: int] :
% 8.57/4.59            ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 8.57/4.59            @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 8.57/4.59              @ ( if_Code_integer
% 8.57/4.59                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.57/4.59                  = zero_zero_int )
% 8.57/4.59                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.57/4.59                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5000_or__int__rec,axiom,
% 8.57/4.59      ( bit_se1409905431419307370or_int
% 8.57/4.59      = ( ^ [K2: int,L2: int] :
% 8.57/4.59            ( plus_plus_int
% 8.57/4.59            @ ( zero_n2684676970156552555ol_int
% 8.57/4.59              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.57/4.59                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 8.57/4.59            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5001_integer__of__int__eq__of__int,axiom,
% 8.57/4.59      code_integer_of_int = ring_18347121197199848620nteger ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5002_finite__atLeastAtMost,axiom,
% 8.57/4.59      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5003_finite__atLeastLessThan,axiom,
% 8.57/4.59      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5004_finite__atMost,axiom,
% 8.57/4.59      ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5005_or__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 8.57/4.59        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.57/4.59          & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5006_or__negative__int__iff,axiom,
% 8.57/4.59      ! [K: int,L: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 8.57/4.59        = ( ( ord_less_int @ K @ zero_zero_int )
% 8.57/4.59          | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5007_or__nat__numerals_I4_J,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5008_or__nat__numerals_I2_J,axiom,
% 8.57/4.59      ! [Y: num] :
% 8.57/4.59        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5009_or__nat__numerals_I1_J,axiom,
% 8.57/4.59      ! [Y: num] :
% 8.57/4.59        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5010_or__nat__numerals_I3_J,axiom,
% 8.57/4.59      ! [X2: num] :
% 8.57/4.59        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5011_or__minus__numerals_I2_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.57/4.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5012_or__minus__numerals_I6_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 8.57/4.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5013_and__minus__minus__numerals,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.59        = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5014_or__minus__minus__numerals,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.59        = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5015_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 8.57/4.59      ! [L: code_integer,U: code_integer] :
% 8.57/4.59        ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 8.57/4.59        = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5016_or__nat__def,axiom,
% 8.57/4.59      ( bit_se1412395901928357646or_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5017_less__eq__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( ord_less_eq_int @ Xa @ X2 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5018_less__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( ord_less_int @ Xa @ X2 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5019_one__integer__def,axiom,
% 8.57/4.59      ( one_one_Code_integer
% 8.57/4.59      = ( code_integer_of_int @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5020_times__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( times_times_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5021_uminus__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [X2: int] :
% 8.57/4.59        ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( uminus_uminus_int @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5022_zero__integer__def,axiom,
% 8.57/4.59      ( zero_z3403309356797280102nteger
% 8.57/4.59      = ( code_integer_of_int @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5023_sgn__integer__code,axiom,
% 8.57/4.59      ( sgn_sgn_Code_integer
% 8.57/4.59      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5024_abs__integer__code,axiom,
% 8.57/4.59      ( abs_abs_Code_integer
% 8.57/4.59      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5025_less__integer__code_I1_J,axiom,
% 8.57/4.59      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5026_minus__integer__code_I2_J,axiom,
% 8.57/4.59      ! [L: code_integer] :
% 8.57/4.59        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 8.57/4.59        = ( uminus1351360451143612070nteger @ L ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5027_minus__integer__code_I1_J,axiom,
% 8.57/4.59      ! [K: code_integer] :
% 8.57/4.59        ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 8.57/4.59        = K ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5028_uminus__integer__code_I1_J,axiom,
% 8.57/4.59      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 8.57/4.59      = zero_z3403309356797280102nteger ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5029_or__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( bit_se1080825931792720795nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_se1409905431419307370or_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5030_plus__integer__code_I2_J,axiom,
% 8.57/4.59      ! [L: code_integer] :
% 8.57/4.59        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 8.57/4.59        = L ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5031_plus__integer__code_I1_J,axiom,
% 8.57/4.59      ! [K: code_integer] :
% 8.57/4.59        ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 8.57/4.59        = K ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5032_times__integer__code_I1_J,axiom,
% 8.57/4.59      ! [K: code_integer] :
% 8.57/4.59        ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 8.57/4.59        = zero_z3403309356797280102nteger ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5033_times__integer__code_I2_J,axiom,
% 8.57/4.59      ! [L: code_integer] :
% 8.57/4.59        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 8.57/4.59        = zero_z3403309356797280102nteger ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5034_plus__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( plus_plus_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5035_minus__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( minus_minus_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5036_abs__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [X2: int] :
% 8.57/4.59        ( ( abs_abs_Code_integer @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( abs_abs_int @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5037_divide__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( divide_divide_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5038_modulo__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( modulo_modulo_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5039_take__bit__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: nat,X2: int] :
% 8.57/4.59        ( ( bit_se1745604003318907178nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_se2923211474154528505it_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5040_not__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [X2: int] :
% 8.57/4.59        ( ( bit_ri7632146776885996613nteger @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_ri7919022796975470100ot_int @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5041_and__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( bit_se3949692690581998587nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_se725231765392027082nd_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5042_bounded__nat__set__is__finite,axiom,
% 8.57/4.59      ! [N4: set_nat,N: nat] :
% 8.57/4.59        ( ! [X3: nat] :
% 8.57/4.59            ( ( member_nat @ X3 @ N4 )
% 8.57/4.59           => ( ord_less_nat @ X3 @ N ) )
% 8.57/4.59       => ( finite_finite_nat @ N4 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5043_finite__nat__set__iff__bounded,axiom,
% 8.57/4.59      ( finite_finite_nat
% 8.57/4.59      = ( ^ [N8: set_nat] :
% 8.57/4.59          ? [M2: nat] :
% 8.57/4.59          ! [X: nat] :
% 8.57/4.59            ( ( member_nat @ X @ N8 )
% 8.57/4.59           => ( ord_less_nat @ X @ M2 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5044_sgn__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [X2: int] :
% 8.57/4.59        ( ( sgn_sgn_Code_integer @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( sgn_sgn_int @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5045_finite__nat__set__iff__bounded__le,axiom,
% 8.57/4.59      ( finite_finite_nat
% 8.57/4.59      = ( ^ [N8: set_nat] :
% 8.57/4.59          ? [M2: nat] :
% 8.57/4.59          ! [X: nat] :
% 8.57/4.59            ( ( member_nat @ X @ N8 )
% 8.57/4.59           => ( ord_less_eq_nat @ X @ M2 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5046_bit__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [X2: int] :
% 8.57/4.59        ( ( bit_se9216721137139052372nteger @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( bit_se1146084159140164899it_int @ X2 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5047_xor__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: int,X2: int] :
% 8.57/4.59        ( ( bit_se3222712562003087583nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_se6526347334894502574or_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5048_push__bit__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: nat,X2: int] :
% 8.57/4.59        ( ( bit_se7788150548672797655nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_se545348938243370406it_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5049_mask__integer_Oabs__eq,axiom,
% 8.57/4.59      ( bit_se2119862282449309892nteger
% 8.57/4.59      = ( ^ [X: nat] : ( code_integer_of_int @ ( bit_se2000444600071755411sk_int @ X ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5050_unset__bit__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: nat,X2: int] :
% 8.57/4.59        ( ( bit_se8260200283734997820nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_se4203085406695923979it_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5051_set__bit__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: nat,X2: int] :
% 8.57/4.59        ( ( bit_se2793503036327961859nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_se7879613467334960850it_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5052_flip__bit__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: nat,X2: int] :
% 8.57/4.59        ( ( bit_se1345352211410354436nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_se2159334234014336723it_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5053_finite__M__bounded__by__nat,axiom,
% 8.57/4.59      ! [P: nat > $o,I: nat] :
% 8.57/4.59        ( finite_finite_nat
% 8.57/4.59        @ ( collect_nat
% 8.57/4.59          @ ^ [K2: nat] :
% 8.57/4.59              ( ( P @ K2 )
% 8.57/4.59              & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5054_finite__less__ub,axiom,
% 8.57/4.59      ! [F: nat > nat,U: nat] :
% 8.57/4.59        ( ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( F @ N2 ) )
% 8.57/4.59       => ( finite_finite_nat
% 8.57/4.59          @ ( collect_nat
% 8.57/4.59            @ ^ [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ U ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5055_or__greater__eq,axiom,
% 8.57/4.59      ! [L: int,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 8.57/4.59       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5056_OR__lower,axiom,
% 8.57/4.59      ! [X2: int,Y: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.59       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.57/4.59         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X2 @ Y ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5057_plus__and__or,axiom,
% 8.57/4.59      ! [X2: int,Y: int] :
% 8.57/4.59        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ ( bit_se1409905431419307370or_int @ X2 @ Y ) )
% 8.57/4.59        = ( plus_plus_int @ X2 @ Y ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5058_nat_Odisc__eq__case_I1_J,axiom,
% 8.57/4.59      ! [Nat: nat] :
% 8.57/4.59        ( ( Nat = zero_zero_nat )
% 8.57/4.59        = ( case_nat_o @ $true
% 8.57/4.59          @ ^ [Uu: nat] : $false
% 8.57/4.59          @ Nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5059_nat_Odisc__eq__case_I2_J,axiom,
% 8.57/4.59      ! [Nat: nat] :
% 8.57/4.59        ( ( Nat != zero_zero_nat )
% 8.57/4.59        = ( case_nat_o @ $false
% 8.57/4.59          @ ^ [Uu: nat] : $true
% 8.57/4.59          @ Nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5060_set__bit__nat__def,axiom,
% 8.57/4.59      ( bit_se7882103937844011126it_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] : ( bit_se1412395901928357646or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5061_or__not__numerals_I1_J,axiom,
% 8.57/4.59      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.57/4.59      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5062_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 8.57/4.59      ! [L: int,U: int] :
% 8.57/4.59        ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 8.57/4.59        = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5063_prod__int__eq,axiom,
% 8.57/4.59      ! [I: nat,J: nat] :
% 8.57/4.59        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 8.57/4.59        = ( groups1705073143266064639nt_int
% 8.57/4.59          @ ^ [X: int] : X
% 8.57/4.59          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5064_set__bit__int__def,axiom,
% 8.57/4.59      ( bit_se7879613467334960850it_int
% 8.57/4.59      = ( ^ [N3: nat,K2: int] : ( bit_se1409905431419307370or_int @ K2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5065_less__eq__nat_Osimps_I2_J,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 8.57/4.59        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5066_finite__divisors__nat,axiom,
% 8.57/4.59      ! [M: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.59       => ( finite_finite_nat
% 8.57/4.59          @ ( collect_nat
% 8.57/4.59            @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5067_subset__eq__atLeast0__atMost__finite,axiom,
% 8.57/4.59      ! [N4: set_nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.57/4.59       => ( finite_finite_nat @ N4 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5068_subset__eq__atLeast0__lessThan__finite,axiom,
% 8.57/4.59      ! [N4: set_nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.57/4.59       => ( finite_finite_nat @ N4 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5069_or__not__numerals_I2_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.57/4.59        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5070_or__not__numerals_I4_J,axiom,
% 8.57/4.59      ! [M: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.57/4.59        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5071_prod__int__plus__eq,axiom,
% 8.57/4.59      ! [I: nat,J: nat] :
% 8.57/4.59        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 8.57/4.59        = ( groups1705073143266064639nt_int
% 8.57/4.59          @ ^ [X: int] : X
% 8.57/4.59          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5072_diff__Suc,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 8.57/4.59        = ( case_nat_nat @ zero_zero_nat
% 8.57/4.59          @ ^ [K2: nat] : K2
% 8.57/4.59          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5073_or__not__numerals_I3_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.57/4.59        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5074_or__not__numerals_I7_J,axiom,
% 8.57/4.59      ! [M: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.57/4.59        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5075_OR__upper,axiom,
% 8.57/4.59      ! [X2: int,N: nat,Y: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.57/4.59       => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.57/4.59         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.57/4.59           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X2 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5076_or__not__numerals_I5_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.57/4.59        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5077_or__Suc__0__eq,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5078_Suc__0__or__eq,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.59        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5079_or__not__numerals_I9_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.57/4.59        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5080_or__not__numerals_I8_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.57/4.59        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5081_or__nat__rec,axiom,
% 8.57/4.59      ( bit_se1412395901928357646or_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] :
% 8.57/4.59            ( plus_plus_nat
% 8.57/4.59            @ ( zero_n2687167440665602831ol_nat
% 8.57/4.59              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 8.57/4.59                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 8.57/4.59            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5082_finite__Collect__le__nat,axiom,
% 8.57/4.59      ! [K: nat] :
% 8.57/4.59        ( finite_finite_nat
% 8.57/4.59        @ ( collect_nat
% 8.57/4.59          @ ^ [N3: nat] : ( ord_less_eq_nat @ N3 @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5083_finite__Collect__less__nat,axiom,
% 8.57/4.59      ! [K: nat] :
% 8.57/4.59        ( finite_finite_nat
% 8.57/4.59        @ ( collect_nat
% 8.57/4.59          @ ^ [N3: nat] : ( ord_less_nat @ N3 @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5084_finite__atLeastAtMost__int,axiom,
% 8.57/4.59      ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5085_finite__atLeastLessThan__int,axiom,
% 8.57/4.59      ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5086_finite__interval__int1,axiom,
% 8.57/4.59      ! [A: int,B: int] :
% 8.57/4.59        ( finite_finite_int
% 8.57/4.59        @ ( collect_int
% 8.57/4.59          @ ^ [I2: int] :
% 8.57/4.59              ( ( ord_less_eq_int @ A @ I2 )
% 8.57/4.59              & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5087_finite__interval__int4,axiom,
% 8.57/4.59      ! [A: int,B: int] :
% 8.57/4.59        ( finite_finite_int
% 8.57/4.59        @ ( collect_int
% 8.57/4.59          @ ^ [I2: int] :
% 8.57/4.59              ( ( ord_less_int @ A @ I2 )
% 8.57/4.59              & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5088_finite__atLeastLessThan__integer,axiom,
% 8.57/4.59      ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5089_finite__atLeastAtMost__integer,axiom,
% 8.57/4.59      ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5090_finite__interval__int3,axiom,
% 8.57/4.59      ! [A: int,B: int] :
% 8.57/4.59        ( finite_finite_int
% 8.57/4.59        @ ( collect_int
% 8.57/4.59          @ ^ [I2: int] :
% 8.57/4.59              ( ( ord_less_int @ A @ I2 )
% 8.57/4.59              & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5091_finite__interval__int2,axiom,
% 8.57/4.59      ! [A: int,B: int] :
% 8.57/4.59        ( finite_finite_int
% 8.57/4.59        @ ( collect_int
% 8.57/4.59          @ ^ [I2: int] :
% 8.57/4.59              ( ( ord_less_eq_int @ A @ I2 )
% 8.57/4.59              & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5092_finite__atLeastZeroLessThan__int,axiom,
% 8.57/4.59      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5093_finite__atLeastZeroLessThan__integer,axiom,
% 8.57/4.59      ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5094_finite__divisors__int,axiom,
% 8.57/4.59      ! [I: int] :
% 8.57/4.59        ( ( I != zero_zero_int )
% 8.57/4.59       => ( finite_finite_int
% 8.57/4.59          @ ( collect_int
% 8.57/4.59            @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5095_or__int__unfold,axiom,
% 8.57/4.59      ( bit_se1409905431419307370or_int
% 8.57/4.59      = ( ^ [K2: int,L2: int] :
% 8.57/4.59            ( if_int
% 8.57/4.59            @ ( ( K2
% 8.57/4.59                = ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.59              | ( L2
% 8.57/4.59                = ( uminus_uminus_int @ one_one_int ) ) )
% 8.57/4.59            @ ( uminus_uminus_int @ one_one_int )
% 8.57/4.59            @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5096_even__set__encode__iff,axiom,
% 8.57/4.59      ! [A4: set_nat] :
% 8.57/4.59        ( ( finite_finite_nat @ A4 )
% 8.57/4.59       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A4 ) )
% 8.57/4.59          = ( ~ ( member_nat @ zero_zero_nat @ A4 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5097_Code__Numeral_Opositive__def,axiom,
% 8.57/4.59      code_positive = numera6620942414471956472nteger ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5098_or__nat__unfold,axiom,
% 8.57/4.59      ( bit_se1412395901928357646or_nat
% 8.57/4.59      = ( ^ [M2: nat,N3: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5099_max__0R,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_max_nat @ N @ zero_zero_nat )
% 8.57/4.59        = N ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5100_max__0L,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_max_nat @ zero_zero_nat @ N )
% 8.57/4.59        = N ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5101_max__nat_Oright__neutral,axiom,
% 8.57/4.59      ! [A: nat] :
% 8.57/4.59        ( ( ord_max_nat @ A @ zero_zero_nat )
% 8.57/4.59        = A ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5102_max__nat_Oneutr__eq__iff,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( zero_zero_nat
% 8.57/4.59          = ( ord_max_nat @ A @ B ) )
% 8.57/4.59        = ( ( A = zero_zero_nat )
% 8.57/4.59          & ( B = zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5103_max__nat_Oleft__neutral,axiom,
% 8.57/4.59      ! [A: nat] :
% 8.57/4.59        ( ( ord_max_nat @ zero_zero_nat @ A )
% 8.57/4.59        = A ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5104_max__nat_Oeq__neutr__iff,axiom,
% 8.57/4.59      ! [A: nat,B: nat] :
% 8.57/4.59        ( ( ( ord_max_nat @ A @ B )
% 8.57/4.59          = zero_zero_nat )
% 8.57/4.59        = ( ( A = zero_zero_nat )
% 8.57/4.59          & ( B = zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5105_max__Suc__Suc,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.57/4.59        = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5106_max__numeral__Suc,axiom,
% 8.57/4.59      ! [K: num,N: nat] :
% 8.57/4.59        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.57/4.59        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5107_max__Suc__numeral,axiom,
% 8.57/4.59      ! [N: nat,K: num] :
% 8.57/4.59        ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.57/4.59        = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5108_nat__mult__max__right,axiom,
% 8.57/4.59      ! [M: nat,N: nat,Q2: nat] :
% 8.57/4.59        ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 8.57/4.59        = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5109_nat__mult__max__left,axiom,
% 8.57/4.59      ! [M: nat,N: nat,Q2: nat] :
% 8.57/4.59        ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 8.57/4.59        = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5110_nat__add__max__left,axiom,
% 8.57/4.59      ! [M: nat,N: nat,Q2: nat] :
% 8.57/4.59        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 8.57/4.59        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5111_nat__add__max__right,axiom,
% 8.57/4.59      ! [M: nat,N: nat,Q2: nat] :
% 8.57/4.59        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 8.57/4.59        = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5112_nat__minus__add__max,axiom,
% 8.57/4.59      ! [N: nat,M: nat] :
% 8.57/4.59        ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 8.57/4.59        = ( ord_max_nat @ N @ M ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5113_max__Suc1,axiom,
% 8.57/4.59      ! [N: nat,M: nat] :
% 8.57/4.59        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 8.57/4.59        = ( case_nat_nat @ ( suc @ N )
% 8.57/4.59          @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ N @ M7 ) )
% 8.57/4.59          @ M ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5114_max__Suc2,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 8.57/4.59        = ( case_nat_nat @ ( suc @ N )
% 8.57/4.59          @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ M7 @ N ) )
% 8.57/4.59          @ M ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5115_set__encode__inf,axiom,
% 8.57/4.59      ! [A4: set_nat] :
% 8.57/4.59        ( ~ ( finite_finite_nat @ A4 )
% 8.57/4.59       => ( ( nat_set_encode @ A4 )
% 8.57/4.59          = zero_zero_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5116_infinite__int__iff__unbounded__le,axiom,
% 8.57/4.59      ! [S3: set_int] :
% 8.57/4.59        ( ( ~ ( finite_finite_int @ S3 ) )
% 8.57/4.59        = ( ! [M2: int] :
% 8.57/4.59            ? [N3: int] :
% 8.57/4.59              ( ( ord_less_eq_int @ M2 @ ( abs_abs_int @ N3 ) )
% 8.57/4.59              & ( member_int @ N3 @ S3 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5117_set__encode__insert,axiom,
% 8.57/4.59      ! [A4: set_nat,N: nat] :
% 8.57/4.59        ( ( finite_finite_nat @ A4 )
% 8.57/4.59       => ( ~ ( member_nat @ N @ A4 )
% 8.57/4.59         => ( ( nat_set_encode @ ( insert_nat @ N @ A4 ) )
% 8.57/4.59            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A4 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5118_atMost__Suc,axiom,
% 8.57/4.59      ! [K: nat] :
% 8.57/4.59        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 8.57/4.59        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5119_atLeast0__atMost__Suc,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.57/4.59        = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5120_atLeast0__lessThan__Suc,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.57/4.59        = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5121_Icc__eq__insert__lb__nat,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59       => ( ( set_or1269000886237332187st_nat @ M @ N )
% 8.57/4.59          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5122_atLeastAtMostSuc__conv,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.57/4.59       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 8.57/4.59          = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5123_atLeastAtMost__insertL,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 8.57/4.59          = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5124_atMost__nat__numeral,axiom,
% 8.57/4.59      ! [K: num] :
% 8.57/4.59        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 8.57/4.59        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5125_set__decode__plus__power__2,axiom,
% 8.57/4.59      ! [N: nat,Z2: nat] :
% 8.57/4.59        ( ~ ( member_nat @ N @ ( nat_set_decode @ Z2 ) )
% 8.57/4.59       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z2 ) )
% 8.57/4.59          = ( insert_nat @ N @ ( nat_set_decode @ Z2 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5126_infinite__nat__iff__unbounded__le,axiom,
% 8.57/4.59      ! [S3: set_nat] :
% 8.57/4.59        ( ( ~ ( finite_finite_nat @ S3 ) )
% 8.57/4.59        = ( ! [M2: nat] :
% 8.57/4.59            ? [N3: nat] :
% 8.57/4.59              ( ( ord_less_eq_nat @ M2 @ N3 )
% 8.57/4.59              & ( member_nat @ N3 @ S3 ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5127_integer__of__num_I3_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( code_integer_of_num @ ( bit1 @ N ) )
% 8.57/4.59        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5128_card__Collect__less__nat,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( finite_card_nat
% 8.57/4.59          @ ( collect_nat
% 8.57/4.59            @ ^ [I2: nat] : ( ord_less_nat @ I2 @ N ) ) )
% 8.57/4.59        = N ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5129_drop__bit__nonnegative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 8.57/4.59        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5130_drop__bit__negative__int__iff,axiom,
% 8.57/4.59      ! [N: nat,K: int] :
% 8.57/4.59        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 8.57/4.59        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5131_drop__bit__minus__one,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 8.57/4.59        = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5132_card__atLeastLessThan,axiom,
% 8.57/4.59      ! [L: nat,U: nat] :
% 8.57/4.59        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 8.57/4.59        = ( minus_minus_nat @ U @ L ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5133_card__atMost,axiom,
% 8.57/4.59      ! [U: nat] :
% 8.57/4.59        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 8.57/4.59        = ( suc @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5134_card__Collect__le__nat,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( finite_card_nat
% 8.57/4.59          @ ( collect_nat
% 8.57/4.59            @ ^ [I2: nat] : ( ord_less_eq_nat @ I2 @ N ) ) )
% 8.57/4.59        = ( suc @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5135_card__atLeastAtMost,axiom,
% 8.57/4.59      ! [L: nat,U: nat] :
% 8.57/4.59        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 8.57/4.59        = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5136_drop__bit__of__Suc__0,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.57/4.59        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5137_card__atLeastLessThan__int,axiom,
% 8.57/4.59      ! [L: int,U: int] :
% 8.57/4.59        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 8.57/4.59        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5138_card__atLeastAtMost__int,axiom,
% 8.57/4.59      ! [L: int,U: int] :
% 8.57/4.59        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 8.57/4.59        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5139_drop__bit__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [Xa: nat,X2: int] :
% 8.57/4.59        ( ( bit_se3928097537394005634nteger @ Xa @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( code_integer_of_int @ ( bit_se8568078237143864401it_int @ Xa @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5140_integer__of__num__def,axiom,
% 8.57/4.59      code_integer_of_num = numera6620942414471956472nteger ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5141_card__less__Suc2,axiom,
% 8.57/4.59      ! [M3: set_nat,I: nat] :
% 8.57/4.59        ( ~ ( member_nat @ zero_zero_nat @ M3 )
% 8.57/4.59       => ( ( finite_card_nat
% 8.57/4.59            @ ( collect_nat
% 8.57/4.59              @ ^ [K2: nat] :
% 8.57/4.59                  ( ( member_nat @ ( suc @ K2 ) @ M3 )
% 8.57/4.59                  & ( ord_less_nat @ K2 @ I ) ) ) )
% 8.57/4.59          = ( finite_card_nat
% 8.57/4.59            @ ( collect_nat
% 8.57/4.59              @ ^ [K2: nat] :
% 8.57/4.59                  ( ( member_nat @ K2 @ M3 )
% 8.57/4.59                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5142_card__less__Suc,axiom,
% 8.57/4.59      ! [M3: set_nat,I: nat] :
% 8.57/4.59        ( ( member_nat @ zero_zero_nat @ M3 )
% 8.57/4.59       => ( ( suc
% 8.57/4.59            @ ( finite_card_nat
% 8.57/4.59              @ ( collect_nat
% 8.57/4.59                @ ^ [K2: nat] :
% 8.57/4.59                    ( ( member_nat @ ( suc @ K2 ) @ M3 )
% 8.57/4.59                    & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 8.57/4.59          = ( finite_card_nat
% 8.57/4.59            @ ( collect_nat
% 8.57/4.59              @ ^ [K2: nat] :
% 8.57/4.59                  ( ( member_nat @ K2 @ M3 )
% 8.57/4.59                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5143_card__less,axiom,
% 8.57/4.59      ! [M3: set_nat,I: nat] :
% 8.57/4.59        ( ( member_nat @ zero_zero_nat @ M3 )
% 8.57/4.59       => ( ( finite_card_nat
% 8.57/4.59            @ ( collect_nat
% 8.57/4.59              @ ^ [K2: nat] :
% 8.57/4.59                  ( ( member_nat @ K2 @ M3 )
% 8.57/4.59                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 8.57/4.59         != zero_zero_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5144_card__atLeastZeroLessThan__int,axiom,
% 8.57/4.59      ! [U: int] :
% 8.57/4.59        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 8.57/4.59        = ( nat2 @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5145_subset__card__intvl__is__intvl,axiom,
% 8.57/4.59      ! [A4: set_nat,K: nat] :
% 8.57/4.59        ( ( ord_less_eq_set_nat @ A4 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) )
% 8.57/4.59       => ( A4
% 8.57/4.59          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5146_atLeastAtMostPlus1__int__conv,axiom,
% 8.57/4.59      ! [M: int,N: int] :
% 8.57/4.59        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 8.57/4.59       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 8.57/4.59          = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5147_subset__eq__atLeast0__lessThan__card,axiom,
% 8.57/4.59      ! [N4: set_nat,N: nat] :
% 8.57/4.59        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.57/4.59       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5148_card__sum__le__nat__sum,axiom,
% 8.57/4.59      ! [S3: set_nat] :
% 8.57/4.59        ( ord_less_eq_nat
% 8.57/4.59        @ ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [X: nat] : X
% 8.57/4.59          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 8.57/4.59        @ ( groups3542108847815614940at_nat
% 8.57/4.59          @ ^ [X: nat] : X
% 8.57/4.59          @ S3 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5149_integer__of__num__triv_I1_J,axiom,
% 8.57/4.59      ( ( code_integer_of_num @ one )
% 8.57/4.59      = one_one_Code_integer ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5150_integer__of__num_I2_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 8.57/4.59        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5151_integer__of__num__triv_I2_J,axiom,
% 8.57/4.59      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 8.57/4.59      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5152_pred__def,axiom,
% 8.57/4.59      ( pred
% 8.57/4.59      = ( case_nat_nat @ zero_zero_nat
% 8.57/4.59        @ ^ [X24: nat] : X24 ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5153_and__int_Osimps,axiom,
% 8.57/4.59      ( bit_se725231765392027082nd_int
% 8.57/4.59      = ( ^ [K2: int,L2: int] :
% 8.57/4.59            ( if_int
% 8.57/4.59            @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.57/4.59              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.57/4.59            @ ( uminus_uminus_int
% 8.57/4.59              @ ( zero_n2684676970156552555ol_int
% 8.57/4.59                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.57/4.59                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 8.57/4.59            @ ( plus_plus_int
% 8.57/4.59              @ ( zero_n2684676970156552555ol_int
% 8.57/4.59                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.57/4.59                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 8.57/4.59              @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5154_and__int_Oelims,axiom,
% 8.57/4.59      ! [X2: int,Xa: int,Y: int] :
% 8.57/4.59        ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa )
% 8.57/4.59          = Y )
% 8.57/4.59       => ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.57/4.59              & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.57/4.59           => ( Y
% 8.57/4.59              = ( uminus_uminus_int
% 8.57/4.59                @ ( zero_n2684676970156552555ol_int
% 8.57/4.59                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 8.57/4.59                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 8.57/4.59          & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.57/4.59                & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.57/4.59           => ( Y
% 8.57/4.59              = ( plus_plus_int
% 8.57/4.59                @ ( zero_n2684676970156552555ol_int
% 8.57/4.59                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 8.57/4.59                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 8.57/4.59                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5155_Suc__funpow,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( compow_nat_nat @ N @ suc )
% 8.57/4.59        = ( plus_plus_nat @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5156_atLeastLessThan__upto,axiom,
% 8.57/4.59      ( set_or4662586982721622107an_int
% 8.57/4.59      = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5157_simp__from__to,axiom,
% 8.57/4.59      ( set_or1266510415728281911st_int
% 8.57/4.59      = ( ^ [I2: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I2 ) @ bot_bot_set_int @ ( insert_int @ I2 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5158_set__decode__zero,axiom,
% 8.57/4.59      ( ( nat_set_decode @ zero_zero_nat )
% 8.57/4.59      = bot_bot_set_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5159_set__encode__empty,axiom,
% 8.57/4.59      ( ( nat_set_encode @ bot_bot_set_nat )
% 8.57/4.59      = zero_zero_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5160_atLeastLessThan__singleton,axiom,
% 8.57/4.59      ! [M: nat] :
% 8.57/4.59        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 8.57/4.59        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5161_atMost__0,axiom,
% 8.57/4.59      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 8.57/4.59      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5162_bot__nat__def,axiom,
% 8.57/4.59      bot_bot_nat = zero_zero_nat ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5163_atLeastLessThan0,axiom,
% 8.57/4.59      ! [M: nat] :
% 8.57/4.59        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 8.57/4.59        = bot_bot_set_nat ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5164_atLeastLessThanSuc,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ( ord_less_eq_nat @ M @ N )
% 8.57/4.59         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 8.57/4.59            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 8.57/4.59        & ( ~ ( ord_less_eq_nat @ M @ N )
% 8.57/4.59         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 8.57/4.59            = bot_bot_set_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5165_atLeast1__atMost__eq__remove0,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.59        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5166_atLeastLessThan__nat__numeral,axiom,
% 8.57/4.59      ! [M: nat,K: num] :
% 8.57/4.59        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 8.57/4.59         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 8.57/4.59            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 8.57/4.59        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 8.57/4.59         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 8.57/4.59            = bot_bot_set_nat ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5167_card__greaterThanLessThan__int,axiom,
% 8.57/4.59      ! [L: int,U: int] :
% 8.57/4.59        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 8.57/4.59        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5168_finite__greaterThanLessThan__int,axiom,
% 8.57/4.59      ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5169_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 8.57/4.59      ! [L: int,U: int] :
% 8.57/4.59        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 8.57/4.59        = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5170_greaterThanLessThan__upto,axiom,
% 8.57/4.59      ( set_or5832277885323065728an_int
% 8.57/4.59      = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5171_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 8.57/4.59      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 8.57/4.59      @ ^ [X: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X )
% 8.57/4.59      @ ^ [X: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5172_finite__greaterThanLessThan,axiom,
% 8.57/4.59      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5173_finite__greaterThanLessThan__integer,axiom,
% 8.57/4.59      ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5174_card__greaterThanLessThan,axiom,
% 8.57/4.59      ! [L: nat,U: nat] :
% 8.57/4.59        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 8.57/4.59        = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5175_atLeastSucLessThan__greaterThanLessThan,axiom,
% 8.57/4.59      ! [L: nat,U: nat] :
% 8.57/4.59        ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 8.57/4.59        = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5176_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 8.57/4.59      ! [N: nat,J: nat,I: nat] :
% 8.57/4.59        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 8.57/4.59       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 8.57/4.59          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5177_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 8.57/4.59      ! [L: code_integer,U: code_integer] :
% 8.57/4.59        ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 8.57/4.59        = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5178_num__of__nat_Osimps_I2_J,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59         => ( ( num_of_nat @ ( suc @ N ) )
% 8.57/4.59            = ( inc @ ( num_of_nat @ N ) ) ) )
% 8.57/4.59        & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59         => ( ( num_of_nat @ ( suc @ N ) )
% 8.57/4.59            = one ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5179_num__of__nat__numeral__eq,axiom,
% 8.57/4.59      ! [Q2: num] :
% 8.57/4.59        ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 8.57/4.59        = Q2 ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5180_pred__numeral__simps_I2_J,axiom,
% 8.57/4.59      ! [K: num] :
% 8.57/4.59        ( ( pred_numeral @ ( bit0 @ K ) )
% 8.57/4.59        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5181_inc__BitM__eq,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( inc @ ( bitM @ N ) )
% 8.57/4.59        = ( bit0 @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5182_BitM__inc__eq,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bitM @ ( inc @ N ) )
% 8.57/4.59        = ( bit1 @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5183_num__of__nat_Osimps_I1_J,axiom,
% 8.57/4.59      ( ( num_of_nat @ zero_zero_nat )
% 8.57/4.59      = one ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5184_eval__nat__numeral_I2_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 8.57/4.59        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5185_BitM__plus__one,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 8.57/4.59        = ( bit0 @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5186_one__plus__BitM,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 8.57/4.59        = ( bit0 @ N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5187_numeral__num__of__nat,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59       => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 8.57/4.59          = N ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5188_num__of__nat__One,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 8.57/4.59       => ( ( num_of_nat @ N )
% 8.57/4.59          = one ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5189_sub__BitM__One__eq,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 8.57/4.59        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5190_num__of__nat__double,axiom,
% 8.57/4.59      ! [N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59       => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 8.57/4.59          = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5191_num__of__nat__plus__distrib,axiom,
% 8.57/4.59      ! [M: nat,N: nat] :
% 8.57/4.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.57/4.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.57/4.59         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 8.57/4.59            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5192_or__minus__numerals_I5_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 8.57/4.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5193_or__minus__numerals_I1_J,axiom,
% 8.57/4.59      ! [N: num] :
% 8.57/4.59        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.57/4.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5194_num__of__integer_Oabs__eq,axiom,
% 8.57/4.59      ! [X2: int] :
% 8.57/4.59        ( ( code_num_of_integer @ ( code_integer_of_int @ X2 ) )
% 8.57/4.59        = ( num_of_nat @ ( nat2 @ X2 ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5195_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 8.57/4.59      ! [N: nat,J: nat,I: nat] :
% 8.57/4.59        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 8.57/4.59       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 8.57/4.59          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5196_take__bit__numeral__minus__numeral__int,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.59        = ( case_option_int_num @ zero_zero_int
% 8.57/4.59          @ ^ [Q6: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q6 ) ) )
% 8.57/4.59          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5197_finite__greaterThanAtMost,axiom,
% 8.57/4.59      ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5198_card__greaterThanAtMost,axiom,
% 8.57/4.59      ! [L: nat,U: nat] :
% 8.57/4.59        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 8.57/4.59        = ( minus_minus_nat @ U @ L ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5199_atLeastSucAtMost__greaterThanAtMost,axiom,
% 8.57/4.59      ! [L: nat,U: nat] :
% 8.57/4.59        ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 8.57/4.59        = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5200_sorted__list__of__set__greaterThanAtMost,axiom,
% 8.57/4.59      ! [I: nat,J: nat] :
% 8.57/4.59        ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 8.57/4.59       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 8.57/4.59          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5201_and__minus__numerals_I7_J,axiom,
% 8.57/4.59      ! [N: num,M: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 8.57/4.59        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5202_and__minus__numerals_I3_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.57/4.59        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5203_and__minus__numerals_I8_J,axiom,
% 8.57/4.59      ! [N: num,M: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 8.57/4.59        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5204_and__minus__numerals_I4_J,axiom,
% 8.57/4.59      ! [M: num,N: num] :
% 8.57/4.59        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.57/4.59        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 8.57/4.59  
% 8.57/4.59  thf(fact_5205_finite__greaterThanAtMost__int,axiom,
% 8.57/4.60      ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5206_finite__greaterThanAtMost__integer,axiom,
% 8.57/4.60      ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5207_card__greaterThanAtMost__int,axiom,
% 8.57/4.60      ! [L: int,U: int] :
% 8.57/4.60        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 8.57/4.60        = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5208_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 8.57/4.60      ! [L: int,U: int] :
% 8.57/4.60        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 8.57/4.60        = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5209_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 8.57/4.60      ! [L: code_integer,U: code_integer] :
% 8.57/4.60        ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 8.57/4.60        = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5210_greaterThanAtMost__upto,axiom,
% 8.57/4.60      ( set_or6656581121297822940st_int
% 8.57/4.60      = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5211_int__numeral__not__and__num,axiom,
% 8.57/4.60      ! [M: num,N: num] :
% 8.57/4.60        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.57/4.60        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5212_int__numeral__and__not__num,axiom,
% 8.57/4.60      ! [M: num,N: num] :
% 8.57/4.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.60        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5213_nat__of__integer__less__iff,axiom,
% 8.57/4.60      ! [X2: code_integer,Y: code_integer] :
% 8.57/4.60        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 8.57/4.60       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 8.57/4.60         => ( ( ord_less_nat @ ( code_nat_of_integer @ X2 ) @ ( code_nat_of_integer @ Y ) )
% 8.57/4.60            = ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5214_nat__of__integer__of__nat,axiom,
% 8.57/4.60      ! [N: nat] :
% 8.57/4.60        ( ( code_nat_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 8.57/4.60        = N ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5215_of__nat__of__integer,axiom,
% 8.57/4.60      ! [K: code_integer] :
% 8.57/4.60        ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 8.57/4.60        = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5216_nat__of__integer__non__positive,axiom,
% 8.57/4.60      ! [K: code_integer] :
% 8.57/4.60        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 8.57/4.60       => ( ( code_nat_of_integer @ K )
% 8.57/4.60          = zero_zero_nat ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5217_nat__of__integer_Oabs__eq,axiom,
% 8.57/4.60      ! [X2: int] :
% 8.57/4.60        ( ( code_nat_of_integer @ ( code_integer_of_int @ X2 ) )
% 8.57/4.60        = ( nat2 @ X2 ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5218_upto__rec2,axiom,
% 8.57/4.60      ! [I: int,J: int] :
% 8.57/4.60        ( ( ord_less_eq_int @ I @ J )
% 8.57/4.60       => ( ( upto @ I @ J )
% 8.57/4.60          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5219_upto__split2,axiom,
% 8.57/4.60      ! [I: int,J: int,K: int] :
% 8.57/4.60        ( ( ord_less_eq_int @ I @ J )
% 8.57/4.60       => ( ( ord_less_eq_int @ J @ K )
% 8.57/4.60         => ( ( upto @ I @ K )
% 8.57/4.60            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5220_upto__split1,axiom,
% 8.57/4.60      ! [I: int,J: int,K: int] :
% 8.57/4.60        ( ( ord_less_eq_int @ I @ J )
% 8.57/4.60       => ( ( ord_less_eq_int @ J @ K )
% 8.57/4.60         => ( ( upto @ I @ K )
% 8.57/4.60            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5221_upto__split3,axiom,
% 8.57/4.60      ! [I: int,J: int,K: int] :
% 8.57/4.60        ( ( ord_less_eq_int @ I @ J )
% 8.57/4.60       => ( ( ord_less_eq_int @ J @ K )
% 8.57/4.60         => ( ( upto @ I @ K )
% 8.57/4.60            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5222_Gcd__remove0__nat,axiom,
% 8.57/4.60      ! [M3: set_nat] :
% 8.57/4.60        ( ( finite_finite_nat @ M3 )
% 8.57/4.60       => ( ( gcd_Gcd_nat @ M3 )
% 8.57/4.60          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M3 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5223_Gcd__nat__eq__one,axiom,
% 8.57/4.60      ! [N4: set_nat] :
% 8.57/4.60        ( ( member_nat @ one_one_nat @ N4 )
% 8.57/4.60       => ( ( gcd_Gcd_nat @ N4 )
% 8.57/4.60          = one_one_nat ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5224_Gcd__dvd__nat,axiom,
% 8.57/4.60      ! [A: nat,A4: set_nat] :
% 8.57/4.60        ( ( member_nat @ A @ A4 )
% 8.57/4.60       => ( dvd_dvd_nat @ ( gcd_Gcd_nat @ A4 ) @ A ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5225_Gcd__greatest__nat,axiom,
% 8.57/4.60      ! [A4: set_nat,A: nat] :
% 8.57/4.60        ( ! [B3: nat] :
% 8.57/4.60            ( ( member_nat @ B3 @ A4 )
% 8.57/4.60           => ( dvd_dvd_nat @ A @ B3 ) )
% 8.57/4.60       => ( dvd_dvd_nat @ A @ ( gcd_Gcd_nat @ A4 ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5226_abs__Gcd__eq,axiom,
% 8.57/4.60      ! [K5: set_int] :
% 8.57/4.60        ( ( abs_abs_int @ ( gcd_Gcd_int @ K5 ) )
% 8.57/4.60        = ( gcd_Gcd_int @ K5 ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5227_finite__lessThan,axiom,
% 8.57/4.60      ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5228_card__lessThan,axiom,
% 8.57/4.60      ! [U: nat] :
% 8.57/4.60        ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 8.57/4.60        = U ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5229_lessThan__0,axiom,
% 8.57/4.60      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 8.57/4.60      = bot_bot_set_nat ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5230_Gcd__dvd__int,axiom,
% 8.57/4.60      ! [A: int,A4: set_int] :
% 8.57/4.60        ( ( member_int @ A @ A4 )
% 8.57/4.60       => ( dvd_dvd_int @ ( gcd_Gcd_int @ A4 ) @ A ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5231_Gcd__greatest__int,axiom,
% 8.57/4.60      ! [A4: set_int,A: int] :
% 8.57/4.60        ( ! [B3: int] :
% 8.57/4.60            ( ( member_int @ B3 @ A4 )
% 8.57/4.60           => ( dvd_dvd_int @ A @ B3 ) )
% 8.57/4.60       => ( dvd_dvd_int @ A @ ( gcd_Gcd_int @ A4 ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5232_lessThan__atLeast0,axiom,
% 8.57/4.60      ( set_ord_lessThan_nat
% 8.57/4.60      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5233_lessThan__Suc__atMost,axiom,
% 8.57/4.60      ! [K: nat] :
% 8.57/4.60        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 8.57/4.60        = ( set_ord_atMost_nat @ K ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5234_lessThan__empty__iff,axiom,
% 8.57/4.60      ! [N: nat] :
% 8.57/4.60        ( ( ( set_ord_lessThan_nat @ N )
% 8.57/4.60          = bot_bot_set_nat )
% 8.57/4.60        = ( N = zero_zero_nat ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5235_lessThan__Suc,axiom,
% 8.57/4.60      ! [K: nat] :
% 8.57/4.60        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 8.57/4.60        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5236_Gcd__int__greater__eq__0,axiom,
% 8.57/4.60      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5237_lessThan__nat__numeral,axiom,
% 8.57/4.60      ! [K: num] :
% 8.57/4.60        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 8.57/4.60        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5238_atLeast1__lessThan__eq__remove0,axiom,
% 8.57/4.60      ! [N: nat] :
% 8.57/4.60        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.57/4.60        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5239_image__atLeastZeroLessThan__integer,axiom,
% 8.57/4.60      ! [U: code_integer] :
% 8.57/4.60        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 8.57/4.60       => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 8.57/4.60          = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5240_take__bit__num__simps_I7_J,axiom,
% 8.57/4.60      ! [R: num,M: num] :
% 8.57/4.60        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 8.57/4.60        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5241_take__bit__num__simps_I4_J,axiom,
% 8.57/4.60      ! [N: nat,M: num] :
% 8.57/4.60        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 8.57/4.60        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5242_and__not__num_Osimps_I8_J,axiom,
% 8.57/4.60      ! [M: num,N: num] :
% 8.57/4.60        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.57/4.60        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 8.57/4.60          @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 8.57/4.60          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5243_image__Suc__atLeastAtMost,axiom,
% 8.57/4.60      ! [I: nat,J: nat] :
% 8.57/4.60        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 8.57/4.60        = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5244_image__Suc__atLeastLessThan,axiom,
% 8.57/4.60      ! [I: nat,J: nat] :
% 8.57/4.60        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 8.57/4.60        = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5245_Gcd__abs__eq,axiom,
% 8.57/4.60      ! [K5: set_int] :
% 8.57/4.60        ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 8.57/4.60        = ( gcd_Gcd_int @ K5 ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5246_Gcd__int__eq,axiom,
% 8.57/4.60      ! [N4: set_nat] :
% 8.57/4.60        ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N4 ) )
% 8.57/4.60        = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N4 ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5247_Gcd__nat__abs__eq,axiom,
% 8.57/4.60      ! [K5: set_int] :
% 8.57/4.60        ( ( gcd_Gcd_nat
% 8.57/4.60          @ ( image_int_nat
% 8.57/4.60            @ ^ [K2: int] : ( nat2 @ ( abs_abs_int @ K2 ) )
% 8.57/4.60            @ K5 ) )
% 8.57/4.60        = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5248_zero__notin__Suc__image,axiom,
% 8.57/4.60      ! [A4: set_nat] :
% 8.57/4.60        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5249_image__int__atLeastAtMost,axiom,
% 8.57/4.60      ! [A: nat,B: nat] :
% 8.57/4.60        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.57/4.60        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5250_image__int__atLeastLessThan,axiom,
% 8.57/4.60      ! [A: nat,B: nat] :
% 8.57/4.60        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 8.57/4.60        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5251_image__Suc__atMost,axiom,
% 8.57/4.60      ! [N: nat] :
% 8.57/4.60        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 8.57/4.60        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5252_image__Suc__lessThan,axiom,
% 8.57/4.60      ! [N: nat] :
% 8.57/4.60        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 8.57/4.60        = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5253_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 8.57/4.60      ! [N: nat] :
% 8.57/4.60        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.57/4.60        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5254_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 8.57/4.60      ! [N: nat] :
% 8.57/4.60        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.57/4.60        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5255_atMost__Suc__eq__insert__0,axiom,
% 8.57/4.60      ! [N: nat] :
% 8.57/4.60        ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 8.57/4.60        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5256_lessThan__Suc__eq__insert__0,axiom,
% 8.57/4.60      ! [N: nat] :
% 8.57/4.60        ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 8.57/4.60        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5257_image__add__int__atLeastLessThan,axiom,
% 8.57/4.60      ! [L: int,U: int] :
% 8.57/4.60        ( ( image_int_int
% 8.57/4.60          @ ^ [X: int] : ( plus_plus_int @ X @ L )
% 8.57/4.60          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 8.57/4.60        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5258_image__add__integer__atLeastLessThan,axiom,
% 8.57/4.60      ! [L: code_integer,U: code_integer] :
% 8.57/4.60        ( ( image_4470545334726330049nteger
% 8.57/4.60          @ ^ [X: code_integer] : ( plus_p5714425477246183910nteger @ X @ L )
% 8.57/4.60          @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 8.57/4.60        = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5259_image__atLeastZeroLessThan__int,axiom,
% 8.57/4.60      ! [U: int] :
% 8.57/4.60        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.57/4.60       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 8.57/4.60          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5260_image__minus__const__atLeastLessThan__nat,axiom,
% 8.57/4.60      ! [C: nat,Y: nat,X2: nat] :
% 8.57/4.60        ( ( ( ord_less_nat @ C @ Y )
% 8.57/4.60         => ( ( image_nat_nat
% 8.57/4.60              @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 8.57/4.60              @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 8.57/4.60            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 8.57/4.60        & ( ~ ( ord_less_nat @ C @ Y )
% 8.57/4.60         => ( ( ( ord_less_nat @ X2 @ Y )
% 8.57/4.60             => ( ( image_nat_nat
% 8.57/4.60                  @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 8.57/4.60                  @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 8.57/4.60                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 8.57/4.60            & ( ~ ( ord_less_nat @ X2 @ Y )
% 8.57/4.60             => ( ( image_nat_nat
% 8.57/4.60                  @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 8.57/4.60                  @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 8.57/4.60                = bot_bot_set_nat ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5261_take__bit__num__simps_I6_J,axiom,
% 8.57/4.60      ! [R: num,M: num] :
% 8.57/4.60        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 8.57/4.60        = ( case_o6005452278849405969um_num @ none_num
% 8.57/4.60          @ ^ [Q6: num] : ( some_num @ ( bit0 @ Q6 ) )
% 8.57/4.60          @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5262_take__bit__num__simps_I1_J,axiom,
% 8.57/4.60      ! [M: num] :
% 8.57/4.60        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 8.57/4.60        = none_num ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5263_take__bit__num__simps_I3_J,axiom,
% 8.57/4.60      ! [N: nat,M: num] :
% 8.57/4.60        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 8.57/4.60        = ( case_o6005452278849405969um_num @ none_num
% 8.57/4.60          @ ^ [Q6: num] : ( some_num @ ( bit0 @ Q6 ) )
% 8.57/4.60          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5264_and__not__num__eq__None__iff,axiom,
% 8.57/4.60      ! [M: num,N: num] :
% 8.57/4.60        ( ( ( bit_and_not_num @ M @ N )
% 8.57/4.60          = none_num )
% 8.57/4.60        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 8.57/4.60          = zero_zero_int ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5265_take__bit__num__def,axiom,
% 8.57/4.60      ( bit_take_bit_num
% 8.57/4.60      = ( ^ [N3: nat,M2: num] :
% 8.57/4.60            ( if_option_num
% 8.57/4.60            @ ( ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M2 ) )
% 8.57/4.60              = zero_zero_nat )
% 8.57/4.60            @ none_num
% 8.57/4.60            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M2 ) ) ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5266_and__not__num_Oelims,axiom,
% 8.57/4.60      ! [X2: num,Xa: num,Y: option_num] :
% 8.57/4.60        ( ( ( bit_and_not_num @ X2 @ Xa )
% 8.57/4.60          = Y )
% 8.57/4.60       => ( ( ( X2 = one )
% 8.57/4.60           => ( ( Xa = one )
% 8.57/4.60             => ( Y != none_num ) ) )
% 8.57/4.60         => ( ( ( X2 = one )
% 8.57/4.60             => ( ? [N2: num] :
% 8.57/4.60                    ( Xa
% 8.57/4.60                    = ( bit0 @ N2 ) )
% 8.57/4.60               => ( Y
% 8.57/4.60                 != ( some_num @ one ) ) ) )
% 8.57/4.60           => ( ( ( X2 = one )
% 8.57/4.60               => ( ? [N2: num] :
% 8.57/4.60                      ( Xa
% 8.57/4.60                      = ( bit1 @ N2 ) )
% 8.57/4.60                 => ( Y != none_num ) ) )
% 8.57/4.60             => ( ! [M4: num] :
% 8.57/4.60                    ( ( X2
% 8.57/4.60                      = ( bit0 @ M4 ) )
% 8.57/4.60                   => ( ( Xa = one )
% 8.57/4.60                     => ( Y
% 8.57/4.60                       != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 8.57/4.60               => ( ! [M4: num] :
% 8.57/4.60                      ( ( X2
% 8.57/4.60                        = ( bit0 @ M4 ) )
% 8.57/4.60                     => ! [N2: num] :
% 8.57/4.60                          ( ( Xa
% 8.57/4.60                            = ( bit0 @ N2 ) )
% 8.57/4.60                         => ( Y
% 8.57/4.60                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 8.57/4.60                 => ( ! [M4: num] :
% 8.57/4.60                        ( ( X2
% 8.57/4.60                          = ( bit0 @ M4 ) )
% 8.57/4.60                       => ! [N2: num] :
% 8.57/4.60                            ( ( Xa
% 8.57/4.60                              = ( bit1 @ N2 ) )
% 8.57/4.60                           => ( Y
% 8.57/4.60                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 8.57/4.60                   => ( ! [M4: num] :
% 8.57/4.60                          ( ( X2
% 8.57/4.60                            = ( bit1 @ M4 ) )
% 8.57/4.60                         => ( ( Xa = one )
% 8.57/4.60                           => ( Y
% 8.57/4.60                             != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 8.57/4.60                     => ( ! [M4: num] :
% 8.57/4.60                            ( ( X2
% 8.57/4.60                              = ( bit1 @ M4 ) )
% 8.57/4.60                           => ! [N2: num] :
% 8.57/4.60                                ( ( Xa
% 8.57/4.60                                  = ( bit0 @ N2 ) )
% 8.57/4.60                               => ( Y
% 8.57/4.60                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 8.57/4.60                                    @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 8.57/4.60                                    @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 8.57/4.60                       => ~ ! [M4: num] :
% 8.57/4.60                              ( ( X2
% 8.57/4.60                                = ( bit1 @ M4 ) )
% 8.57/4.60                             => ! [N2: num] :
% 8.57/4.60                                  ( ( Xa
% 8.57/4.60                                    = ( bit1 @ N2 ) )
% 8.57/4.60                                 => ( Y
% 8.57/4.60                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5267_Gcd__int__def,axiom,
% 8.57/4.60      ( gcd_Gcd_int
% 8.57/4.60      = ( ^ [K6: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K6 ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5268_and__num_Oelims,axiom,
% 8.57/4.60      ! [X2: num,Xa: num,Y: option_num] :
% 8.57/4.60        ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa )
% 8.57/4.60          = Y )
% 8.57/4.60       => ( ( ( X2 = one )
% 8.57/4.60           => ( ( Xa = one )
% 8.57/4.60             => ( Y
% 8.57/4.60               != ( some_num @ one ) ) ) )
% 8.57/4.60         => ( ( ( X2 = one )
% 8.57/4.60             => ( ? [N2: num] :
% 8.57/4.60                    ( Xa
% 8.57/4.60                    = ( bit0 @ N2 ) )
% 8.57/4.60               => ( Y != none_num ) ) )
% 8.57/4.60           => ( ( ( X2 = one )
% 8.57/4.60               => ( ? [N2: num] :
% 8.57/4.60                      ( Xa
% 8.57/4.60                      = ( bit1 @ N2 ) )
% 8.57/4.60                 => ( Y
% 8.57/4.60                   != ( some_num @ one ) ) ) )
% 8.57/4.60             => ( ( ? [M4: num] :
% 8.57/4.60                      ( X2
% 8.57/4.60                      = ( bit0 @ M4 ) )
% 8.57/4.60                 => ( ( Xa = one )
% 8.57/4.60                   => ( Y != none_num ) ) )
% 8.57/4.60               => ( ! [M4: num] :
% 8.57/4.60                      ( ( X2
% 8.57/4.60                        = ( bit0 @ M4 ) )
% 8.57/4.60                     => ! [N2: num] :
% 8.57/4.60                          ( ( Xa
% 8.57/4.60                            = ( bit0 @ N2 ) )
% 8.57/4.60                         => ( Y
% 8.57/4.60                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 8.57/4.60                 => ( ! [M4: num] :
% 8.57/4.60                        ( ( X2
% 8.57/4.60                          = ( bit0 @ M4 ) )
% 8.57/4.60                       => ! [N2: num] :
% 8.57/4.60                            ( ( Xa
% 8.57/4.60                              = ( bit1 @ N2 ) )
% 8.57/4.60                           => ( Y
% 8.57/4.60                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 8.57/4.60                   => ( ( ? [M4: num] :
% 8.57/4.60                            ( X2
% 8.57/4.60                            = ( bit1 @ M4 ) )
% 8.57/4.60                       => ( ( Xa = one )
% 8.57/4.60                         => ( Y
% 8.57/4.60                           != ( some_num @ one ) ) ) )
% 8.57/4.60                     => ( ! [M4: num] :
% 8.57/4.60                            ( ( X2
% 8.57/4.60                              = ( bit1 @ M4 ) )
% 8.57/4.60                           => ! [N2: num] :
% 8.57/4.60                                ( ( Xa
% 8.57/4.60                                  = ( bit0 @ N2 ) )
% 8.57/4.60                               => ( Y
% 8.57/4.60                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 8.57/4.60                       => ~ ! [M4: num] :
% 8.57/4.60                              ( ( X2
% 8.57/4.60                                = ( bit1 @ M4 ) )
% 8.57/4.60                             => ! [N2: num] :
% 8.57/4.60                                  ( ( Xa
% 8.57/4.60                                    = ( bit1 @ N2 ) )
% 8.57/4.60                                 => ( Y
% 8.57/4.60                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 8.57/4.60                                      @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 8.57/4.60                                      @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.57/4.60  
% 8.57/4.60  thf(fact_5269_and__num_Osimps_I9_J,axiom,
% 8.57/4.60      ! [M: num,N: num] :
% 8.57/4.60        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.60/4.60        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 8.60/4.60          @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 8.60/4.60          @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5270_Code__Numeral_Onegative__def,axiom,
% 8.60/4.60      ( code_negative
% 8.60/4.60      = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5271_measure__function__int,axiom,
% 8.60/4.60      fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5272_nat__of__integer__code,axiom,
% 8.60/4.60      ( code_nat_of_integer
% 8.60/4.60      = ( ^ [K2: code_integer] :
% 8.60/4.60            ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 8.60/4.60            @ ( produc1555791787009142072er_nat
% 8.60/4.60              @ ^ [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 ) )
% 8.60/4.60              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5273_num__of__integer__code,axiom,
% 8.60/4.60      ( code_num_of_integer
% 8.60/4.60      = ( ^ [K2: code_integer] :
% 8.60/4.60            ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 8.60/4.60            @ ( produc7336495610019696514er_num
% 8.60/4.60              @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 8.60/4.60              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5274_int__of__integer__code,axiom,
% 8.60/4.60      ( code_int_of_integer
% 8.60/4.60      = ( ^ [K2: code_integer] :
% 8.60/4.60            ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 8.60/4.60            @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 8.60/4.60              @ ( produc1553301316500091796er_int
% 8.60/4.60                @ ^ [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 ) )
% 8.60/4.60                @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5275_int__of__integer__inverse,axiom,
% 8.60/4.60      ! [X2: code_integer] :
% 8.60/4.60        ( ( code_integer_of_int @ ( code_int_of_integer @ X2 ) )
% 8.60/4.60        = X2 ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5276_int__of__integer__integer__of__int,axiom,
% 8.60/4.60      ! [K: int] :
% 8.60/4.60        ( ( code_int_of_integer @ ( code_integer_of_int @ K ) )
% 8.60/4.60        = K ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5277_integer__of__int__int__of__integer,axiom,
% 8.60/4.60      ! [K: code_integer] :
% 8.60/4.60        ( ( code_integer_of_int @ ( code_int_of_integer @ K ) )
% 8.60/4.60        = K ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5278_int__of__integer__sub,axiom,
% 8.60/4.60      ! [K: num,L: num] :
% 8.60/4.60        ( ( code_int_of_integer @ ( neg_nu5755505904847501662nteger @ K @ L ) )
% 8.60/4.60        = ( neg_numeral_sub_int @ K @ L ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5279_of__int__integer__of,axiom,
% 8.60/4.60      ! [K: code_integer] :
% 8.60/4.60        ( ( ring_18347121197199848620nteger @ ( code_int_of_integer @ K ) )
% 8.60/4.60        = K ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5280_int__of__integer__of__int,axiom,
% 8.60/4.60      ! [K: int] :
% 8.60/4.60        ( ( code_int_of_integer @ ( ring_18347121197199848620nteger @ K ) )
% 8.60/4.60        = K ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5281_zero__integer_Orep__eq,axiom,
% 8.60/4.60      ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 8.60/4.60      = zero_zero_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5282_int__of__integer__numeral,axiom,
% 8.60/4.60      ! [K: num] :
% 8.60/4.60        ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 8.60/4.60        = ( numeral_numeral_int @ K ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5283_plus__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( plus_plus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5284_one__integer_Orep__eq,axiom,
% 8.60/4.60      ( ( code_int_of_integer @ one_one_Code_integer )
% 8.60/4.60      = one_one_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5285_uminus__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X2 ) )
% 8.60/4.60        = ( uminus_uminus_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5286_times__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( times_times_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5287_minus__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( minus_minus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5288_abs__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( abs_abs_Code_integer @ X2 ) )
% 8.60/4.60        = ( abs_abs_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5289_divide__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( divide_divide_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5290_modulo__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( modulo_modulo_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5291_int__of__integer__of__nat,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 8.60/4.60        = ( semiri1314217659103216013at_int @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5292_sgn__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( sgn_sgn_Code_integer @ X2 ) )
% 8.60/4.60        = ( sgn_sgn_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5293_int__of__integer__max,axiom,
% 8.60/4.60      ! [K: code_integer,L: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( ord_max_Code_integer @ K @ L ) )
% 8.60/4.60        = ( ord_max_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5294_integer__eq__iff,axiom,
% 8.60/4.60      ( ( ^ [Y3: code_integer,Z: code_integer] : ( Y3 = Z ) )
% 8.60/4.60      = ( ^ [K2: code_integer,L2: code_integer] :
% 8.60/4.60            ( ( code_int_of_integer @ K2 )
% 8.60/4.60            = ( code_int_of_integer @ L2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5295_integer__eqI,axiom,
% 8.60/4.60      ! [K: code_integer,L: code_integer] :
% 8.60/4.60        ( ( ( code_int_of_integer @ K )
% 8.60/4.60          = ( code_int_of_integer @ L ) )
% 8.60/4.60       => ( K = L ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5296_int__of__integer__inject,axiom,
% 8.60/4.60      ! [X2: code_integer,Y: code_integer] :
% 8.60/4.60        ( ( ( code_int_of_integer @ X2 )
% 8.60/4.60          = ( code_int_of_integer @ Y ) )
% 8.60/4.60        = ( X2 = Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5297_less__integer_Orep__eq,axiom,
% 8.60/4.60      ( ord_le6747313008572928689nteger
% 8.60/4.60      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5298_integer__less__iff,axiom,
% 8.60/4.60      ( ord_le6747313008572928689nteger
% 8.60/4.60      = ( ^ [K2: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5299_int__of__integer__less__iff,axiom,
% 8.60/4.60      ! [X2: code_integer,Y: code_integer] :
% 8.60/4.60        ( ( ord_less_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Y ) )
% 8.60/4.60        = ( ord_le6747313008572928689nteger @ X2 @ Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5300_less__eq__integer_Orep__eq,axiom,
% 8.60/4.60      ( ord_le3102999989581377725nteger
% 8.60/4.60      = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5301_integer__less__eq__iff,axiom,
% 8.60/4.60      ( ord_le3102999989581377725nteger
% 8.60/4.60      = ( ^ [K2: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5302_nat__of__integer_Orep__eq,axiom,
% 8.60/4.60      ( code_nat_of_integer
% 8.60/4.60      = ( ^ [X: code_integer] : ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5303_take__bit__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: nat,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se1745604003318907178nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( bit_se2923211474154528505it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5304_not__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_ri7632146776885996613nteger @ X2 ) )
% 8.60/4.60        = ( bit_ri7919022796975470100ot_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5305_and__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se3949692690581998587nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( bit_se725231765392027082nd_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5306_or__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se1080825931792720795nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( bit_se1409905431419307370or_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5307_bit__integer_Orep__eq,axiom,
% 8.60/4.60      ( bit_se9216721137139052372nteger
% 8.60/4.60      = ( ^ [X: code_integer] : ( bit_se1146084159140164899it_int @ ( code_int_of_integer @ X ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5308_xor__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se3222712562003087583nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( bit_se6526347334894502574or_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5309_push__bit__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: nat,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se7788150548672797655nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( bit_se545348938243370406it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5310_drop__bit__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: nat,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se3928097537394005634nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( bit_se8568078237143864401it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5311_mask__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: nat] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se2119862282449309892nteger @ X2 ) )
% 8.60/4.60        = ( bit_se2000444600071755411sk_int @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5312_unset__bit__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: nat,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se8260200283734997820nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( bit_se4203085406695923979it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5313_set__bit__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: nat,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se2793503036327961859nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( bit_se7879613467334960850it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5314_flip__bit__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: nat,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( bit_se1345352211410354436nteger @ X2 @ Xa ) )
% 8.60/4.60        = ( bit_se2159334234014336723it_int @ X2 @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5315_num__of__integer_Orep__eq,axiom,
% 8.60/4.60      ( code_num_of_integer
% 8.60/4.60      = ( ^ [X: code_integer] : ( num_of_nat @ ( nat2 @ ( code_int_of_integer @ X ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5316_int__ge__less__than__def,axiom,
% 8.60/4.60      ( int_ge_less_than
% 8.60/4.60      = ( ^ [D4: int] :
% 8.60/4.60            ( collec213857154873943460nt_int
% 8.60/4.60            @ ( produc4947309494688390418_int_o
% 8.60/4.60              @ ^ [Z7: int,Z3: int] :
% 8.60/4.60                  ( ( ord_less_eq_int @ D4 @ Z7 )
% 8.60/4.60                  & ( ord_less_int @ Z7 @ Z3 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5317_int__ge__less__than2__def,axiom,
% 8.60/4.60      ( int_ge_less_than2
% 8.60/4.60      = ( ^ [D4: int] :
% 8.60/4.60            ( collec213857154873943460nt_int
% 8.60/4.60            @ ( produc4947309494688390418_int_o
% 8.60/4.60              @ ^ [Z7: int,Z3: int] :
% 8.60/4.60                  ( ( ord_less_eq_int @ D4 @ Z3 )
% 8.60/4.60                  & ( ord_less_int @ Z7 @ Z3 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5318_Divides_Oadjust__div__def,axiom,
% 8.60/4.60      ( adjust_div
% 8.60/4.60      = ( produc8211389475949308722nt_int
% 8.60/4.60        @ ^ [Q6: int,R2: int] : ( plus_plus_int @ Q6 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5319_divmod__step__integer__def,axiom,
% 8.60/4.60      ( unique4921790084139445826nteger
% 8.60/4.60      = ( ^ [L2: num] :
% 8.60/4.60            ( produc6916734918728496179nteger
% 8.60/4.60            @ ^ [Q6: code_integer,R2: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ R2 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5320_divmod__integer__def,axiom,
% 8.60/4.60      ( code_divmod_integer
% 8.60/4.60      = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K2 @ L2 ) @ ( modulo364778990260209775nteger @ K2 @ L2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5321_Divides_Oadjust__div__eq,axiom,
% 8.60/4.60      ! [Q2: int,R: int] :
% 8.60/4.60        ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.60/4.60        = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5322_divmod__step__nat__def,axiom,
% 8.60/4.60      ( unique5026877609467782581ep_nat
% 8.60/4.60      = ( ^ [L2: num] :
% 8.60/4.60            ( produc2626176000494625587at_nat
% 8.60/4.60            @ ^ [Q6: nat,R2: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ R2 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5323_divmod__step__int__def,axiom,
% 8.60/4.60      ( unique5024387138958732305ep_int
% 8.60/4.60      = ( ^ [L2: num] :
% 8.60/4.60            ( produc4245557441103728435nt_int
% 8.60/4.60            @ ^ [Q6: int,R2: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ R2 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5324_take__bit__num__code,axiom,
% 8.60/4.60      ( bit_take_bit_num
% 8.60/4.60      = ( ^ [N3: nat,M2: num] :
% 8.60/4.60            ( produc478579273971653890on_num
% 8.60/4.60            @ ^ [A2: nat,X: num] :
% 8.60/4.60                ( case_nat_option_num @ none_num
% 8.60/4.60                @ ^ [O: nat] :
% 8.60/4.60                    ( case_num_option_num @ ( some_num @ one )
% 8.60/4.60                    @ ^ [P6: num] :
% 8.60/4.60                        ( case_o6005452278849405969um_num @ none_num
% 8.60/4.60                        @ ^ [Q6: num] : ( some_num @ ( bit0 @ Q6 ) )
% 8.60/4.60                        @ ( bit_take_bit_num @ O @ P6 ) )
% 8.60/4.60                    @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 8.60/4.60                    @ X )
% 8.60/4.60                @ A2 )
% 8.60/4.60            @ ( product_Pair_nat_num @ N3 @ M2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5325_minus__one__div__numeral,axiom,
% 8.60/4.60      ! [N: num] :
% 8.60/4.60        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 8.60/4.60        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5326_one__div__minus__numeral,axiom,
% 8.60/4.60      ! [N: num] :
% 8.60/4.60        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.60/4.60        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5327_divmod__BitM__2__eq,axiom,
% 8.60/4.60      ! [M: num] :
% 8.60/4.60        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 8.60/4.60        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5328_divmod__integer_H__def,axiom,
% 8.60/4.60      ( unique3479559517661332726nteger
% 8.60/4.60      = ( ^ [M2: num,N3: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N3 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N3 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5329_divmod__nat__if,axiom,
% 8.60/4.60      ( divmod_nat
% 8.60/4.60      = ( ^ [M2: nat,N3: nat] :
% 8.60/4.60            ( if_Pro6206227464963214023at_nat
% 8.60/4.60            @ ( ( N3 = zero_zero_nat )
% 8.60/4.60              | ( ord_less_nat @ M2 @ N3 ) )
% 8.60/4.60            @ ( product_Pair_nat_nat @ zero_zero_nat @ M2 )
% 8.60/4.60            @ ( produc2626176000494625587at_nat
% 8.60/4.60              @ ^ [Q6: nat] : ( product_Pair_nat_nat @ ( suc @ Q6 ) )
% 8.60/4.60              @ ( divmod_nat @ ( minus_minus_nat @ M2 @ N3 ) @ N3 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5330_neg__eucl__rel__int__mult__2,axiom,
% 8.60/4.60      ! [B: int,A: int,Q2: int,R: int] :
% 8.60/4.60        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.60/4.60       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.60/4.60         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5331_eucl__rel__int__by0,axiom,
% 8.60/4.60      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5332_eucl__rel__int__dividesI,axiom,
% 8.60/4.60      ! [L: int,K: int,Q2: int] :
% 8.60/4.60        ( ( L != zero_zero_int )
% 8.60/4.60       => ( ( K
% 8.60/4.60            = ( times_times_int @ Q2 @ L ) )
% 8.60/4.60         => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5333_zminus1__lemma,axiom,
% 8.60/4.60      ! [A: int,B: int,Q2: int,R: int] :
% 8.60/4.60        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.60/4.60       => ( ( B != zero_zero_int )
% 8.60/4.60         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5334_eucl__rel__int__iff,axiom,
% 8.60/4.60      ! [K: int,L: int,Q2: int,R: int] :
% 8.60/4.60        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.60/4.60        = ( ( K
% 8.60/4.60            = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R ) )
% 8.60/4.60          & ( ( ord_less_int @ zero_zero_int @ L )
% 8.60/4.60           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 8.60/4.60              & ( ord_less_int @ R @ L ) ) )
% 8.60/4.60          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 8.60/4.60           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 8.60/4.60               => ( ( ord_less_int @ L @ R )
% 8.60/4.60                  & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 8.60/4.60              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 8.60/4.60               => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5335_eucl__rel__int__remainderI,axiom,
% 8.60/4.60      ! [R: int,L: int,K: int,Q2: int] :
% 8.60/4.60        ( ( ( sgn_sgn_int @ R )
% 8.60/4.60          = ( sgn_sgn_int @ L ) )
% 8.60/4.60       => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L ) )
% 8.60/4.60         => ( ( K
% 8.60/4.60              = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R ) )
% 8.60/4.60           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5336_eucl__rel__int_Osimps,axiom,
% 8.60/4.60      ( eucl_rel_int
% 8.60/4.60      = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 8.60/4.60            ( ? [K2: int] :
% 8.60/4.60                ( ( A1 = K2 )
% 8.60/4.60                & ( A22 = zero_zero_int )
% 8.60/4.60                & ( A32
% 8.60/4.60                  = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 8.60/4.60            | ? [L2: int,K2: int,Q6: int] :
% 8.60/4.60                ( ( A1 = K2 )
% 8.60/4.60                & ( A22 = L2 )
% 8.60/4.60                & ( A32
% 8.60/4.60                  = ( product_Pair_int_int @ Q6 @ zero_zero_int ) )
% 8.60/4.60                & ( L2 != zero_zero_int )
% 8.60/4.60                & ( K2
% 8.60/4.60                  = ( times_times_int @ Q6 @ L2 ) ) )
% 8.60/4.60            | ? [R2: int,L2: int,K2: int,Q6: int] :
% 8.60/4.60                ( ( A1 = K2 )
% 8.60/4.60                & ( A22 = L2 )
% 8.60/4.60                & ( A32
% 8.60/4.60                  = ( product_Pair_int_int @ Q6 @ R2 ) )
% 8.60/4.60                & ( ( sgn_sgn_int @ R2 )
% 8.60/4.60                  = ( sgn_sgn_int @ L2 ) )
% 8.60/4.60                & ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L2 ) )
% 8.60/4.60                & ( K2
% 8.60/4.60                  = ( plus_plus_int @ ( times_times_int @ Q6 @ L2 ) @ R2 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5337_eucl__rel__int_Ocases,axiom,
% 8.60/4.60      ! [A12: int,A23: int,A33: product_prod_int_int] :
% 8.60/4.60        ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 8.60/4.60       => ( ( ( A23 = zero_zero_int )
% 8.60/4.60           => ( A33
% 8.60/4.60             != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 8.60/4.60         => ( ! [Q4: int] :
% 8.60/4.60                ( ( A33
% 8.60/4.60                  = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 8.60/4.60               => ( ( A23 != zero_zero_int )
% 8.60/4.60                 => ( A12
% 8.60/4.60                   != ( times_times_int @ Q4 @ A23 ) ) ) )
% 8.60/4.60           => ~ ! [R5: int,Q4: int] :
% 8.60/4.60                  ( ( A33
% 8.60/4.60                    = ( product_Pair_int_int @ Q4 @ R5 ) )
% 8.60/4.60                 => ( ( ( sgn_sgn_int @ R5 )
% 8.60/4.60                      = ( sgn_sgn_int @ A23 ) )
% 8.60/4.60                   => ( ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ A23 ) )
% 8.60/4.60                     => ( A12
% 8.60/4.60                       != ( plus_plus_int @ ( times_times_int @ Q4 @ A23 ) @ R5 ) ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5338_pos__eucl__rel__int__mult__2,axiom,
% 8.60/4.60      ! [B: int,A: int,Q2: int,R: int] :
% 8.60/4.60        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.60/4.60         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5339_and__int_Opsimps,axiom,
% 8.60/4.60      ! [K: int,L: int] :
% 8.60/4.60        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 8.60/4.60       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.60/4.60              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.60/4.60           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 8.60/4.60              = ( uminus_uminus_int
% 8.60/4.60                @ ( zero_n2684676970156552555ol_int
% 8.60/4.60                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 8.60/4.60                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 8.60/4.60          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.60/4.60                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.60/4.60           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 8.60/4.60              = ( plus_plus_int
% 8.60/4.60                @ ( zero_n2684676970156552555ol_int
% 8.60/4.60                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 8.60/4.60                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 8.60/4.60                @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5340_and__int_Opelims,axiom,
% 8.60/4.60      ! [X2: int,Xa: int,Y: int] :
% 8.60/4.60        ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa ) )
% 8.60/4.60         => ~ ( ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.60/4.60                    & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.60/4.60                 => ( Y
% 8.60/4.60                    = ( uminus_uminus_int
% 8.60/4.60                      @ ( zero_n2684676970156552555ol_int
% 8.60/4.60                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 8.60/4.60                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 8.60/4.60                & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.60/4.60                      & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.60/4.60                 => ( Y
% 8.60/4.60                    = ( plus_plus_int
% 8.60/4.60                      @ ( zero_n2684676970156552555ol_int
% 8.60/4.60                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 8.60/4.60                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 8.60/4.60                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 8.60/4.60             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5341_and__int_Opinduct,axiom,
% 8.60/4.60      ! [A0: int,A12: int,P: int > int > $o] :
% 8.60/4.60        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 8.60/4.60       => ( ! [K3: int,L3: int] :
% 8.60/4.60              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L3 ) )
% 8.60/4.60             => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.60/4.60                      & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.60/4.60                 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.60/4.60               => ( P @ K3 @ L3 ) ) )
% 8.60/4.60         => ( P @ A0 @ A12 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5342_upto_Opelims,axiom,
% 8.60/4.60      ! [X2: int,Xa: int,Y: list_int] :
% 8.60/4.60        ( ( ( upto @ X2 @ Xa )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa ) )
% 8.60/4.60         => ~ ( ( ( ( ord_less_eq_int @ X2 @ Xa )
% 8.60/4.60                 => ( Y
% 8.60/4.60                    = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa ) ) ) )
% 8.60/4.60                & ( ~ ( ord_less_eq_int @ X2 @ Xa )
% 8.60/4.60                 => ( Y = nil_int ) ) )
% 8.60/4.60             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5343_upto_Opsimps,axiom,
% 8.60/4.60      ! [I: int,J: int] :
% 8.60/4.60        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 8.60/4.60       => ( ( ( ord_less_eq_int @ I @ J )
% 8.60/4.60           => ( ( upto @ I @ J )
% 8.60/4.60              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 8.60/4.60          & ( ~ ( ord_less_eq_int @ I @ J )
% 8.60/4.60           => ( ( upto @ I @ J )
% 8.60/4.60              = nil_int ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5344_upto_Opinduct,axiom,
% 8.60/4.60      ! [A0: int,A12: int,P: int > int > $o] :
% 8.60/4.60        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 8.60/4.60       => ( ! [I3: int,J2: int] :
% 8.60/4.60              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 8.60/4.60             => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 8.60/4.60                 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 8.60/4.60               => ( P @ I3 @ J2 ) ) )
% 8.60/4.60         => ( P @ A0 @ A12 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5345_divmod__integer__eq__cases,axiom,
% 8.60/4.60      ( code_divmod_integer
% 8.60/4.60      = ( ^ [K2: code_integer,L2: code_integer] :
% 8.60/4.60            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 8.60/4.60            @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 8.60/4.60              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 8.60/4.60                @ ( if_Pro6119634080678213985nteger
% 8.60/4.60                  @ ( ( sgn_sgn_Code_integer @ K2 )
% 8.60/4.60                    = ( sgn_sgn_Code_integer @ L2 ) )
% 8.60/4.60                  @ ( code_divmod_abs @ K2 @ L2 )
% 8.60/4.60                  @ ( produc6916734918728496179nteger
% 8.60/4.60                    @ ^ [R2: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R2 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S4 ) ) )
% 8.60/4.60                    @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5346_divmod__abs__code_I6_J,axiom,
% 8.60/4.60      ! [J: code_integer] :
% 8.60/4.60        ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 8.60/4.60        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5347_divmod__abs__code_I5_J,axiom,
% 8.60/4.60      ! [J: code_integer] :
% 8.60/4.60        ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 8.60/4.60        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5348_divmod__integer__code,axiom,
% 8.60/4.60      ( code_divmod_integer
% 8.60/4.60      = ( ^ [K2: code_integer,L2: code_integer] :
% 8.60/4.60            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 8.60/4.60            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 8.60/4.60              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L2 )
% 8.60/4.60                @ ( produc6916734918728496179nteger
% 8.60/4.60                  @ ^ [R2: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R2 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S4 ) ) )
% 8.60/4.60                  @ ( code_divmod_abs @ K2 @ L2 ) ) )
% 8.60/4.60              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 8.60/4.60                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 8.60/4.60                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L2 )
% 8.60/4.60                    @ ( produc6916734918728496179nteger
% 8.60/4.60                      @ ^ [R2: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R2 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S4 ) ) )
% 8.60/4.60                      @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5349_divmod__abs__def,axiom,
% 8.60/4.60      ( code_divmod_abs
% 8.60/4.60      = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5350_bit__cut__integer__code,axiom,
% 8.60/4.60      ( code_bit_cut_integer
% 8.60/4.60      = ( ^ [K2: code_integer] :
% 8.60/4.60            ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 8.60/4.60            @ ( produc9125791028180074456eger_o
% 8.60/4.60              @ ^ [R2: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R2 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R2 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 8.60/4.60              @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5351_normalize__negative,axiom,
% 8.60/4.60      ! [Q2: int,P3: int] :
% 8.60/4.60        ( ( ord_less_int @ Q2 @ zero_zero_int )
% 8.60/4.60       => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q2 ) )
% 8.60/4.60          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P3 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5352_bit__cut__integer__def,axiom,
% 8.60/4.60      ( code_bit_cut_integer
% 8.60/4.60      = ( ^ [K2: code_integer] :
% 8.60/4.60            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.60/4.60            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5353_normalize__denom__zero,axiom,
% 8.60/4.60      ! [P3: int] :
% 8.60/4.60        ( ( normalize @ ( product_Pair_int_int @ P3 @ zero_zero_int ) )
% 8.60/4.60        = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5354_normalize__denom__pos,axiom,
% 8.60/4.60      ! [R: product_prod_int_int,P3: int,Q2: int] :
% 8.60/4.60        ( ( ( normalize @ R )
% 8.60/4.60          = ( product_Pair_int_int @ P3 @ Q2 ) )
% 8.60/4.60       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5355_normalize__crossproduct,axiom,
% 8.60/4.60      ! [Q2: int,S: int,P3: int,R: int] :
% 8.60/4.60        ( ( Q2 != zero_zero_int )
% 8.60/4.60       => ( ( S != zero_zero_int )
% 8.60/4.60         => ( ( ( normalize @ ( product_Pair_int_int @ P3 @ Q2 ) )
% 8.60/4.60              = ( normalize @ ( product_Pair_int_int @ R @ S ) ) )
% 8.60/4.60           => ( ( times_times_int @ P3 @ S )
% 8.60/4.60              = ( times_times_int @ R @ Q2 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5356_prod__decode__aux_Oelims,axiom,
% 8.60/4.60      ! [X2: nat,Xa: nat,Y: product_prod_nat_nat] :
% 8.60/4.60        ( ( ( nat_prod_decode_aux @ X2 @ Xa )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( ( ord_less_eq_nat @ Xa @ X2 )
% 8.60/4.60           => ( Y
% 8.60/4.60              = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X2 @ Xa ) ) ) )
% 8.60/4.60          & ( ~ ( ord_less_eq_nat @ Xa @ X2 )
% 8.60/4.60           => ( Y
% 8.60/4.60              = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa @ ( suc @ X2 ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5357_prod__decode__aux_Osimps,axiom,
% 8.60/4.60      ( nat_prod_decode_aux
% 8.60/4.60      = ( ^ [K2: nat,M2: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M2 @ K2 ) @ ( product_Pair_nat_nat @ M2 @ ( minus_minus_nat @ K2 @ M2 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M2 @ ( suc @ K2 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5358_bezw__0,axiom,
% 8.60/4.60      ! [X2: nat] :
% 8.60/4.60        ( ( bezw @ X2 @ zero_zero_nat )
% 8.60/4.60        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5359_times__int_Oabs__eq,axiom,
% 8.60/4.60      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 8.60/4.60        ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 8.60/4.60        = ( abs_Integ
% 8.60/4.60          @ ( produc27273713700761075at_nat
% 8.60/4.60            @ ^ [X: nat,Y4: nat] :
% 8.60/4.60                ( produc2626176000494625587at_nat
% 8.60/4.60                @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) )
% 8.60/4.60            @ Xa
% 8.60/4.60            @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5360_int_Oabs__induct,axiom,
% 8.60/4.60      ! [P: int > $o,X2: int] :
% 8.60/4.60        ( ! [Y2: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y2 ) )
% 8.60/4.60       => ( P @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5361_eq__Abs__Integ,axiom,
% 8.60/4.60      ! [Z2: int] :
% 8.60/4.60        ~ ! [X3: nat,Y2: nat] :
% 8.60/4.60            ( Z2
% 8.60/4.60           != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5362_nat_Oabs__eq,axiom,
% 8.60/4.60      ! [X2: product_prod_nat_nat] :
% 8.60/4.60        ( ( nat2 @ ( abs_Integ @ X2 ) )
% 8.60/4.60        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5363_zero__int__def,axiom,
% 8.60/4.60      ( zero_zero_int
% 8.60/4.60      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5364_int__def,axiom,
% 8.60/4.60      ( semiri1314217659103216013at_int
% 8.60/4.60      = ( ^ [N3: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N3 @ zero_zero_nat ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5365_uminus__int_Oabs__eq,axiom,
% 8.60/4.60      ! [X2: product_prod_nat_nat] :
% 8.60/4.60        ( ( uminus_uminus_int @ ( abs_Integ @ X2 ) )
% 8.60/4.60        = ( abs_Integ
% 8.60/4.60          @ ( produc2626176000494625587at_nat
% 8.60/4.60            @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X )
% 8.60/4.60            @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5366_one__int__def,axiom,
% 8.60/4.60      ( one_one_int
% 8.60/4.60      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5367_less__int_Oabs__eq,axiom,
% 8.60/4.60      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 8.60/4.60        ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 8.60/4.60        = ( produc8739625826339149834_nat_o
% 8.60/4.60          @ ^ [X: nat,Y4: nat] :
% 8.60/4.60              ( produc6081775807080527818_nat_o
% 8.60/4.60              @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) )
% 8.60/4.60          @ Xa
% 8.60/4.60          @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5368_less__eq__int_Oabs__eq,axiom,
% 8.60/4.60      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 8.60/4.60        ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 8.60/4.60        = ( produc8739625826339149834_nat_o
% 8.60/4.60          @ ^ [X: nat,Y4: nat] :
% 8.60/4.60              ( produc6081775807080527818_nat_o
% 8.60/4.60              @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) )
% 8.60/4.60          @ Xa
% 8.60/4.60          @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5369_plus__int_Oabs__eq,axiom,
% 8.60/4.60      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 8.60/4.60        ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 8.60/4.60        = ( abs_Integ
% 8.60/4.60          @ ( produc27273713700761075at_nat
% 8.60/4.60            @ ^ [X: nat,Y4: nat] :
% 8.60/4.60                ( produc2626176000494625587at_nat
% 8.60/4.60                @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) )
% 8.60/4.60            @ Xa
% 8.60/4.60            @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5370_minus__int_Oabs__eq,axiom,
% 8.60/4.60      ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 8.60/4.60        ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 8.60/4.60        = ( abs_Integ
% 8.60/4.60          @ ( produc27273713700761075at_nat
% 8.60/4.60            @ ^ [X: nat,Y4: nat] :
% 8.60/4.60                ( produc2626176000494625587at_nat
% 8.60/4.60                @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) )
% 8.60/4.60            @ Xa
% 8.60/4.60            @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5371_rat__minus__code,axiom,
% 8.60/4.60      ! [P3: rat,Q2: rat] :
% 8.60/4.60        ( ( quotient_of @ ( minus_minus_rat @ P3 @ Q2 ) )
% 8.60/4.60        = ( produc4245557441103728435nt_int
% 8.60/4.60          @ ^ [A2: int,C4: int] :
% 8.60/4.60              ( produc4245557441103728435nt_int
% 8.60/4.60              @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ B2 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 8.60/4.60              @ ( quotient_of @ Q2 ) )
% 8.60/4.60          @ ( quotient_of @ P3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5372_rat__plus__code,axiom,
% 8.60/4.60      ! [P3: rat,Q2: rat] :
% 8.60/4.60        ( ( quotient_of @ ( plus_plus_rat @ P3 @ Q2 ) )
% 8.60/4.60        = ( produc4245557441103728435nt_int
% 8.60/4.60          @ ^ [A2: int,C4: int] :
% 8.60/4.60              ( produc4245557441103728435nt_int
% 8.60/4.60              @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ B2 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 8.60/4.60              @ ( quotient_of @ Q2 ) )
% 8.60/4.60          @ ( quotient_of @ P3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5373_sort__upto,axiom,
% 8.60/4.60      ! [I: int,J: int] :
% 8.60/4.60        ( ( linord1735203802627413978nt_int
% 8.60/4.60          @ ^ [X: int] : X
% 8.60/4.60          @ ( upto @ I @ J ) )
% 8.60/4.60        = ( upto @ I @ J ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5374_rat__one__code,axiom,
% 8.60/4.60      ( ( quotient_of @ one_one_rat )
% 8.60/4.60      = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5375_rat__zero__code,axiom,
% 8.60/4.60      ( ( quotient_of @ zero_zero_rat )
% 8.60/4.60      = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5376_quotient__of__number_I3_J,axiom,
% 8.60/4.60      ! [K: num] :
% 8.60/4.60        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 8.60/4.60        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5377_quotient__of__number_I4_J,axiom,
% 8.60/4.60      ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.60/4.60      = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5378_quotient__of__number_I5_J,axiom,
% 8.60/4.60      ! [K: num] :
% 8.60/4.60        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 8.60/4.60        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5379_diff__rat__def,axiom,
% 8.60/4.60      ( minus_minus_rat
% 8.60/4.60      = ( ^ [Q6: rat,R2: rat] : ( plus_plus_rat @ Q6 @ ( uminus_uminus_rat @ R2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5380_quotient__of__denom__pos,axiom,
% 8.60/4.60      ! [R: rat,P3: int,Q2: int] :
% 8.60/4.60        ( ( ( quotient_of @ R )
% 8.60/4.60          = ( product_Pair_int_int @ P3 @ Q2 ) )
% 8.60/4.60       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5381_rat__floor__code,axiom,
% 8.60/4.60      ( archim3151403230148437115or_rat
% 8.60/4.60      = ( ^ [P6: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P6 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5382_rat__uminus__code,axiom,
% 8.60/4.60      ! [P3: rat] :
% 8.60/4.60        ( ( quotient_of @ ( uminus_uminus_rat @ P3 ) )
% 8.60/4.60        = ( produc4245557441103728435nt_int
% 8.60/4.60          @ ^ [A2: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A2 ) )
% 8.60/4.60          @ ( quotient_of @ P3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5383_rat__abs__code,axiom,
% 8.60/4.60      ! [P3: rat] :
% 8.60/4.60        ( ( quotient_of @ ( abs_abs_rat @ P3 ) )
% 8.60/4.60        = ( produc4245557441103728435nt_int
% 8.60/4.60          @ ^ [A2: int] : ( product_Pair_int_int @ ( abs_abs_int @ A2 ) )
% 8.60/4.60          @ ( quotient_of @ P3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5384_rat__less__eq__code,axiom,
% 8.60/4.60      ( ord_less_eq_rat
% 8.60/4.60      = ( ^ [P6: rat,Q6: rat] :
% 8.60/4.60            ( produc4947309494688390418_int_o
% 8.60/4.60            @ ^ [A2: int,C4: int] :
% 8.60/4.60                ( produc4947309494688390418_int_o
% 8.60/4.60                @ ^ [B2: int,D4: int] : ( ord_less_eq_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ C4 @ B2 ) )
% 8.60/4.60                @ ( quotient_of @ Q6 ) )
% 8.60/4.60            @ ( quotient_of @ P6 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5385_rat__less__code,axiom,
% 8.60/4.60      ( ord_less_rat
% 8.60/4.60      = ( ^ [P6: rat,Q6: rat] :
% 8.60/4.60            ( produc4947309494688390418_int_o
% 8.60/4.60            @ ^ [A2: int,C4: int] :
% 8.60/4.60                ( produc4947309494688390418_int_o
% 8.60/4.60                @ ^ [B2: int,D4: int] : ( ord_less_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ C4 @ B2 ) )
% 8.60/4.60                @ ( quotient_of @ Q6 ) )
% 8.60/4.60            @ ( quotient_of @ P6 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5386_rat__divide__code,axiom,
% 8.60/4.60      ! [P3: rat,Q2: rat] :
% 8.60/4.60        ( ( quotient_of @ ( divide_divide_rat @ P3 @ Q2 ) )
% 8.60/4.60        = ( produc4245557441103728435nt_int
% 8.60/4.60          @ ^ [A2: int,C4: int] :
% 8.60/4.60              ( produc4245557441103728435nt_int
% 8.60/4.60              @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A2 @ D4 ) @ ( times_times_int @ C4 @ B2 ) ) )
% 8.60/4.60              @ ( quotient_of @ Q2 ) )
% 8.60/4.60          @ ( quotient_of @ P3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5387_rat__times__code,axiom,
% 8.60/4.60      ! [P3: rat,Q2: rat] :
% 8.60/4.60        ( ( quotient_of @ ( times_times_rat @ P3 @ Q2 ) )
% 8.60/4.60        = ( produc4245557441103728435nt_int
% 8.60/4.60          @ ^ [A2: int,C4: int] :
% 8.60/4.60              ( produc4245557441103728435nt_int
% 8.60/4.60              @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ C4 @ D4 ) ) )
% 8.60/4.60              @ ( quotient_of @ Q2 ) )
% 8.60/4.60          @ ( quotient_of @ P3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5388_quotient__of__int,axiom,
% 8.60/4.60      ! [A: int] :
% 8.60/4.60        ( ( quotient_of @ ( of_int @ A ) )
% 8.60/4.60        = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5389_rat__inverse__code,axiom,
% 8.60/4.60      ! [P3: rat] :
% 8.60/4.60        ( ( quotient_of @ ( inverse_inverse_rat @ P3 ) )
% 8.60/4.60        = ( produc4245557441103728435nt_int
% 8.60/4.60          @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A2 ) @ B2 ) @ ( abs_abs_int @ A2 ) ) )
% 8.60/4.60          @ ( quotient_of @ P3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5390_sgn__rat__def,axiom,
% 8.60/4.60      ( sgn_sgn_rat
% 8.60/4.60      = ( ^ [A2: rat] : ( if_rat @ ( A2 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A2 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5391_Frct__code__post_I5_J,axiom,
% 8.60/4.60      ! [K: num] :
% 8.60/4.60        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 8.60/4.60        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5392_pow_Osimps_I1_J,axiom,
% 8.60/4.60      ! [X2: num] :
% 8.60/4.60        ( ( pow @ X2 @ one )
% 8.60/4.60        = X2 ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5393_Frct__code__post_I1_J,axiom,
% 8.60/4.60      ! [A: int] :
% 8.60/4.60        ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 8.60/4.60        = zero_zero_rat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5394_Frct__code__post_I2_J,axiom,
% 8.60/4.60      ! [A: int] :
% 8.60/4.60        ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 8.60/4.60        = zero_zero_rat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5395_Frct__code__post_I3_J,axiom,
% 8.60/4.60      ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 8.60/4.60      = one_one_rat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5396_Frct__code__post_I4_J,axiom,
% 8.60/4.60      ! [K: num] :
% 8.60/4.60        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 8.60/4.60        = ( numeral_numeral_rat @ K ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5397_less__eq__int_Orep__eq,axiom,
% 8.60/4.60      ( ord_less_eq_int
% 8.60/4.60      = ( ^ [X: int,Xa4: int] :
% 8.60/4.60            ( produc8739625826339149834_nat_o
% 8.60/4.60            @ ^ [Y4: nat,Z3: nat] :
% 8.60/4.60                ( produc6081775807080527818_nat_o
% 8.60/4.60                @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y4 @ V3 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 8.60/4.60            @ ( rep_Integ @ X )
% 8.60/4.60            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5398_nat_Orep__eq,axiom,
% 8.60/4.60      ( nat2
% 8.60/4.60      = ( ^ [X: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5399_less__int_Orep__eq,axiom,
% 8.60/4.60      ( ord_less_int
% 8.60/4.60      = ( ^ [X: int,Xa4: int] :
% 8.60/4.60            ( produc8739625826339149834_nat_o
% 8.60/4.60            @ ^ [Y4: nat,Z3: nat] :
% 8.60/4.60                ( produc6081775807080527818_nat_o
% 8.60/4.60                @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y4 @ V3 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 8.60/4.60            @ ( rep_Integ @ X )
% 8.60/4.60            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5400_sort__upt,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( linord738340561235409698at_nat
% 8.60/4.60          @ ^ [X: nat] : X
% 8.60/4.60          @ ( upt @ M @ N ) )
% 8.60/4.60        = ( upt @ M @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5401_upt__0__eq__Nil__conv,axiom,
% 8.60/4.60      ! [J: nat] :
% 8.60/4.60        ( ( ( upt @ zero_zero_nat @ J )
% 8.60/4.60          = nil_nat )
% 8.60/4.60        = ( J = zero_zero_nat ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5402_upt__merge,axiom,
% 8.60/4.60      ! [I: nat,J: nat,K: nat] :
% 8.60/4.60        ( ( ( ord_less_eq_nat @ I @ J )
% 8.60/4.60          & ( ord_less_eq_nat @ J @ K ) )
% 8.60/4.60       => ( ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ K ) )
% 8.60/4.60          = ( upt @ I @ K ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5403_upt__conv__Nil,axiom,
% 8.60/4.60      ! [J: nat,I: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ J @ I )
% 8.60/4.60       => ( ( upt @ I @ J )
% 8.60/4.60          = nil_nat ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5404_drop__upt,axiom,
% 8.60/4.60      ! [M: nat,I: nat,J: nat] :
% 8.60/4.60        ( ( drop_nat @ M @ ( upt @ I @ J ) )
% 8.60/4.60        = ( upt @ ( plus_plus_nat @ I @ M ) @ J ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5405_upt__eq__Nil__conv,axiom,
% 8.60/4.60      ! [I: nat,J: nat] :
% 8.60/4.60        ( ( ( upt @ I @ J )
% 8.60/4.60          = nil_nat )
% 8.60/4.60        = ( ( J = zero_zero_nat )
% 8.60/4.60          | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5406_take__upt,axiom,
% 8.60/4.60      ! [I: nat,M: nat,N: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 8.60/4.60       => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 8.60/4.60          = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5407_length__upt,axiom,
% 8.60/4.60      ! [I: nat,J: nat] :
% 8.60/4.60        ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 8.60/4.60        = ( minus_minus_nat @ J @ I ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5408_last__upt,axiom,
% 8.60/4.60      ! [I: nat,J: nat] :
% 8.60/4.60        ( ( ord_less_nat @ I @ J )
% 8.60/4.60       => ( ( last_nat @ ( upt @ I @ J ) )
% 8.60/4.60          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5409_nth__upt,axiom,
% 8.60/4.60      ! [I: nat,K: nat,J: nat] :
% 8.60/4.60        ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 8.60/4.60       => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 8.60/4.60          = ( plus_plus_nat @ I @ K ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5410_map__add__upt_H,axiom,
% 8.60/4.60      ! [Ofs: nat,A: nat,B: nat] :
% 8.60/4.60        ( ( map_nat_nat
% 8.60/4.60          @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ Ofs )
% 8.60/4.60          @ ( upt @ A @ B ) )
% 8.60/4.60        = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5411_upt__eq__append__conv,axiom,
% 8.60/4.60      ! [I: nat,J: nat,Xs: list_nat,Ys: list_nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ I @ J )
% 8.60/4.60       => ( ( ( upt @ I @ J )
% 8.60/4.60            = ( append_nat @ Xs @ Ys ) )
% 8.60/4.60          = ( ? [K2: nat] :
% 8.60/4.60                ( ( ord_less_eq_nat @ I @ K2 )
% 8.60/4.60                & ( ord_less_eq_nat @ K2 @ J )
% 8.60/4.60                & ( ( upt @ I @ K2 )
% 8.60/4.60                  = Xs )
% 8.60/4.60                & ( ( upt @ K2 @ J )
% 8.60/4.60                  = Ys ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5412_upt__0,axiom,
% 8.60/4.60      ! [I: nat] :
% 8.60/4.60        ( ( upt @ I @ zero_zero_nat )
% 8.60/4.60        = nil_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5413_upt__append,axiom,
% 8.60/4.60      ! [I: nat,J: nat] :
% 8.60/4.60        ( ( ord_less_nat @ I @ J )
% 8.60/4.60       => ( ( append_nat @ ( upt @ zero_zero_nat @ I ) @ ( upt @ I @ J ) )
% 8.60/4.60          = ( upt @ zero_zero_nat @ J ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5414_upt__add__eq__append,axiom,
% 8.60/4.60      ! [I: nat,J: nat,K: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ I @ J )
% 8.60/4.60       => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 8.60/4.60          = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5415_butlast__upt,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( butlast_nat @ ( upt @ M @ N ) )
% 8.60/4.60        = ( upt @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5416_atLeast__upt,axiom,
% 8.60/4.60      ( set_ord_lessThan_nat
% 8.60/4.60      = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N3 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5417_map__add__upt,axiom,
% 8.60/4.60      ! [N: nat,M: nat] :
% 8.60/4.60        ( ( map_nat_nat
% 8.60/4.60          @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ N )
% 8.60/4.60          @ ( upt @ zero_zero_nat @ M ) )
% 8.60/4.60        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5418_sorted__upt,axiom,
% 8.60/4.60      ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5419_atMost__upto,axiom,
% 8.60/4.60      ( set_ord_atMost_nat
% 8.60/4.60      = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N3 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5420_upt__Suc__append,axiom,
% 8.60/4.60      ! [I: nat,J: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ I @ J )
% 8.60/4.60       => ( ( upt @ I @ ( suc @ J ) )
% 8.60/4.60          = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5421_upt__Suc,axiom,
% 8.60/4.60      ! [I: nat,J: nat] :
% 8.60/4.60        ( ( ( ord_less_eq_nat @ I @ J )
% 8.60/4.60         => ( ( upt @ I @ ( suc @ J ) )
% 8.60/4.60            = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 8.60/4.60        & ( ~ ( ord_less_eq_nat @ I @ J )
% 8.60/4.60         => ( ( upt @ I @ ( suc @ J ) )
% 8.60/4.60            = nil_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5422_upt__filter__extend,axiom,
% 8.60/4.60      ! [U: nat,U3: nat,P: nat > $o] :
% 8.60/4.60        ( ( ord_less_eq_nat @ U @ U3 )
% 8.60/4.60       => ( ! [I3: nat] :
% 8.60/4.60              ( ( ( ord_less_eq_nat @ U @ I3 )
% 8.60/4.60                & ( ord_less_nat @ I3 @ U3 ) )
% 8.60/4.60             => ~ ( P @ I3 ) )
% 8.60/4.60         => ( ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U ) )
% 8.60/4.60            = ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U3 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5423_map__decr__upt,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( map_nat_nat
% 8.60/4.60          @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 8.60/4.60          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 8.60/4.60        = ( upt @ M @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5424_upt__eq__lel__conv,axiom,
% 8.60/4.60      ! [L: nat,H: nat,Is1: list_nat,I: nat,Is2: list_nat] :
% 8.60/4.60        ( ( ( upt @ L @ H )
% 8.60/4.60          = ( append_nat @ Is1 @ ( cons_nat @ I @ Is2 ) ) )
% 8.60/4.60        = ( ( Is1
% 8.60/4.60            = ( upt @ L @ I ) )
% 8.60/4.60          & ( Is2
% 8.60/4.60            = ( upt @ ( suc @ I ) @ H ) )
% 8.60/4.60          & ( ord_less_eq_nat @ L @ I )
% 8.60/4.60          & ( ord_less_nat @ I @ H ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5425_upt__eq__Cons__conv,axiom,
% 8.60/4.60      ! [I: nat,J: nat,X2: nat,Xs: list_nat] :
% 8.60/4.60        ( ( ( upt @ I @ J )
% 8.60/4.60          = ( cons_nat @ X2 @ Xs ) )
% 8.60/4.60        = ( ( ord_less_nat @ I @ J )
% 8.60/4.60          & ( I = X2 )
% 8.60/4.60          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 8.60/4.60            = Xs ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5426_sum__list__upt,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ M @ N )
% 8.60/4.60       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 8.60/4.60          = ( groups3542108847815614940at_nat
% 8.60/4.60            @ ^ [X: nat] : X
% 8.60/4.60            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5427_card__length__sum__list__rec,axiom,
% 8.60/4.60      ! [M: nat,N4: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 8.60/4.60       => ( ( finite_card_list_nat
% 8.60/4.60            @ ( collect_list_nat
% 8.60/4.60              @ ^ [L2: list_nat] :
% 8.60/4.60                  ( ( ( size_size_list_nat @ L2 )
% 8.60/4.60                    = M )
% 8.60/4.60                  & ( ( groups4561878855575611511st_nat @ L2 )
% 8.60/4.60                    = N4 ) ) ) )
% 8.60/4.60          = ( plus_plus_nat
% 8.60/4.60            @ ( finite_card_list_nat
% 8.60/4.60              @ ( collect_list_nat
% 8.60/4.60                @ ^ [L2: list_nat] :
% 8.60/4.60                    ( ( ( size_size_list_nat @ L2 )
% 8.60/4.60                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 8.60/4.60                    & ( ( groups4561878855575611511st_nat @ L2 )
% 8.60/4.60                      = N4 ) ) ) )
% 8.60/4.60            @ ( finite_card_list_nat
% 8.60/4.60              @ ( collect_list_nat
% 8.60/4.60                @ ^ [L2: list_nat] :
% 8.60/4.60                    ( ( ( size_size_list_nat @ L2 )
% 8.60/4.60                      = M )
% 8.60/4.60                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 8.60/4.60                      = N4 ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5428_card__length__sum__list,axiom,
% 8.60/4.60      ! [M: nat,N4: nat] :
% 8.60/4.60        ( ( finite_card_list_nat
% 8.60/4.60          @ ( collect_list_nat
% 8.60/4.60            @ ^ [L2: list_nat] :
% 8.60/4.60                ( ( ( size_size_list_nat @ L2 )
% 8.60/4.60                  = M )
% 8.60/4.60                & ( ( groups4561878855575611511st_nat @ L2 )
% 8.60/4.60                  = N4 ) ) ) )
% 8.60/4.60        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5429_floor__rat__def,axiom,
% 8.60/4.60      ( archim3151403230148437115or_rat
% 8.60/4.60      = ( ^ [X: rat] :
% 8.60/4.60            ( the_int
% 8.60/4.60            @ ^ [Z3: int] :
% 8.60/4.60                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 8.60/4.60                & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5430_uminus__int__def,axiom,
% 8.60/4.60      ( uminus_uminus_int
% 8.60/4.60      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 8.60/4.60        @ ( produc2626176000494625587at_nat
% 8.60/4.60          @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5431_times__int__def,axiom,
% 8.60/4.60      ( times_times_int
% 8.60/4.60      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 8.60/4.60        @ ( produc27273713700761075at_nat
% 8.60/4.60          @ ^ [X: nat,Y4: nat] :
% 8.60/4.60              ( produc2626176000494625587at_nat
% 8.60/4.60              @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5432_minus__int__def,axiom,
% 8.60/4.60      ( minus_minus_int
% 8.60/4.60      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 8.60/4.60        @ ( produc27273713700761075at_nat
% 8.60/4.60          @ ^ [X: nat,Y4: nat] :
% 8.60/4.60              ( produc2626176000494625587at_nat
% 8.60/4.60              @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5433_plus__int__def,axiom,
% 8.60/4.60      ( plus_plus_int
% 8.60/4.60      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 8.60/4.60        @ ( produc27273713700761075at_nat
% 8.60/4.60          @ ^ [X: nat,Y4: nat] :
% 8.60/4.60              ( produc2626176000494625587at_nat
% 8.60/4.60              @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5434_prod__encode__def,axiom,
% 8.60/4.60      ( nat_prod_encode
% 8.60/4.60      = ( produc6842872674320459806at_nat
% 8.60/4.60        @ ^ [M2: nat,N3: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M2 @ N3 ) ) @ M2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5435_le__prod__encode__1,axiom,
% 8.60/4.60      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5436_le__prod__encode__2,axiom,
% 8.60/4.60      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5437_prod__encode__prod__decode__aux,axiom,
% 8.60/4.60      ! [K: nat,M: nat] :
% 8.60/4.60        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 8.60/4.60        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5438_list__encode_Oelims,axiom,
% 8.60/4.60      ! [X2: list_nat,Y: nat] :
% 8.60/4.60        ( ( ( nat_list_encode @ X2 )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( ( X2 = nil_nat )
% 8.60/4.60           => ( Y != zero_zero_nat ) )
% 8.60/4.60         => ~ ! [X3: nat,Xs2: list_nat] :
% 8.60/4.60                ( ( X2
% 8.60/4.60                  = ( cons_nat @ X3 @ Xs2 ) )
% 8.60/4.60               => ( Y
% 8.60/4.60                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5439_list__encode_Opelims,axiom,
% 8.60/4.60      ! [X2: list_nat,Y: nat] :
% 8.60/4.60        ( ( ( nat_list_encode @ X2 )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( accp_list_nat @ nat_list_encode_rel @ X2 )
% 8.60/4.60         => ( ( ( X2 = nil_nat )
% 8.60/4.60             => ( ( Y = zero_zero_nat )
% 8.60/4.60               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 8.60/4.60           => ~ ! [X3: nat,Xs2: list_nat] :
% 8.60/4.60                  ( ( X2
% 8.60/4.60                    = ( cons_nat @ X3 @ Xs2 ) )
% 8.60/4.60                 => ( ( Y
% 8.60/4.60                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 8.60/4.60                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs2 ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5440_list__encode_Osimps_I1_J,axiom,
% 8.60/4.60      ( ( nat_list_encode @ nil_nat )
% 8.60/4.60      = zero_zero_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5441_rat__floor__lemma,axiom,
% 8.60/4.60      ! [A: int,B: int] :
% 8.60/4.60        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 8.60/4.60        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5442_less__rat,axiom,
% 8.60/4.60      ! [B: int,D: int,A: int,C: int] :
% 8.60/4.60        ( ( B != zero_zero_int )
% 8.60/4.60       => ( ( D != zero_zero_int )
% 8.60/4.60         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.60/4.60            = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5443_le__rat,axiom,
% 8.60/4.60      ! [B: int,D: int,A: int,C: int] :
% 8.60/4.60        ( ( B != zero_zero_int )
% 8.60/4.60       => ( ( D != zero_zero_int )
% 8.60/4.60         => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.60/4.60            = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5444_add__rat,axiom,
% 8.60/4.60      ! [B: int,D: int,A: int,C: int] :
% 8.60/4.60        ( ( B != zero_zero_int )
% 8.60/4.60       => ( ( D != zero_zero_int )
% 8.60/4.60         => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.60/4.60            = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5445_diff__rat,axiom,
% 8.60/4.60      ! [B: int,D: int,A: int,C: int] :
% 8.60/4.60        ( ( B != zero_zero_int )
% 8.60/4.60       => ( ( D != zero_zero_int )
% 8.60/4.60         => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.60/4.60            = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5446_eq__rat_I3_J,axiom,
% 8.60/4.60      ! [A: int,C: int] :
% 8.60/4.60        ( ( fract @ zero_zero_int @ A )
% 8.60/4.60        = ( fract @ zero_zero_int @ C ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5447_Rat__induct__pos,axiom,
% 8.60/4.60      ! [P: rat > $o,Q2: rat] :
% 8.60/4.60        ( ! [A3: int,B3: int] :
% 8.60/4.60            ( ( ord_less_int @ zero_zero_int @ B3 )
% 8.60/4.60           => ( P @ ( fract @ A3 @ B3 ) ) )
% 8.60/4.60       => ( P @ Q2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5448_eq__rat_I2_J,axiom,
% 8.60/4.60      ! [A: int] :
% 8.60/4.60        ( ( fract @ A @ zero_zero_int )
% 8.60/4.60        = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5449_mult__rat__cancel,axiom,
% 8.60/4.60      ! [C: int,A: int,B: int] :
% 8.60/4.60        ( ( C != zero_zero_int )
% 8.60/4.60       => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.60/4.60          = ( fract @ A @ B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5450_eq__rat_I1_J,axiom,
% 8.60/4.60      ! [B: int,D: int,A: int,C: int] :
% 8.60/4.60        ( ( B != zero_zero_int )
% 8.60/4.60       => ( ( D != zero_zero_int )
% 8.60/4.60         => ( ( ( fract @ A @ B )
% 8.60/4.60              = ( fract @ C @ D ) )
% 8.60/4.60            = ( ( times_times_int @ A @ D )
% 8.60/4.60              = ( times_times_int @ C @ B ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5451_Fract__of__nat__eq,axiom,
% 8.60/4.60      ! [K: nat] :
% 8.60/4.60        ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 8.60/4.60        = ( semiri681578069525770553at_rat @ K ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5452_rat__number__collapse_I1_J,axiom,
% 8.60/4.60      ! [K: int] :
% 8.60/4.60        ( ( fract @ zero_zero_int @ K )
% 8.60/4.60        = zero_zero_rat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5453_rat__number__collapse_I6_J,axiom,
% 8.60/4.60      ! [K: int] :
% 8.60/4.60        ( ( fract @ K @ zero_zero_int )
% 8.60/4.60        = zero_zero_rat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5454_One__rat__def,axiom,
% 8.60/4.60      ( one_one_rat
% 8.60/4.60      = ( fract @ one_one_int @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5455_Fract__of__int__eq,axiom,
% 8.60/4.60      ! [K: int] :
% 8.60/4.60        ( ( fract @ K @ one_one_int )
% 8.60/4.60        = ( ring_1_of_int_rat @ K ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5456_Zero__rat__def,axiom,
% 8.60/4.60      ( zero_zero_rat
% 8.60/4.60      = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5457_rat__number__expand_I3_J,axiom,
% 8.60/4.60      ( numeral_numeral_rat
% 8.60/4.60      = ( ^ [K2: num] : ( fract @ ( numeral_numeral_int @ K2 ) @ one_one_int ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5458_rat__number__collapse_I3_J,axiom,
% 8.60/4.60      ! [W2: num] :
% 8.60/4.60        ( ( fract @ ( numeral_numeral_int @ W2 ) @ one_one_int )
% 8.60/4.60        = ( numeral_numeral_rat @ W2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5459_zero__less__Fract__iff,axiom,
% 8.60/4.60      ! [B: int,A: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 8.60/4.60          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5460_Fract__less__zero__iff,axiom,
% 8.60/4.60      ! [B: int,A: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 8.60/4.60          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5461_Fract__less__one__iff,axiom,
% 8.60/4.60      ! [B: int,A: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 8.60/4.60          = ( ord_less_int @ A @ B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5462_one__less__Fract__iff,axiom,
% 8.60/4.60      ! [B: int,A: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 8.60/4.60          = ( ord_less_int @ B @ A ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5463_rat__number__collapse_I5_J,axiom,
% 8.60/4.60      ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 8.60/4.60      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5464_Fract__add__one,axiom,
% 8.60/4.60      ! [N: int,M: int] :
% 8.60/4.60        ( ( N != zero_zero_int )
% 8.60/4.60       => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 8.60/4.60          = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5465_Fract__le__zero__iff,axiom,
% 8.60/4.60      ! [B: int,A: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 8.60/4.60          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5466_zero__le__Fract__iff,axiom,
% 8.60/4.60      ! [B: int,A: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 8.60/4.60          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5467_Fract__le__one__iff,axiom,
% 8.60/4.60      ! [B: int,A: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 8.60/4.60          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5468_one__le__Fract__iff,axiom,
% 8.60/4.60      ! [B: int,A: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 8.60/4.60          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5469_rat__number__expand_I5_J,axiom,
% 8.60/4.60      ! [K: num] :
% 8.60/4.60        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 8.60/4.60        = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5470_rat__number__collapse_I4_J,axiom,
% 8.60/4.60      ! [W2: num] :
% 8.60/4.60        ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ one_one_int )
% 8.60/4.60        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5471_pow_Osimps_I3_J,axiom,
% 8.60/4.60      ! [X2: num,Y: num] :
% 8.60/4.60        ( ( pow @ X2 @ ( bit1 @ Y ) )
% 8.60/4.60        = ( times_times_num @ ( sqr @ ( pow @ X2 @ Y ) ) @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5472_of__nat__eq__id,axiom,
% 8.60/4.60      semiri1316708129612266289at_nat = id_nat ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5473_sqr_Osimps_I2_J,axiom,
% 8.60/4.60      ! [N: num] :
% 8.60/4.60        ( ( sqr @ ( bit0 @ N ) )
% 8.60/4.60        = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5474_sqr_Osimps_I1_J,axiom,
% 8.60/4.60      ( ( sqr @ one )
% 8.60/4.60      = one ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5475_less__int__def,axiom,
% 8.60/4.60      ( ord_less_int
% 8.60/4.60      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 8.60/4.60        @ ( produc8739625826339149834_nat_o
% 8.60/4.60          @ ^ [X: nat,Y4: nat] :
% 8.60/4.60              ( produc6081775807080527818_nat_o
% 8.60/4.60              @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5476_less__eq__int__def,axiom,
% 8.60/4.60      ( ord_less_eq_int
% 8.60/4.60      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 8.60/4.60        @ ( produc8739625826339149834_nat_o
% 8.60/4.60          @ ^ [X: nat,Y4: nat] :
% 8.60/4.60              ( produc6081775807080527818_nat_o
% 8.60/4.60              @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5477_sqr__conv__mult,axiom,
% 8.60/4.60      ( sqr
% 8.60/4.60      = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5478_nat__def,axiom,
% 8.60/4.60      ( nat2
% 8.60/4.60      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5479_pow_Osimps_I2_J,axiom,
% 8.60/4.60      ! [X2: num,Y: num] :
% 8.60/4.60        ( ( pow @ X2 @ ( bit0 @ Y ) )
% 8.60/4.60        = ( sqr @ ( pow @ X2 @ Y ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5480_sqr_Osimps_I3_J,axiom,
% 8.60/4.60      ! [N: num] :
% 8.60/4.60        ( ( sqr @ ( bit1 @ N ) )
% 8.60/4.60        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5481_positive__rat,axiom,
% 8.60/4.60      ! [A: int,B: int] :
% 8.60/4.60        ( ( positive @ ( fract @ A @ B ) )
% 8.60/4.60        = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5482_less__eq__integer__def,axiom,
% 8.60/4.60      ( ord_le3102999989581377725nteger
% 8.60/4.60      = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_eq_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5483_less__integer__def,axiom,
% 8.60/4.60      ( ord_le6747313008572928689nteger
% 8.60/4.60      = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5484_plus__integer__def,axiom,
% 8.60/4.60      ( plus_p5714425477246183910nteger
% 8.60/4.60      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ plus_plus_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5485_times__integer__def,axiom,
% 8.60/4.60      ( times_3573771949741848930nteger
% 8.60/4.60      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ times_times_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5486_minus__integer__def,axiom,
% 8.60/4.60      ( minus_8373710615458151222nteger
% 8.60/4.60      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ minus_minus_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5487_divide__integer__def,axiom,
% 8.60/4.60      ( divide6298287555418463151nteger
% 8.60/4.60      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ divide_divide_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5488_modulo__integer__def,axiom,
% 8.60/4.60      ( modulo364778990260209775nteger
% 8.60/4.60      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ modulo_modulo_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5489_positive__add,axiom,
% 8.60/4.60      ! [X2: rat,Y: rat] :
% 8.60/4.60        ( ( positive @ X2 )
% 8.60/4.60       => ( ( positive @ Y )
% 8.60/4.60         => ( positive @ ( plus_plus_rat @ X2 @ Y ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5490_and__integer__def,axiom,
% 8.60/4.60      ( bit_se3949692690581998587nteger
% 8.60/4.60      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se725231765392027082nd_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5491_or__integer__def,axiom,
% 8.60/4.60      ( bit_se1080825931792720795nteger
% 8.60/4.60      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se1409905431419307370or_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5492_take__bit__integer__def,axiom,
% 8.60/4.60      ( bit_se1745604003318907178nteger
% 8.60/4.60      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se2923211474154528505it_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5493_xor__integer__def,axiom,
% 8.60/4.60      ( bit_se3222712562003087583nteger
% 8.60/4.60      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se6526347334894502574or_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5494_drop__bit__integer__def,axiom,
% 8.60/4.60      ( bit_se3928097537394005634nteger
% 8.60/4.60      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se8568078237143864401it_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5495_push__bit__integer__def,axiom,
% 8.60/4.60      ( bit_se7788150548672797655nteger
% 8.60/4.60      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se545348938243370406it_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5496_unset__bit__integer__def,axiom,
% 8.60/4.60      ( bit_se8260200283734997820nteger
% 8.60/4.60      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se4203085406695923979it_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5497_set__bit__integer__def,axiom,
% 8.60/4.60      ( bit_se2793503036327961859nteger
% 8.60/4.60      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se7879613467334960850it_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5498_flip__bit__integer__def,axiom,
% 8.60/4.60      ( bit_se1345352211410354436nteger
% 8.60/4.60      = ( map_fu8224359078269604234nteger @ id_nat @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ bit_se2159334234014336723it_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5499_nat__of__integer__def,axiom,
% 8.60/4.60      ( code_nat_of_integer
% 8.60/4.60      = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ nat2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5500_bit__integer__def,axiom,
% 8.60/4.60      ( bit_se9216721137139052372nteger
% 8.60/4.60      = ( map_fu186220595405829473_nat_o @ code_int_of_integer @ id_nat_o @ bit_se1146084159140164899it_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5501_uminus__integer__def,axiom,
% 8.60/4.60      ( uminus1351360451143612070nteger
% 8.60/4.60      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ uminus_uminus_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5502_abs__integer__def,axiom,
% 8.60/4.60      ( abs_abs_Code_integer
% 8.60/4.60      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ abs_abs_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5503_mask__integer__def,axiom,
% 8.60/4.60      ( bit_se2119862282449309892nteger
% 8.60/4.60      = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ bit_se2000444600071755411sk_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5504_sgn__integer__def,axiom,
% 8.60/4.60      ( sgn_sgn_Code_integer
% 8.60/4.60      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ sgn_sgn_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5505_not__integer__def,axiom,
% 8.60/4.60      ( bit_ri7632146776885996613nteger
% 8.60/4.60      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ bit_ri7919022796975470100ot_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5506_num__of__integer__def,axiom,
% 8.60/4.60      ( code_num_of_integer
% 8.60/4.60      = ( map_fu1227494855608507351um_num @ code_int_of_integer @ id_num @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5507_min__0R,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( ord_min_nat @ N @ zero_zero_nat )
% 8.60/4.60        = zero_zero_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5508_min__0L,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( ord_min_nat @ zero_zero_nat @ N )
% 8.60/4.60        = zero_zero_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5509_min__Suc__Suc,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.60/4.60        = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5510_min__Suc__gt_I2_J,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( ord_less_nat @ A @ B )
% 8.60/4.60       => ( ( ord_min_nat @ B @ ( suc @ A ) )
% 8.60/4.60          = ( suc @ A ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5511_min__Suc__gt_I1_J,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( ord_less_nat @ A @ B )
% 8.60/4.60       => ( ( ord_min_nat @ ( suc @ A ) @ B )
% 8.60/4.60          = ( suc @ A ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5512_min__numeral__Suc,axiom,
% 8.60/4.60      ! [K: num,N: nat] :
% 8.60/4.60        ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.60/4.60        = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5513_min__Suc__numeral,axiom,
% 8.60/4.60      ! [N: nat,K: num] :
% 8.60/4.60        ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.60/4.60        = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5514_nat__mult__min__left,axiom,
% 8.60/4.60      ! [M: nat,N: nat,Q2: nat] :
% 8.60/4.60        ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 8.60/4.60        = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5515_nat__mult__min__right,axiom,
% 8.60/4.60      ! [M: nat,N: nat,Q2: nat] :
% 8.60/4.60        ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 8.60/4.60        = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5516_inf__nat__def,axiom,
% 8.60/4.60      inf_inf_nat = ord_min_nat ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5517_min__diff,axiom,
% 8.60/4.60      ! [M: nat,I: nat,N: nat] :
% 8.60/4.60        ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 8.60/4.60        = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5518_min__Suc1,axiom,
% 8.60/4.60      ! [N: nat,M: nat] :
% 8.60/4.60        ( ( ord_min_nat @ ( suc @ N ) @ M )
% 8.60/4.60        = ( case_nat_nat @ zero_zero_nat
% 8.60/4.60          @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ N @ M7 ) )
% 8.60/4.60          @ M ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5519_min__Suc2,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( ord_min_nat @ M @ ( suc @ N ) )
% 8.60/4.60        = ( case_nat_nat @ zero_zero_nat
% 8.60/4.60          @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ M7 @ N ) )
% 8.60/4.60          @ M ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5520_integer__of__nat__def,axiom,
% 8.60/4.60      ( code_integer_of_nat
% 8.60/4.60      = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5521_nat__of__integer__integer__of__nat,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( code_nat_of_integer @ ( code_integer_of_nat @ N ) )
% 8.60/4.60        = N ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5522_fst__divmod__integer,axiom,
% 8.60/4.60      ! [K: code_integer,L: code_integer] :
% 8.60/4.60        ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L ) )
% 8.60/4.60        = ( divide6298287555418463151nteger @ K @ L ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5523_int__of__integer__min,axiom,
% 8.60/4.60      ! [K: code_integer,L: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( ord_min_Code_integer @ K @ L ) )
% 8.60/4.60        = ( ord_min_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5524_int__of__integer__integer__of__nat,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( code_int_of_integer @ ( code_integer_of_nat @ N ) )
% 8.60/4.60        = ( semiri1314217659103216013at_int @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5525_integer__of__nat_Orep__eq,axiom,
% 8.60/4.60      ! [X2: nat] :
% 8.60/4.60        ( ( code_int_of_integer @ ( code_integer_of_nat @ X2 ) )
% 8.60/4.60        = ( semiri1314217659103216013at_int @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5526_fst__divmod__abs,axiom,
% 8.60/4.60      ! [K: code_integer,L: code_integer] :
% 8.60/4.60        ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L ) )
% 8.60/4.60        = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5527_Suc__0__div__numeral,axiom,
% 8.60/4.60      ! [K: num] :
% 8.60/4.60        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 8.60/4.60        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5528_inf__int__def,axiom,
% 8.60/4.60      inf_inf_int = ord_min_int ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5529_integer__of__nat__eq__of__nat,axiom,
% 8.60/4.60      code_integer_of_nat = semiri4939895301339042750nteger ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5530_integer__of__nat__0,axiom,
% 8.60/4.60      ( ( code_integer_of_nat @ zero_zero_nat )
% 8.60/4.60      = zero_z3403309356797280102nteger ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5531_integer__of__nat_Oabs__eq,axiom,
% 8.60/4.60      ( code_integer_of_nat
% 8.60/4.60      = ( ^ [X: nat] : ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5532_integer__of__nat__numeral,axiom,
% 8.60/4.60      ! [N: num] :
% 8.60/4.60        ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N ) )
% 8.60/4.60        = ( numera6620942414471956472nteger @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5533_integer__of__nat__1,axiom,
% 8.60/4.60      ( ( code_integer_of_nat @ one_one_nat )
% 8.60/4.60      = one_one_Code_integer ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5534_rat__sgn__code,axiom,
% 8.60/4.60      ! [P3: rat] :
% 8.60/4.60        ( ( quotient_of @ ( sgn_sgn_rat @ P3 ) )
% 8.60/4.60        = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P3 ) ) ) @ one_one_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5535_bezw_Oelims,axiom,
% 8.60/4.60      ! [X2: nat,Xa: nat,Y: product_prod_int_int] :
% 8.60/4.60        ( ( ( bezw @ X2 @ Xa )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( ( Xa = zero_zero_nat )
% 8.60/4.60           => ( Y
% 8.60/4.60              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 8.60/4.60          & ( ( Xa != zero_zero_nat )
% 8.60/4.60           => ( Y
% 8.60/4.60              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa ) ) ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5536_bezw_Osimps,axiom,
% 8.60/4.60      ( bezw
% 8.60/4.60      = ( ^ [X: nat,Y4: nat] : ( if_Pro3027730157355071871nt_int @ ( Y4 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y4 ) ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5537_quotient__of__denom__pos_H,axiom,
% 8.60/4.60      ! [R: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5538_bezw__non__0,axiom,
% 8.60/4.60      ! [Y: nat,X2: nat] :
% 8.60/4.60        ( ( ord_less_nat @ zero_zero_nat @ Y )
% 8.60/4.60       => ( ( bezw @ X2 @ Y )
% 8.60/4.60          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5539_minus__one__mod__numeral,axiom,
% 8.60/4.60      ! [N: num] :
% 8.60/4.60        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 8.60/4.60        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5540_one__mod__minus__numeral,axiom,
% 8.60/4.60      ! [N: num] :
% 8.60/4.60        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.60/4.60        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5541_snd__divmod__integer,axiom,
% 8.60/4.60      ! [K: code_integer,L: code_integer] :
% 8.60/4.60        ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 8.60/4.60        = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5542_snd__divmod__abs,axiom,
% 8.60/4.60      ! [K: code_integer,L: code_integer] :
% 8.60/4.60        ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 8.60/4.60        = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5543_Suc__0__mod__numeral,axiom,
% 8.60/4.60      ! [K: num] :
% 8.60/4.60        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 8.60/4.60        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5544_Divides_Oadjust__mod__def,axiom,
% 8.60/4.60      ( adjust_mod
% 8.60/4.60      = ( ^ [L2: int,R2: int] : ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5545_positive__def,axiom,
% 8.60/4.60      ( positive
% 8.60/4.60      = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 8.60/4.60        @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5546_bezw_Opelims,axiom,
% 8.60/4.60      ! [X2: nat,Xa: nat,Y: product_prod_int_int] :
% 8.60/4.60        ( ( ( bezw @ X2 @ Xa )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) )
% 8.60/4.60         => ~ ( ( ( ( Xa = zero_zero_nat )
% 8.60/4.60                 => ( Y
% 8.60/4.60                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 8.60/4.60                & ( ( Xa != zero_zero_nat )
% 8.60/4.60                 => ( Y
% 8.60/4.60                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa ) ) ) ) ) ) ) )
% 8.60/4.60             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5547_positive_Orep__eq,axiom,
% 8.60/4.60      ( positive
% 8.60/4.60      = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5548_prod__decode__aux_Opelims,axiom,
% 8.60/4.60      ! [X2: nat,Xa: nat,Y: product_prod_nat_nat] :
% 8.60/4.60        ( ( ( nat_prod_decode_aux @ X2 @ Xa )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) )
% 8.60/4.60         => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X2 )
% 8.60/4.60                 => ( Y
% 8.60/4.60                    = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X2 @ Xa ) ) ) )
% 8.60/4.60                & ( ~ ( ord_less_eq_nat @ Xa @ X2 )
% 8.60/4.60                 => ( Y
% 8.60/4.60                    = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa @ ( suc @ X2 ) ) ) ) ) )
% 8.60/4.60             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5549_plus__rat__def,axiom,
% 8.60/4.60      ( plus_plus_rat
% 8.60/4.60      = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 8.60/4.60        @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5550_inverse__rat__def,axiom,
% 8.60/4.60      ( inverse_inverse_rat
% 8.60/4.60      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 8.60/4.60        @ ^ [X: product_prod_int_int] :
% 8.60/4.60            ( if_Pro3027730157355071871nt_int
% 8.60/4.60            @ ( ( product_fst_int_int @ X )
% 8.60/4.60              = zero_zero_int )
% 8.60/4.60            @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 8.60/4.60            @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5551_one__rat__def,axiom,
% 8.60/4.60      ( one_one_rat
% 8.60/4.60      = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5552_Fract_Oabs__eq,axiom,
% 8.60/4.60      ( fract
% 8.60/4.60      = ( ^ [Xa4: int,X: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5553_zero__rat__def,axiom,
% 8.60/4.60      ( zero_zero_rat
% 8.60/4.60      = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5554_Fract__def,axiom,
% 8.60/4.60      ( fract
% 8.60/4.60      = ( map_fu7831380289885515383nt_rat @ id_int @ ( map_fu3424225382358772769nt_rat @ id_int @ abs_Rat )
% 8.60/4.60        @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5555_uminus__rat__def,axiom,
% 8.60/4.60      ( uminus_uminus_rat
% 8.60/4.60      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 8.60/4.60        @ ^ [X: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5556_times__rat__def,axiom,
% 8.60/4.60      ( times_times_rat
% 8.60/4.60      = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 8.60/4.60        @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5557_normalize__def,axiom,
% 8.60/4.60      ( normalize
% 8.60/4.60      = ( ^ [P6: product_prod_int_int] :
% 8.60/4.60            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P6 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) )
% 8.60/4.60            @ ( if_Pro3027730157355071871nt_int
% 8.60/4.60              @ ( ( product_snd_int_int @ P6 )
% 8.60/4.60                = zero_zero_int )
% 8.60/4.60              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 8.60/4.60              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5558_of__int__eq__id,axiom,
% 8.60/4.60      ring_1_of_int_int = id_int ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5559_gcd__1__int,axiom,
% 8.60/4.60      ! [M: int] :
% 8.60/4.60        ( ( gcd_gcd_int @ M @ one_one_int )
% 8.60/4.60        = one_one_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5560_gcd__neg1__int,axiom,
% 8.60/4.60      ! [X2: int,Y: int] :
% 8.60/4.60        ( ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ Y )
% 8.60/4.60        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5561_gcd__neg2__int,axiom,
% 8.60/4.60      ! [X2: int,Y: int] :
% 8.60/4.60        ( ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ Y ) )
% 8.60/4.60        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5562_gcd__abs2__int,axiom,
% 8.60/4.60      ! [X2: int,Y: int] :
% 8.60/4.60        ( ( gcd_gcd_int @ X2 @ ( abs_abs_int @ Y ) )
% 8.60/4.60        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5563_gcd__abs1__int,axiom,
% 8.60/4.60      ! [X2: int,Y: int] :
% 8.60/4.60        ( ( gcd_gcd_int @ ( abs_abs_int @ X2 ) @ Y )
% 8.60/4.60        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5564_abs__gcd__int,axiom,
% 8.60/4.60      ! [X2: int,Y: int] :
% 8.60/4.60        ( ( abs_abs_int @ ( gcd_gcd_int @ X2 @ Y ) )
% 8.60/4.60        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5565_gcd__pos__int,axiom,
% 8.60/4.60      ! [M: int,N: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 8.60/4.60        = ( ( M != zero_zero_int )
% 8.60/4.60          | ( N != zero_zero_int ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5566_gcd__neg__numeral__2__int,axiom,
% 8.60/4.60      ! [X2: int,N: num] :
% 8.60/4.60        ( ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.60/4.60        = ( gcd_gcd_int @ X2 @ ( numeral_numeral_int @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5567_gcd__neg__numeral__1__int,axiom,
% 8.60/4.60      ! [N: num,X2: int] :
% 8.60/4.60        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X2 )
% 8.60/4.60        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5568_gcd__0__int,axiom,
% 8.60/4.60      ! [X2: int] :
% 8.60/4.60        ( ( gcd_gcd_int @ X2 @ zero_zero_int )
% 8.60/4.60        = ( abs_abs_int @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5569_gcd__0__left__int,axiom,
% 8.60/4.60      ! [X2: int] :
% 8.60/4.60        ( ( gcd_gcd_int @ zero_zero_int @ X2 )
% 8.60/4.60        = ( abs_abs_int @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5570_gcd__proj2__if__dvd__int,axiom,
% 8.60/4.60      ! [Y: int,X2: int] :
% 8.60/4.60        ( ( dvd_dvd_int @ Y @ X2 )
% 8.60/4.60       => ( ( gcd_gcd_int @ X2 @ Y )
% 8.60/4.60          = ( abs_abs_int @ Y ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5571_gcd__proj1__if__dvd__int,axiom,
% 8.60/4.60      ! [X2: int,Y: int] :
% 8.60/4.60        ( ( dvd_dvd_int @ X2 @ Y )
% 8.60/4.60       => ( ( gcd_gcd_int @ X2 @ Y )
% 8.60/4.60          = ( abs_abs_int @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5572_gcd__idem__int,axiom,
% 8.60/4.60      ! [X2: int] :
% 8.60/4.60        ( ( gcd_gcd_int @ X2 @ X2 )
% 8.60/4.60        = ( abs_abs_int @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5573_gcd__red__int,axiom,
% 8.60/4.60      ( gcd_gcd_int
% 8.60/4.60      = ( ^ [X: int,Y4: int] : ( gcd_gcd_int @ Y4 @ ( modulo_modulo_int @ X @ Y4 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5574_gcd__ge__0__int,axiom,
% 8.60/4.60      ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X2 @ Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5575_bezout__int,axiom,
% 8.60/4.60      ! [X2: int,Y: int] :
% 8.60/4.60      ? [U4: int,V4: int] :
% 8.60/4.60        ( ( plus_plus_int @ ( times_times_int @ U4 @ X2 ) @ ( times_times_int @ V4 @ Y ) )
% 8.60/4.60        = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5576_gcd__mult__distrib__int,axiom,
% 8.60/4.60      ! [K: int,M: int,N: int] :
% 8.60/4.60        ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 8.60/4.60        = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5577_gcd__le2__int,axiom,
% 8.60/4.60      ! [B: int,A: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.60       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5578_gcd__le1__int,axiom,
% 8.60/4.60      ! [A: int,B: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.60       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5579_gcd__cases__int,axiom,
% 8.60/4.60      ! [X2: int,Y: int,P: int > $o] :
% 8.60/4.60        ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.60/4.60         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.60/4.60           => ( P @ ( gcd_gcd_int @ X2 @ Y ) ) ) )
% 8.60/4.60       => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 8.60/4.60           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 8.60/4.60             => ( P @ ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ Y ) ) ) ) )
% 8.60/4.60         => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 8.60/4.60             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.60/4.60               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ Y ) ) ) )
% 8.60/4.60           => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 8.60/4.60               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 8.60/4.60                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 8.60/4.60             => ( P @ ( gcd_gcd_int @ X2 @ Y ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5580_gcd__unique__int,axiom,
% 8.60/4.60      ! [D: int,A: int,B: int] :
% 8.60/4.60        ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 8.60/4.60          & ( dvd_dvd_int @ D @ A )
% 8.60/4.60          & ( dvd_dvd_int @ D @ B )
% 8.60/4.60          & ! [E4: int] :
% 8.60/4.60              ( ( ( dvd_dvd_int @ E4 @ A )
% 8.60/4.60                & ( dvd_dvd_int @ E4 @ B ) )
% 8.60/4.60             => ( dvd_dvd_int @ E4 @ D ) ) )
% 8.60/4.60        = ( D
% 8.60/4.60          = ( gcd_gcd_int @ A @ B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5581_gcd__non__0__int,axiom,
% 8.60/4.60      ! [Y: int,X2: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ Y )
% 8.60/4.60       => ( ( gcd_gcd_int @ X2 @ Y )
% 8.60/4.60          = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X2 @ Y ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5582_gcd__code__int,axiom,
% 8.60/4.60      ( gcd_gcd_int
% 8.60/4.60      = ( ^ [K2: int,L2: int] : ( abs_abs_int @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( gcd_gcd_int @ L2 @ ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5583_Code__Numeral_Odup__def,axiom,
% 8.60/4.60      ( code_dup
% 8.60/4.60      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int
% 8.60/4.60        @ ^ [K2: int] : ( plus_plus_int @ K2 @ K2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5584_gcd__nat_Oeq__neutr__iff,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( ( gcd_gcd_nat @ A @ B )
% 8.60/4.60          = zero_zero_nat )
% 8.60/4.60        = ( ( A = zero_zero_nat )
% 8.60/4.60          & ( B = zero_zero_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5585_gcd__nat_Oleft__neutral,axiom,
% 8.60/4.60      ! [A: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 8.60/4.60        = A ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5586_gcd__nat_Oneutr__eq__iff,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( zero_zero_nat
% 8.60/4.60          = ( gcd_gcd_nat @ A @ B ) )
% 8.60/4.60        = ( ( A = zero_zero_nat )
% 8.60/4.60          & ( B = zero_zero_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5587_gcd__nat_Oright__neutral,axiom,
% 8.60/4.60      ! [A: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 8.60/4.60        = A ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5588_gcd__0__nat,axiom,
% 8.60/4.60      ! [X2: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ X2 @ zero_zero_nat )
% 8.60/4.60        = X2 ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5589_gcd__0__left__nat,axiom,
% 8.60/4.60      ! [X2: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ zero_zero_nat @ X2 )
% 8.60/4.60        = X2 ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5590_gcd__1__nat,axiom,
% 8.60/4.60      ! [M: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 8.60/4.60        = one_one_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5591_gcd__nat_Oabsorb1,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ A @ B )
% 8.60/4.60       => ( ( gcd_gcd_nat @ A @ B )
% 8.60/4.60          = A ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5592_gcd__nat_Oabsorb2,axiom,
% 8.60/4.60      ! [B: nat,A: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ B @ A )
% 8.60/4.60       => ( ( gcd_gcd_nat @ A @ B )
% 8.60/4.60          = B ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5593_gcd__nat_Obounded__iff,axiom,
% 8.60/4.60      ! [A: nat,B: nat,C: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) )
% 8.60/4.60        = ( ( dvd_dvd_nat @ A @ B )
% 8.60/4.60          & ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5594_gcd__proj1__if__dvd__nat,axiom,
% 8.60/4.60      ! [X2: nat,Y: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ X2 @ Y )
% 8.60/4.60       => ( ( gcd_gcd_nat @ X2 @ Y )
% 8.60/4.60          = X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5595_gcd__proj2__if__dvd__nat,axiom,
% 8.60/4.60      ! [Y: nat,X2: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ Y @ X2 )
% 8.60/4.60       => ( ( gcd_gcd_nat @ X2 @ Y )
% 8.60/4.60          = Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5596_gcd__Suc__0,axiom,
% 8.60/4.60      ! [M: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 8.60/4.60        = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5597_gcd__pos__nat,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 8.60/4.60        = ( ( M != zero_zero_nat )
% 8.60/4.60          | ( N != zero_zero_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5598_gcd__int__int__eq,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.60/4.60        = ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ M @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5599_gcd__nat__abs__left__eq,axiom,
% 8.60/4.60      ! [K: int,N: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 8.60/4.60        = ( nat2 @ ( gcd_gcd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5600_gcd__nat__abs__right__eq,axiom,
% 8.60/4.60      ! [N: nat,K: int] :
% 8.60/4.60        ( ( gcd_gcd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 8.60/4.60        = ( nat2 @ ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5601_gcd__mult__distrib__nat,axiom,
% 8.60/4.60      ! [K: nat,M: nat,N: nat] :
% 8.60/4.60        ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 8.60/4.60        = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5602_gcd__nat_Omono,axiom,
% 8.60/4.60      ! [A: nat,C: nat,B: nat,D: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ A @ C )
% 8.60/4.60       => ( ( dvd_dvd_nat @ B @ D )
% 8.60/4.60         => ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ ( gcd_gcd_nat @ C @ D ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5603_gcd__nat_OorderE,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ A @ B )
% 8.60/4.60       => ( A
% 8.60/4.60          = ( gcd_gcd_nat @ A @ B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5604_gcd__nat_OorderI,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( A
% 8.60/4.60          = ( gcd_gcd_nat @ A @ B ) )
% 8.60/4.60       => ( dvd_dvd_nat @ A @ B ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5605_gcd__nat_Oabsorb3,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( ( dvd_dvd_nat @ A @ B )
% 8.60/4.60          & ( A != B ) )
% 8.60/4.60       => ( ( gcd_gcd_nat @ A @ B )
% 8.60/4.60          = A ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5606_gcd__nat_Oabsorb4,axiom,
% 8.60/4.60      ! [B: nat,A: nat] :
% 8.60/4.60        ( ( ( dvd_dvd_nat @ B @ A )
% 8.60/4.60          & ( B != A ) )
% 8.60/4.60       => ( ( gcd_gcd_nat @ A @ B )
% 8.60/4.60          = B ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5607_gcd__nat_OboundedE,axiom,
% 8.60/4.60      ! [A: nat,B: nat,C: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) )
% 8.60/4.60       => ~ ( ( dvd_dvd_nat @ A @ B )
% 8.60/4.60           => ~ ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5608_gcd__nat_OboundedI,axiom,
% 8.60/4.60      ! [A: nat,B: nat,C: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ A @ B )
% 8.60/4.60       => ( ( dvd_dvd_nat @ A @ C )
% 8.60/4.60         => ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5609_gcd__nat_Oorder__iff,axiom,
% 8.60/4.60      ( dvd_dvd_nat
% 8.60/4.60      = ( ^ [A2: nat,B2: nat] :
% 8.60/4.60            ( A2
% 8.60/4.60            = ( gcd_gcd_nat @ A2 @ B2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5610_gcd__nat_Ocobounded1,axiom,
% 8.60/4.60      ! [A: nat,B: nat] : ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5611_gcd__nat_Ocobounded2,axiom,
% 8.60/4.60      ! [A: nat,B: nat] : ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5612_gcd__nat_Oabsorb__iff1,axiom,
% 8.60/4.60      ( dvd_dvd_nat
% 8.60/4.60      = ( ^ [A2: nat,B2: nat] :
% 8.60/4.60            ( ( gcd_gcd_nat @ A2 @ B2 )
% 8.60/4.60            = A2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5613_gcd__nat_Oabsorb__iff2,axiom,
% 8.60/4.60      ( dvd_dvd_nat
% 8.60/4.60      = ( ^ [B2: nat,A2: nat] :
% 8.60/4.60            ( ( gcd_gcd_nat @ A2 @ B2 )
% 8.60/4.60            = B2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5614_gcd__nat_OcoboundedI1,axiom,
% 8.60/4.60      ! [A: nat,C: nat,B: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ A @ C )
% 8.60/4.60       => ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5615_gcd__nat_OcoboundedI2,axiom,
% 8.60/4.60      ! [B: nat,C: nat,A: nat] :
% 8.60/4.60        ( ( dvd_dvd_nat @ B @ C )
% 8.60/4.60       => ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5616_gcd__nat_Ostrict__boundedE,axiom,
% 8.60/4.60      ! [A: nat,B: nat,C: nat] :
% 8.60/4.60        ( ( ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) )
% 8.60/4.60          & ( A
% 8.60/4.60           != ( gcd_gcd_nat @ B @ C ) ) )
% 8.60/4.60       => ~ ( ( ( dvd_dvd_nat @ A @ B )
% 8.60/4.60              & ( A != B ) )
% 8.60/4.60           => ~ ( ( dvd_dvd_nat @ A @ C )
% 8.60/4.60                & ( A != C ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5617_gcd__nat_Ostrict__order__iff,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( ( dvd_dvd_nat @ A @ B )
% 8.60/4.60          & ( A != B ) )
% 8.60/4.60        = ( ( A
% 8.60/4.60            = ( gcd_gcd_nat @ A @ B ) )
% 8.60/4.60          & ( A != B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5618_gcd__nat_Ostrict__coboundedI1,axiom,
% 8.60/4.60      ! [A: nat,C: nat,B: nat] :
% 8.60/4.60        ( ( ( dvd_dvd_nat @ A @ C )
% 8.60/4.60          & ( A != C ) )
% 8.60/4.60       => ( ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C )
% 8.60/4.60          & ( ( gcd_gcd_nat @ A @ B )
% 8.60/4.60           != C ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5619_gcd__nat_Ostrict__coboundedI2,axiom,
% 8.60/4.60      ! [B: nat,C: nat,A: nat] :
% 8.60/4.60        ( ( ( dvd_dvd_nat @ B @ C )
% 8.60/4.60          & ( B != C ) )
% 8.60/4.60       => ( ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C )
% 8.60/4.60          & ( ( gcd_gcd_nat @ A @ B )
% 8.60/4.60           != C ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5620_gcd__unique__nat,axiom,
% 8.60/4.60      ! [D: nat,A: nat,B: nat] :
% 8.60/4.60        ( ( ( dvd_dvd_nat @ D @ A )
% 8.60/4.60          & ( dvd_dvd_nat @ D @ B )
% 8.60/4.60          & ! [E4: nat] :
% 8.60/4.60              ( ( ( dvd_dvd_nat @ E4 @ A )
% 8.60/4.60                & ( dvd_dvd_nat @ E4 @ B ) )
% 8.60/4.60             => ( dvd_dvd_nat @ E4 @ D ) ) )
% 8.60/4.60        = ( D
% 8.60/4.60          = ( gcd_gcd_nat @ A @ B ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5621_gcd__red__nat,axiom,
% 8.60/4.60      ( gcd_gcd_nat
% 8.60/4.60      = ( ^ [X: nat,Y4: nat] : ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5622_gcd__le1__nat,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( A != zero_zero_nat )
% 8.60/4.60       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5623_gcd__le2__nat,axiom,
% 8.60/4.60      ! [B: nat,A: nat] :
% 8.60/4.60        ( ( B != zero_zero_nat )
% 8.60/4.60       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5624_gcd__diff2__nat,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ M @ N )
% 8.60/4.60       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 8.60/4.60          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5625_gcd__diff1__nat,axiom,
% 8.60/4.60      ! [N: nat,M: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ N @ M )
% 8.60/4.60       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 8.60/4.60          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5626_gcd__non__0__nat,axiom,
% 8.60/4.60      ! [Y: nat,X2: nat] :
% 8.60/4.60        ( ( Y != zero_zero_nat )
% 8.60/4.60       => ( ( gcd_gcd_nat @ X2 @ Y )
% 8.60/4.60          = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5627_gcd__nat_Osimps,axiom,
% 8.60/4.60      ( gcd_gcd_nat
% 8.60/4.60      = ( ^ [X: nat,Y4: nat] : ( if_nat @ ( Y4 = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5628_gcd__nat_Oelims,axiom,
% 8.60/4.60      ! [X2: nat,Xa: nat,Y: nat] :
% 8.60/4.60        ( ( ( gcd_gcd_nat @ X2 @ Xa )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( ( Xa = zero_zero_nat )
% 8.60/4.60           => ( Y = X2 ) )
% 8.60/4.60          & ( ( Xa != zero_zero_nat )
% 8.60/4.60           => ( Y
% 8.60/4.60              = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5629_gcd__integer_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer,Xa: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( gcd_gcd_Code_integer @ X2 @ Xa ) )
% 8.60/4.60        = ( gcd_gcd_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5630_gcd__integer_Oabs__eq,axiom,
% 8.60/4.60      ! [Xa: int,X2: int] :
% 8.60/4.60        ( ( gcd_gcd_Code_integer @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 8.60/4.60        = ( code_integer_of_int @ ( gcd_gcd_int @ Xa @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5631_Code__Numeral_Odup__code_I1_J,axiom,
% 8.60/4.60      ( ( code_dup @ zero_z3403309356797280102nteger )
% 8.60/4.60      = zero_z3403309356797280102nteger ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5632_Gcd__in,axiom,
% 8.60/4.60      ! [A4: set_nat] :
% 8.60/4.60        ( ! [A3: nat,B3: nat] :
% 8.60/4.60            ( ( member_nat @ A3 @ A4 )
% 8.60/4.60           => ( ( member_nat @ B3 @ A4 )
% 8.60/4.60             => ( member_nat @ ( gcd_gcd_nat @ A3 @ B3 ) @ A4 ) ) )
% 8.60/4.60       => ( ( A4 != bot_bot_set_nat )
% 8.60/4.60         => ( member_nat @ ( gcd_Gcd_nat @ A4 ) @ A4 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5633_bezout__nat,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( A != zero_zero_nat )
% 8.60/4.60       => ? [X3: nat,Y2: nat] :
% 8.60/4.60            ( ( times_times_nat @ A @ X3 )
% 8.60/4.60            = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5634_bezout__gcd__nat_H,axiom,
% 8.60/4.60      ! [B: nat,A: nat] :
% 8.60/4.60      ? [X3: nat,Y2: nat] :
% 8.60/4.60        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y2 ) @ ( times_times_nat @ A @ X3 ) )
% 8.60/4.60          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y2 ) )
% 8.60/4.60            = ( gcd_gcd_nat @ A @ B ) ) )
% 8.60/4.60        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y2 ) @ ( times_times_nat @ B @ X3 ) )
% 8.60/4.60          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y2 ) )
% 8.60/4.60            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5635_gcd__code__integer,axiom,
% 8.60/4.60      ( gcd_gcd_Code_integer
% 8.60/4.60      = ( ^ [K2: code_integer,L2: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L2 = zero_z3403309356797280102nteger ) @ K2 @ ( gcd_gcd_Code_integer @ L2 @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5636_dup_Orep__eq,axiom,
% 8.60/4.60      ! [X2: code_integer] :
% 8.60/4.60        ( ( code_int_of_integer @ ( code_dup @ X2 ) )
% 8.60/4.60        = ( plus_plus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5637_dup_Oabs__eq,axiom,
% 8.60/4.60      ! [X2: int] :
% 8.60/4.60        ( ( code_dup @ ( code_integer_of_int @ X2 ) )
% 8.60/4.60        = ( code_integer_of_int @ ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5638_gcd__int__def,axiom,
% 8.60/4.60      ( gcd_gcd_int
% 8.60/4.60      = ( ^ [X: int,Y4: int] : ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ X ) ) @ ( nat2 @ ( abs_abs_int @ Y4 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5639_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 8.60/4.60      ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 8.60/4.60      @ ^ [M2: nat,N3: nat] :
% 8.60/4.60          ( ( dvd_dvd_nat @ M2 @ N3 )
% 8.60/4.60          & ( M2 != N3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5640_gcd__integer__def,axiom,
% 8.60/4.60      ( gcd_gcd_Code_integer
% 8.60/4.60      = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ gcd_gcd_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5641_bezw__aux,axiom,
% 8.60/4.60      ! [X2: nat,Y: nat] :
% 8.60/4.60        ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X2 @ Y ) )
% 8.60/4.60        = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X2 @ Y ) ) @ ( semiri1314217659103216013at_int @ X2 ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X2 @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5642_gcd__nat_Opelims,axiom,
% 8.60/4.60      ! [X2: nat,Xa: nat,Y: nat] :
% 8.60/4.60        ( ( ( gcd_gcd_nat @ X2 @ Xa )
% 8.60/4.60          = Y )
% 8.60/4.60       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) )
% 8.60/4.60         => ~ ( ( ( ( Xa = zero_zero_nat )
% 8.60/4.60                 => ( Y = X2 ) )
% 8.60/4.60                & ( ( Xa != zero_zero_nat )
% 8.60/4.60                 => ( Y
% 8.60/4.60                    = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) ) )
% 8.60/4.60             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5643_plus__rat_Oabs__eq,axiom,
% 8.60/4.60      ! [Xa: product_prod_int_int,X2: product_prod_int_int] :
% 8.60/4.60        ( ( ratrel @ Xa @ Xa )
% 8.60/4.60       => ( ( ratrel @ X2 @ X2 )
% 8.60/4.60         => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X2 ) )
% 8.60/4.60            = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X2 ) ) @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5644_gcd__idem__nat,axiom,
% 8.60/4.60      ! [X2: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ X2 @ X2 )
% 8.60/4.60        = X2 ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5645_gcd__nat_Oright__idem,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ ( gcd_gcd_nat @ A @ B ) @ B )
% 8.60/4.60        = ( gcd_gcd_nat @ A @ B ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5646_gcd__nat_Oleft__idem,axiom,
% 8.60/4.60      ! [A: nat,B: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ A @ ( gcd_gcd_nat @ A @ B ) )
% 8.60/4.60        = ( gcd_gcd_nat @ A @ B ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5647_gcd__nat_Oidem,axiom,
% 8.60/4.60      ! [A: nat] :
% 8.60/4.60        ( ( gcd_gcd_nat @ A @ A )
% 8.60/4.60        = A ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5648_ratrel__iff,axiom,
% 8.60/4.60      ( ratrel
% 8.60/4.60      = ( ^ [X: product_prod_int_int,Y4: product_prod_int_int] :
% 8.60/4.60            ( ( ( product_snd_int_int @ X )
% 8.60/4.60             != zero_zero_int )
% 8.60/4.60            & ( ( product_snd_int_int @ Y4 )
% 8.60/4.60             != zero_zero_int )
% 8.60/4.60            & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) )
% 8.60/4.60              = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5649_one__rat_Orsp,axiom,
% 8.60/4.60      ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5650_zero__rat_Orsp,axiom,
% 8.60/4.60      ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5651_ratrel__def,axiom,
% 8.60/4.60      ( ratrel
% 8.60/4.60      = ( ^ [X: product_prod_int_int,Y4: product_prod_int_int] :
% 8.60/4.60            ( ( ( product_snd_int_int @ X )
% 8.60/4.60             != zero_zero_int )
% 8.60/4.60            & ( ( product_snd_int_int @ Y4 )
% 8.60/4.60             != zero_zero_int )
% 8.60/4.60            & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) )
% 8.60/4.60              = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5652_positive_Oabs__eq,axiom,
% 8.60/4.60      ! [X2: product_prod_int_int] :
% 8.60/4.60        ( ( ratrel @ X2 @ X2 )
% 8.60/4.60       => ( ( positive @ ( abs_Rat @ X2 ) )
% 8.60/4.60          = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5653_inverse__rat_Oabs__eq,axiom,
% 8.60/4.60      ! [X2: product_prod_int_int] :
% 8.60/4.60        ( ( ratrel @ X2 @ X2 )
% 8.60/4.60       => ( ( inverse_inverse_rat @ ( abs_Rat @ X2 ) )
% 8.60/4.60          = ( abs_Rat
% 8.60/4.60            @ ( if_Pro3027730157355071871nt_int
% 8.60/4.60              @ ( ( product_fst_int_int @ X2 )
% 8.60/4.60                = zero_zero_int )
% 8.60/4.60              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 8.60/4.60              @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5654_Code__Numeral_Osub__code_I9_J,axiom,
% 8.60/4.60      ! [M: num,N: num] :
% 8.60/4.60        ( ( code_sub @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.60/4.60        = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5655_Code__Numeral_Osub__code_I8_J,axiom,
% 8.60/4.60      ! [M: num,N: num] :
% 8.60/4.60        ( ( code_sub @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.60/4.60        = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5656_Code__Numeral_Osub__code_I1_J,axiom,
% 8.60/4.60      ( ( code_sub @ one @ one )
% 8.60/4.60      = zero_z3403309356797280102nteger ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5657_Code__Numeral_Osub__code_I6_J,axiom,
% 8.60/4.60      ! [M: num,N: num] :
% 8.60/4.60        ( ( code_sub @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 8.60/4.60        = ( code_dup @ ( code_sub @ M @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5658_Code__Numeral_Osub__code_I7_J,axiom,
% 8.60/4.60      ! [M: num,N: num] :
% 8.60/4.60        ( ( code_sub @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.60/4.60        = ( code_dup @ ( code_sub @ M @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5659_sub_Orep__eq,axiom,
% 8.60/4.60      ! [X2: num,Xa: num] :
% 8.60/4.60        ( ( code_int_of_integer @ ( code_sub @ X2 @ Xa ) )
% 8.60/4.60        = ( minus_minus_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Xa ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5660_sub_Oabs__eq,axiom,
% 8.60/4.60      ( code_sub
% 8.60/4.60      = ( ^ [Xa4: num,X: num] : ( code_integer_of_int @ ( minus_minus_int @ ( numeral_numeral_int @ Xa4 ) @ ( numeral_numeral_int @ X ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5661_Code__Numeral_Osub__def,axiom,
% 8.60/4.60      ( code_sub
% 8.60/4.60      = ( map_fu6891787308814931657nteger @ id_num @ ( map_fu8638147718074629079nteger @ id_num @ code_integer_of_int )
% 8.60/4.60        @ ^ [M2: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5662_cr__rat__def,axiom,
% 8.60/4.60      ( cr_rat
% 8.60/4.60      = ( ^ [X: product_prod_int_int,Y4: rat] :
% 8.60/4.60            ( ( ratrel @ X @ X )
% 8.60/4.60            & ( ( abs_Rat @ X )
% 8.60/4.60              = Y4 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5663_card__UNIV__unit,axiom,
% 8.60/4.60      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 8.60/4.60      = one_one_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5664_infinite__UNIV__int,axiom,
% 8.60/4.60      ~ ( finite_finite_int @ top_top_set_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5665_integer__of__int__cases,axiom,
% 8.60/4.60      ! [X2: code_integer] :
% 8.60/4.60        ~ ! [Y2: int] :
% 8.60/4.60            ( ( X2
% 8.60/4.60              = ( code_integer_of_int @ Y2 ) )
% 8.60/4.60           => ~ ( member_int @ Y2 @ top_top_set_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5666_integer__of__int__induct,axiom,
% 8.60/4.60      ! [P: code_integer > $o,X2: code_integer] :
% 8.60/4.60        ( ! [Y2: int] :
% 8.60/4.60            ( ( member_int @ Y2 @ top_top_set_int )
% 8.60/4.60           => ( P @ ( code_integer_of_int @ Y2 ) ) )
% 8.60/4.60       => ( P @ X2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5667_integer__of__int__inject,axiom,
% 8.60/4.60      ! [X2: int,Y: int] :
% 8.60/4.60        ( ( member_int @ X2 @ top_top_set_int )
% 8.60/4.60       => ( ( member_int @ Y @ top_top_set_int )
% 8.60/4.60         => ( ( ( code_integer_of_int @ X2 )
% 8.60/4.60              = ( code_integer_of_int @ Y ) )
% 8.60/4.60            = ( X2 = Y ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5668_int__of__integer,axiom,
% 8.60/4.60      ! [X2: code_integer] : ( member_int @ ( code_int_of_integer @ X2 ) @ top_top_set_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5669_int__of__integer__cases,axiom,
% 8.60/4.60      ! [Y: int] :
% 8.60/4.60        ( ( member_int @ Y @ top_top_set_int )
% 8.60/4.60       => ~ ! [X3: code_integer] :
% 8.60/4.60              ( Y
% 8.60/4.60             != ( code_int_of_integer @ X3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5670_int__of__integer__induct,axiom,
% 8.60/4.60      ! [Y: int,P: int > $o] :
% 8.60/4.60        ( ( member_int @ Y @ top_top_set_int )
% 8.60/4.60       => ( ! [X3: code_integer] : ( P @ ( code_int_of_integer @ X3 ) )
% 8.60/4.60         => ( P @ Y ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5671_integer__of__int__inverse,axiom,
% 8.60/4.60      ! [Y: int] :
% 8.60/4.60        ( ( member_int @ Y @ top_top_set_int )
% 8.60/4.60       => ( ( code_int_of_integer @ ( code_integer_of_int @ Y ) )
% 8.60/4.60          = Y ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5672_int__in__range__abs,axiom,
% 8.60/4.60      ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5673_range__mod,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.60       => ( ( image_nat_nat
% 8.60/4.60            @ ^ [M2: nat] : ( modulo_modulo_nat @ M2 @ N )
% 8.60/4.60            @ top_top_set_nat )
% 8.60/4.60          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5674_UN__atMost__UNIV,axiom,
% 8.60/4.60      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 8.60/4.60      = top_top_set_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5675_UN__lessThan__UNIV,axiom,
% 8.60/4.60      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 8.60/4.60      = top_top_set_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5676_Sup__nat__empty,axiom,
% 8.60/4.60      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 8.60/4.60      = zero_zero_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5677_natLess__def,axiom,
% 8.60/4.60      ( bNF_Ca8459412986667044542atLess
% 8.60/4.60      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5678_Gcd__eq__Max,axiom,
% 8.60/4.60      ! [M3: set_nat] :
% 8.60/4.60        ( ( finite_finite_nat @ M3 )
% 8.60/4.60       => ( ( M3 != bot_bot_set_nat )
% 8.60/4.60         => ( ~ ( member_nat @ zero_zero_nat @ M3 )
% 8.60/4.60           => ( ( gcd_Gcd_nat @ M3 )
% 8.60/4.60              = ( lattic8265883725875713057ax_nat
% 8.60/4.60                @ ( comple7806235888213564991et_nat
% 8.60/4.60                  @ ( image_nat_set_nat
% 8.60/4.60                    @ ^ [M2: nat] :
% 8.60/4.60                        ( collect_nat
% 8.60/4.60                        @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M2 ) )
% 8.60/4.60                    @ M3 ) ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5679_Max__divisors__self__nat,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( N != zero_zero_nat )
% 8.60/4.60       => ( ( lattic8265883725875713057ax_nat
% 8.60/4.60            @ ( collect_nat
% 8.60/4.60              @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N ) ) )
% 8.60/4.60          = N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5680_Sup__nat__def,axiom,
% 8.60/4.60      ( complete_Sup_Sup_nat
% 8.60/4.60      = ( ^ [X5: set_nat] : ( if_nat @ ( X5 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X5 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5681_card__le__Suc__Max,axiom,
% 8.60/4.60      ! [S3: set_nat] :
% 8.60/4.60        ( ( finite_finite_nat @ S3 )
% 8.60/4.60       => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5682_divide__nat__def,axiom,
% 8.60/4.60      ( divide_divide_nat
% 8.60/4.60      = ( ^ [M2: nat,N3: nat] :
% 8.60/4.60            ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 8.60/4.60            @ ( lattic8265883725875713057ax_nat
% 8.60/4.60              @ ( collect_nat
% 8.60/4.60                @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N3 ) @ M2 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5683_gcd__is__Max__divisors__nat,axiom,
% 8.60/4.60      ! [N: nat,M: nat] :
% 8.60/4.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.60       => ( ( gcd_gcd_nat @ M @ N )
% 8.60/4.60          = ( lattic8265883725875713057ax_nat
% 8.60/4.60            @ ( collect_nat
% 8.60/4.60              @ ^ [D4: nat] :
% 8.60/4.60                  ( ( dvd_dvd_nat @ D4 @ M )
% 8.60/4.60                  & ( dvd_dvd_nat @ D4 @ N ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5684_Max__divisors__self__int,axiom,
% 8.60/4.60      ! [N: int] :
% 8.60/4.60        ( ( N != zero_zero_int )
% 8.60/4.60       => ( ( lattic8263393255366662781ax_int
% 8.60/4.60            @ ( collect_int
% 8.60/4.60              @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N ) ) )
% 8.60/4.60          = ( abs_abs_int @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5685_gcd__is__Max__divisors__int,axiom,
% 8.60/4.60      ! [N: int,M: int] :
% 8.60/4.60        ( ( N != zero_zero_int )
% 8.60/4.60       => ( ( gcd_gcd_int @ M @ N )
% 8.60/4.60          = ( lattic8263393255366662781ax_int
% 8.60/4.60            @ ( collect_int
% 8.60/4.60              @ ^ [D4: int] :
% 8.60/4.60                  ( ( dvd_dvd_int @ D4 @ M )
% 8.60/4.60                  & ( dvd_dvd_int @ D4 @ N ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5686_INT__greaterThan__UNIV,axiom,
% 8.60/4.60      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 8.60/4.60      = bot_bot_set_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5687_atLeastLessThan__add__Un,axiom,
% 8.60/4.60      ! [I: nat,J: nat,K: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ I @ J )
% 8.60/4.60       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 8.60/4.60          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5688_greaterThan__0,axiom,
% 8.60/4.60      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 8.60/4.60      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5689_greaterThan__Suc,axiom,
% 8.60/4.60      ! [K: nat] :
% 8.60/4.60        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 8.60/4.60        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5690_atLeast__0,axiom,
% 8.60/4.60      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 8.60/4.60      = top_top_set_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5691_sup__nat__def,axiom,
% 8.60/4.60      sup_sup_nat = ord_max_nat ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5692_sup__int__def,axiom,
% 8.60/4.60      sup_sup_int = ord_max_int ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5693_atLeast__Suc__greaterThan,axiom,
% 8.60/4.60      ! [K: nat] :
% 8.60/4.60        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 8.60/4.60        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5694_atLeast__Suc,axiom,
% 8.60/4.60      ! [K: nat] :
% 8.60/4.60        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 8.60/4.60        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5695_UN__atLeast__UNIV,axiom,
% 8.60/4.60      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 8.60/4.60      = top_top_set_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5696_range__abs__Nats,axiom,
% 8.60/4.60      ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 8.60/4.60      = semiring_1_Nats_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5697_binomial__def,axiom,
% 8.60/4.60      ( binomial
% 8.60/4.60      = ( ^ [N3: nat,K2: nat] :
% 8.60/4.60            ( finite_card_set_nat
% 8.60/4.60            @ ( collect_set_nat
% 8.60/4.60              @ ^ [K6: set_nat] :
% 8.60/4.60                  ( ( member_set_nat @ K6 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) )
% 8.60/4.60                  & ( ( finite_card_nat @ K6 )
% 8.60/4.60                    = K2 ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5698_pred__nat__def,axiom,
% 8.60/4.60      ( pred_nat
% 8.60/4.60      = ( collec3392354462482085612at_nat
% 8.60/4.60        @ ( produc6081775807080527818_nat_o
% 8.60/4.60          @ ^ [M2: nat,N3: nat] :
% 8.60/4.60              ( N3
% 8.60/4.60              = ( suc @ M2 ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5699_pred__nat__trancl__eq__le,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 8.60/4.60        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5700_vimage__Suc__insert__0,axiom,
% 8.60/4.60      ! [A4: set_nat] :
% 8.60/4.60        ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A4 ) )
% 8.60/4.60        = ( vimage_nat_nat @ suc @ A4 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5701_mono__Suc,axiom,
% 8.60/4.60      order_mono_nat_nat @ suc ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5702_mono__times__nat,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.60       => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5703_mono__ge2__power__minus__self,axiom,
% 8.60/4.60      ! [K: nat] :
% 8.60/4.60        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.60/4.60       => ( order_mono_nat_nat
% 8.60/4.60          @ ^ [M2: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ M2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5704_quotient__of__def,axiom,
% 8.60/4.60      ( quotient_of
% 8.60/4.60      = ( ^ [X: rat] :
% 8.60/4.60            ( the_Pr4378521158711661632nt_int
% 8.60/4.60            @ ^ [Pair: product_prod_int_int] :
% 8.60/4.60                ( ( X
% 8.60/4.60                  = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 8.60/4.60                & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 8.60/4.60                & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5705_normalize__stable,axiom,
% 8.60/4.60      ! [Q2: int,P3: int] :
% 8.60/4.60        ( ( ord_less_int @ zero_zero_int @ Q2 )
% 8.60/4.60       => ( ( algebr932160517623751201me_int @ P3 @ Q2 )
% 8.60/4.60         => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q2 ) )
% 8.60/4.60            = ( product_Pair_int_int @ P3 @ Q2 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5706_inj__on__diff__nat,axiom,
% 8.60/4.60      ! [N4: set_nat,K: nat] :
% 8.60/4.60        ( ! [N2: nat] :
% 8.60/4.60            ( ( member_nat @ N2 @ N4 )
% 8.60/4.60           => ( ord_less_eq_nat @ K @ N2 ) )
% 8.60/4.60       => ( inj_on_nat_nat
% 8.60/4.60          @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ K )
% 8.60/4.60          @ N4 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5707_coprime__crossproduct__int,axiom,
% 8.60/4.60      ! [A: int,D: int,B: int,C: int] :
% 8.60/4.60        ( ( algebr932160517623751201me_int @ A @ D )
% 8.60/4.60       => ( ( algebr932160517623751201me_int @ B @ C )
% 8.60/4.60         => ( ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ C ) )
% 8.60/4.60              = ( times_times_int @ ( abs_abs_int @ B ) @ ( abs_abs_int @ D ) ) )
% 8.60/4.60            = ( ( ( abs_abs_int @ A )
% 8.60/4.60                = ( abs_abs_int @ B ) )
% 8.60/4.60              & ( ( abs_abs_int @ C )
% 8.60/4.60                = ( abs_abs_int @ D ) ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5708_inj__Suc,axiom,
% 8.60/4.60      ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5709_Rat__cases,axiom,
% 8.60/4.60      ! [Q2: rat] :
% 8.60/4.60        ~ ! [A3: int,B3: int] :
% 8.60/4.60            ( ( Q2
% 8.60/4.60              = ( fract @ A3 @ B3 ) )
% 8.60/4.60           => ( ( ord_less_int @ zero_zero_int @ B3 )
% 8.60/4.60             => ~ ( algebr932160517623751201me_int @ A3 @ B3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5710_Rat__induct,axiom,
% 8.60/4.60      ! [P: rat > $o,Q2: rat] :
% 8.60/4.60        ( ! [A3: int,B3: int] :
% 8.60/4.60            ( ( ord_less_int @ zero_zero_int @ B3 )
% 8.60/4.60           => ( ( algebr932160517623751201me_int @ A3 @ B3 )
% 8.60/4.60             => ( P @ ( fract @ A3 @ B3 ) ) ) )
% 8.60/4.60       => ( P @ Q2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5711_coprime__common__divisor__int,axiom,
% 8.60/4.60      ! [A: int,B: int,X2: int] :
% 8.60/4.60        ( ( algebr932160517623751201me_int @ A @ B )
% 8.60/4.60       => ( ( dvd_dvd_int @ X2 @ A )
% 8.60/4.60         => ( ( dvd_dvd_int @ X2 @ B )
% 8.60/4.60           => ( ( abs_abs_int @ X2 )
% 8.60/4.60              = one_one_int ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5712_Rat__cases__nonzero,axiom,
% 8.60/4.60      ! [Q2: rat] :
% 8.60/4.60        ( ! [A3: int,B3: int] :
% 8.60/4.60            ( ( Q2
% 8.60/4.60              = ( fract @ A3 @ B3 ) )
% 8.60/4.60           => ( ( ord_less_int @ zero_zero_int @ B3 )
% 8.60/4.60             => ( ( A3 != zero_zero_int )
% 8.60/4.60               => ~ ( algebr932160517623751201me_int @ A3 @ B3 ) ) ) )
% 8.60/4.60       => ( Q2 = zero_zero_rat ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5713_quotient__of__unique,axiom,
% 8.60/4.60      ! [R: rat] :
% 8.60/4.60      ? [X3: product_prod_int_int] :
% 8.60/4.60        ( ( R
% 8.60/4.60          = ( fract @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 8.60/4.60        & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X3 ) )
% 8.60/4.60        & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) )
% 8.60/4.60        & ! [Y5: product_prod_int_int] :
% 8.60/4.60            ( ( ( R
% 8.60/4.60                = ( fract @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 8.60/4.60              & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y5 ) )
% 8.60/4.60              & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 8.60/4.60           => ( Y5 = X3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5714_coprime__int__iff,axiom,
% 8.60/4.60      ! [M: nat,N: nat] :
% 8.60/4.60        ( ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.60/4.60        = ( algebr934650988132801477me_nat @ M @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5715_coprime__nat__abs__left__iff,axiom,
% 8.60/4.60      ! [K: int,N: nat] :
% 8.60/4.60        ( ( algebr934650988132801477me_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 8.60/4.60        = ( algebr932160517623751201me_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5716_coprime__nat__abs__right__iff,axiom,
% 8.60/4.60      ! [N: nat,K: int] :
% 8.60/4.60        ( ( algebr934650988132801477me_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 8.60/4.60        = ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5717_coprime__common__divisor__nat,axiom,
% 8.60/4.60      ! [A: nat,B: nat,X2: nat] :
% 8.60/4.60        ( ( algebr934650988132801477me_nat @ A @ B )
% 8.60/4.60       => ( ( dvd_dvd_nat @ X2 @ A )
% 8.60/4.60         => ( ( dvd_dvd_nat @ X2 @ B )
% 8.60/4.60           => ( X2 = one_one_nat ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5718_coprime__Suc__right__nat,axiom,
% 8.60/4.60      ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5719_coprime__Suc__left__nat,axiom,
% 8.60/4.60      ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5720_coprime__crossproduct__nat,axiom,
% 8.60/4.60      ! [A: nat,D: nat,B: nat,C: nat] :
% 8.60/4.60        ( ( algebr934650988132801477me_nat @ A @ D )
% 8.60/4.60       => ( ( algebr934650988132801477me_nat @ B @ C )
% 8.60/4.60         => ( ( ( times_times_nat @ A @ C )
% 8.60/4.60              = ( times_times_nat @ B @ D ) )
% 8.60/4.60            = ( ( A = B )
% 8.60/4.60              & ( C = D ) ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5721_coprime__Suc__0__left,axiom,
% 8.60/4.60      ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5722_coprime__Suc__0__right,axiom,
% 8.60/4.60      ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5723_coprime__diff__one__left__nat,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.60       => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5724_coprime__diff__one__right__nat,axiom,
% 8.60/4.60      ! [N: nat] :
% 8.60/4.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.60       => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5725_positive_Orsp,axiom,
% 8.60/4.60      ( bNF_re8699439704749558557nt_o_o @ ratrel
% 8.60/4.60      @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 8.60/4.60      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 8.60/4.60      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5726_Fract_Orsp,axiom,
% 8.60/4.60      ( bNF_re157797125943740599nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re6250860962936578807nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ratrel )
% 8.60/4.60      @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) )
% 8.60/4.60      @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5727_less__eq__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re3403563459893282935_int_o
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5089333283451836215nt_o_o
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.60      @ ord_less_eq_int
% 8.60/4.60      @ ord_less_eq_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5728_less__eq__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re578469030762574527_nat_o
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4705727531993890431at_o_o
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.60      @ ord_less_eq_nat
% 8.60/4.60      @ ord_less_eq_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5729_uminus__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4712519889275205905nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ uminus_uminus_int
% 8.60/4.60      @ uminus_uminus_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5730_minus__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ minus_minus_nat
% 8.60/4.60      @ minus_minus_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5731_minus__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re711492959462206631nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ minus_minus_int
% 8.60/4.60      @ minus_minus_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5732_sub_Orsp,axiom,
% 8.60/4.60      ( bNF_re8402795839162346335um_int
% 8.60/4.60      @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re1822329894187522285nt_int
% 8.60/4.60        @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ ^ [M2: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N3 ) )
% 8.60/4.60      @ ^ [M2: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N3 ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5733_gcd__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re711492959462206631nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ gcd_gcd_int
% 8.60/4.60      @ gcd_gcd_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5734_integer__of__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re6650684261131312217nt_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ semiri1314217659103216013at_int
% 8.60/4.60      @ semiri1314217659103216013at_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5735_dup_Orsp,axiom,
% 8.60/4.60      ( bNF_re4712519889275205905nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ^ [K2: int] : ( plus_plus_int @ K2 @ K2 )
% 8.60/4.60      @ ^ [K2: int] : ( plus_plus_int @ K2 @ K2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5736_sgn__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4712519889275205905nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ sgn_sgn_int
% 8.60/4.60      @ sgn_sgn_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5737_plus__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ plus_plus_nat
% 8.60/4.60      @ plus_plus_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5738_plus__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re711492959462206631nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ plus_plus_int
% 8.60/4.60      @ plus_plus_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5739_bit__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re578469030762574527_nat_o
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: nat > $o,Z: nat > $o] : ( Y3 = Z )
% 8.60/4.60      @ bit_se1148574629649215175it_nat
% 8.60/4.60      @ bit_se1148574629649215175it_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5740_Suc_Orsp,axiom,
% 8.60/4.60      ( bNF_re5653821019739307937at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ suc
% 8.60/4.60      @ suc ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5741_natural__of__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re3715656647883201625at_nat
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ nat2
% 8.60/4.60      @ nat2 ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5742_not__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4712519889275205905nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ bit_ri7919022796975470100ot_int
% 8.60/4.60      @ bit_ri7919022796975470100ot_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5743_and__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se727722235901077358nd_nat
% 8.60/4.60      @ bit_se727722235901077358nd_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5744_and__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re711492959462206631nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se725231765392027082nd_int
% 8.60/4.60      @ bit_se725231765392027082nd_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5745_take__bit__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se2925701944663578781it_nat
% 8.60/4.60      @ bit_se2925701944663578781it_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5746_take__bit__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4785983289428654063nt_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se2923211474154528505it_int
% 8.60/4.60      @ bit_se2923211474154528505it_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5747_modulo__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ modulo_modulo_nat
% 8.60/4.60      @ modulo_modulo_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5748_modulo__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re711492959462206631nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ modulo_modulo_int
% 8.60/4.60      @ modulo_modulo_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5749_unset__bit__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se4205575877204974255it_nat
% 8.60/4.60      @ bit_se4205575877204974255it_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5750_unset__bit__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4785983289428654063nt_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se4203085406695923979it_int
% 8.60/4.60      @ bit_se4203085406695923979it_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5751_set__bit__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se7882103937844011126it_nat
% 8.60/4.60      @ bit_se7882103937844011126it_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5752_set__bit__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4785983289428654063nt_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se7879613467334960850it_int
% 8.60/4.60      @ bit_se7879613467334960850it_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5753_flip__bit__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4785983289428654063nt_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se2159334234014336723it_int
% 8.60/4.60      @ bit_se2159334234014336723it_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5754_flip__bit__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se2161824704523386999it_nat
% 8.60/4.60      @ bit_se2161824704523386999it_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5755_push__bit__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se547839408752420682it_nat
% 8.60/4.60      @ bit_se547839408752420682it_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5756_push__bit__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4785983289428654063nt_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se545348938243370406it_int
% 8.60/4.60      @ bit_se545348938243370406it_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5757_xor__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se6528837805403552850or_nat
% 8.60/4.60      @ bit_se6528837805403552850or_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5758_xor__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re711492959462206631nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se6526347334894502574or_int
% 8.60/4.60      @ bit_se6526347334894502574or_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5759_bit__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re3376528473927230327_nat_o
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: nat > $o,Z: nat > $o] : ( Y3 = Z )
% 8.60/4.60      @ bit_se1146084159140164899it_int
% 8.60/4.60      @ bit_se1146084159140164899it_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5760_or__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re711492959462206631nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se1409905431419307370or_int
% 8.60/4.60      @ bit_se1409905431419307370or_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5761_or__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se1412395901928357646or_nat
% 8.60/4.60      @ bit_se1412395901928357646or_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5762_drop__bit__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4785983289428654063nt_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se8568078237143864401it_int
% 8.60/4.60      @ bit_se8568078237143864401it_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5763_drop__bit__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ bit_se8570568707652914677it_nat
% 8.60/4.60      @ bit_se8570568707652914677it_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5764_mask__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re6650684261131312217nt_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ bit_se2000444600071755411sk_int
% 8.60/4.60      @ bit_se2000444600071755411sk_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5765_mask__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re5653821019739307937at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ bit_se2002935070580805687sk_nat
% 8.60/4.60      @ bit_se2002935070580805687sk_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5766_abs__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re4712519889275205905nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ abs_abs_int
% 8.60/4.60      @ abs_abs_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5767_divide__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re711492959462206631nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ divide_divide_int
% 8.60/4.60      @ divide_divide_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5768_divide__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ divide_divide_nat
% 8.60/4.60      @ divide_divide_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5769_times__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re1345281282404953727at_nat
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5653821019739307937at_nat
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.60      @ times_times_nat
% 8.60/4.60      @ times_times_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5770_times__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re711492959462206631nt_int
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4712519889275205905nt_int
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.60      @ times_times_int
% 8.60/4.60      @ times_times_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5771_less__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re3403563459893282935_int_o
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re5089333283451836215nt_o_o
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.60      @ ord_less_int
% 8.60/4.60      @ ord_less_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5772_less__natural_Orsp,axiom,
% 8.60/4.60      ( bNF_re578469030762574527_nat_o
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re4705727531993890431at_o_o
% 8.60/4.60        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.60      @ ord_less_nat
% 8.60/4.60      @ ord_less_nat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5773_times__rat_Orsp,axiom,
% 8.60/4.60      ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 8.60/4.60      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) )
% 8.60/4.60      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5774_plus__rat_Orsp,axiom,
% 8.60/4.60      ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 8.60/4.60      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) )
% 8.60/4.60      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5775_num__of__integer_Orsp,axiom,
% 8.60/4.60      ( bNF_re7626690874201225453um_num
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 8.60/4.60      @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 8.60/4.60      @ ( comp_nat_num_int @ num_of_nat @ nat2 ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5776_uminus__rat_Orsp,axiom,
% 8.60/4.60      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 8.60/4.60      @ ^ [X: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) )
% 8.60/4.60      @ ^ [X: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5777_inverse__rat_Orsp,axiom,
% 8.60/4.60      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 8.60/4.60      @ ^ [X: product_prod_int_int] :
% 8.60/4.60          ( if_Pro3027730157355071871nt_int
% 8.60/4.60          @ ( ( product_fst_int_int @ X )
% 8.60/4.60            = zero_zero_int )
% 8.60/4.60          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 8.60/4.60          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) )
% 8.60/4.60      @ ^ [X: product_prod_int_int] :
% 8.60/4.60          ( if_Pro3027730157355071871nt_int
% 8.60/4.60          @ ( ( product_fst_int_int @ X )
% 8.60/4.60            = zero_zero_int )
% 8.60/4.60          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 8.60/4.60          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5778_plus__rat_Otransfer,axiom,
% 8.60/4.60      ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 8.60/4.60      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) )
% 8.60/4.60      @ plus_plus_rat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5779_inverse__rat_Otransfer,axiom,
% 8.60/4.60      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 8.60/4.60      @ ^ [X: product_prod_int_int] :
% 8.60/4.60          ( if_Pro3027730157355071871nt_int
% 8.60/4.60          @ ( ( product_fst_int_int @ X )
% 8.60/4.60            = zero_zero_int )
% 8.60/4.60          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 8.60/4.60          @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) )
% 8.60/4.60      @ inverse_inverse_rat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5780_one__rat_Otransfer,axiom,
% 8.60/4.60      pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5781_zero__rat_Otransfer,axiom,
% 8.60/4.60      pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5782_Fract_Otransfer,axiom,
% 8.60/4.60      ( bNF_re3461391660133120880nt_rat
% 8.60/4.60      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60      @ ( bNF_re2214769303045360666nt_rat
% 8.60/4.60        @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.60        @ pcr_rat )
% 8.60/4.60      @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) )
% 8.60/4.60      @ fract ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5783_uminus__rat_Otransfer,axiom,
% 8.60/4.60      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 8.60/4.60      @ ^ [X: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) )
% 8.60/4.60      @ uminus_uminus_rat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5784_times__rat_Otransfer,axiom,
% 8.60/4.60      ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 8.60/4.60      @ ^ [X: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y4 ) ) )
% 8.60/4.60      @ times_times_rat ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5785_positive_Otransfer,axiom,
% 8.60/4.60      ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 8.60/4.60      @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 8.60/4.60      @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 8.60/4.60      @ positive ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5786_times__int_Otransfer,axiom,
% 8.60/4.60      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 8.60/4.60      @ ( produc27273713700761075at_nat
% 8.60/4.60        @ ^ [X: nat,Y4: nat] :
% 8.60/4.60            ( produc2626176000494625587at_nat
% 8.60/4.60            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 8.60/4.60      @ times_times_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5787_zero__int_Otransfer,axiom,
% 8.60/4.60      pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5788_int__transfer,axiom,
% 8.60/4.60      ( bNF_re6830278522597306478at_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ pcr_int
% 8.60/4.60      @ ^ [N3: nat] : ( product_Pair_nat_nat @ N3 @ zero_zero_nat )
% 8.60/4.60      @ semiri1314217659103216013at_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5789_uminus__int_Otransfer,axiom,
% 8.60/4.60      ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 8.60/4.60      @ ( produc2626176000494625587at_nat
% 8.60/4.60        @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X ) )
% 8.60/4.60      @ uminus_uminus_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5790_nat_Otransfer,axiom,
% 8.60/4.60      ( bNF_re4555766996558763186at_nat @ pcr_int
% 8.60/4.60      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.60      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 8.60/4.60      @ nat2 ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5791_one__int_Otransfer,axiom,
% 8.60/4.60      pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5792_less__int_Otransfer,axiom,
% 8.60/4.60      ( bNF_re717283939379294677_int_o @ pcr_int
% 8.60/4.60      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 8.60/4.60        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.60      @ ( produc8739625826339149834_nat_o
% 8.60/4.60        @ ^ [X: nat,Y4: nat] :
% 8.60/4.60            ( produc6081775807080527818_nat_o
% 8.60/4.60            @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 8.60/4.60      @ ord_less_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5793_less__eq__int_Otransfer,axiom,
% 8.60/4.60      ( bNF_re717283939379294677_int_o @ pcr_int
% 8.60/4.60      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 8.60/4.60        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.60      @ ( produc8739625826339149834_nat_o
% 8.60/4.60        @ ^ [X: nat,Y4: nat] :
% 8.60/4.60            ( produc6081775807080527818_nat_o
% 8.60/4.60            @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 8.60/4.60      @ ord_less_eq_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5794_plus__int_Otransfer,axiom,
% 8.60/4.60      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 8.60/4.60      @ ( produc27273713700761075at_nat
% 8.60/4.60        @ ^ [X: nat,Y4: nat] :
% 8.60/4.60            ( produc2626176000494625587at_nat
% 8.60/4.60            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 8.60/4.60      @ plus_plus_int ) ).
% 8.60/4.60  
% 8.60/4.60  thf(fact_5795_minus__int_Otransfer,axiom,
% 8.60/4.60      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 8.60/4.60      @ ( produc27273713700761075at_nat
% 8.60/4.60        @ ^ [X: nat,Y4: nat] :
% 8.60/4.60            ( produc2626176000494625587at_nat
% 8.60/4.60            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 8.60/4.61      @ minus_minus_int ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5796_times__int_Orsp,axiom,
% 8.60/4.61      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 8.60/4.61      @ ( produc27273713700761075at_nat
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc2626176000494625587at_nat
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 8.60/4.61      @ ( produc27273713700761075at_nat
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc2626176000494625587at_nat
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5797_intrel__iff,axiom,
% 8.60/4.61      ! [X2: nat,Y: nat,U: nat,V: nat] :
% 8.60/4.61        ( ( intrel @ ( product_Pair_nat_nat @ X2 @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 8.60/4.61        = ( ( plus_plus_nat @ X2 @ V )
% 8.60/4.61          = ( plus_plus_nat @ U @ Y ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5798_int_Orel__eq__transfer,axiom,
% 8.60/4.61      ( bNF_re717283939379294677_int_o @ pcr_int
% 8.60/4.61      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 8.60/4.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.61      @ intrel
% 8.60/4.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5799_zero__int_Orsp,axiom,
% 8.60/4.61      intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5800_int_Oabs__eq__iff,axiom,
% 8.60/4.61      ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.60/4.61        ( ( ( abs_Integ @ X2 )
% 8.60/4.61          = ( abs_Integ @ Y ) )
% 8.60/4.61        = ( intrel @ X2 @ Y ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5801_uminus__int_Orsp,axiom,
% 8.60/4.61      ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 8.60/4.61      @ ( produc2626176000494625587at_nat
% 8.60/4.61        @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X ) )
% 8.60/4.61      @ ( produc2626176000494625587at_nat
% 8.60/4.61        @ ^ [X: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5802_nat_Orsp,axiom,
% 8.60/4.61      ( bNF_re8246922863344978751at_nat @ intrel
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 8.60/4.61      @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5803_one__int_Orsp,axiom,
% 8.60/4.61      intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5804_intrel__def,axiom,
% 8.60/4.61      ( intrel
% 8.60/4.61      = ( produc8739625826339149834_nat_o
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc6081775807080527818_nat_o
% 8.60/4.61            @ ^ [U2: nat,V3: nat] :
% 8.60/4.61                ( ( plus_plus_nat @ X @ V3 )
% 8.60/4.61                = ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5805_less__int_Orsp,axiom,
% 8.60/4.61      ( bNF_re4202695980764964119_nat_o @ intrel
% 8.60/4.61      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 8.60/4.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.61      @ ( produc8739625826339149834_nat_o
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc6081775807080527818_nat_o
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 8.60/4.61      @ ( produc8739625826339149834_nat_o
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc6081775807080527818_nat_o
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5806_less__eq__int_Orsp,axiom,
% 8.60/4.61      ( bNF_re4202695980764964119_nat_o @ intrel
% 8.60/4.61      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 8.60/4.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.61      @ ( produc8739625826339149834_nat_o
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc6081775807080527818_nat_o
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 8.60/4.61      @ ( produc8739625826339149834_nat_o
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc6081775807080527818_nat_o
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5807_minus__int_Orsp,axiom,
% 8.60/4.61      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 8.60/4.61      @ ( produc27273713700761075at_nat
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc2626176000494625587at_nat
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 8.60/4.61      @ ( produc27273713700761075at_nat
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc2626176000494625587at_nat
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5808_plus__int_Orsp,axiom,
% 8.60/4.61      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 8.60/4.61      @ ( produc27273713700761075at_nat
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc2626176000494625587at_nat
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 8.60/4.61      @ ( produc27273713700761075at_nat
% 8.60/4.61        @ ^ [X: nat,Y4: nat] :
% 8.60/4.61            ( produc2626176000494625587at_nat
% 8.60/4.61            @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5809_le__enumerate,axiom,
% 8.60/4.61      ! [S3: set_nat,N: nat] :
% 8.60/4.61        ( ~ ( finite_finite_nat @ S3 )
% 8.60/4.61       => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5810_finite__le__enumerate,axiom,
% 8.60/4.61      ! [S3: set_nat,N: nat] :
% 8.60/4.61        ( ( finite_finite_nat @ S3 )
% 8.60/4.61       => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 8.60/4.61         => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5811_Least__eq__0,axiom,
% 8.60/4.61      ! [P: nat > $o] :
% 8.60/4.61        ( ( P @ zero_zero_nat )
% 8.60/4.61       => ( ( ord_Least_nat @ P )
% 8.60/4.61          = zero_zero_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5812_Least__Suc2,axiom,
% 8.60/4.61      ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 8.60/4.61        ( ( P @ N )
% 8.60/4.61       => ( ( Q @ M )
% 8.60/4.61         => ( ~ ( P @ zero_zero_nat )
% 8.60/4.61           => ( ! [K3: nat] :
% 8.60/4.61                  ( ( P @ ( suc @ K3 ) )
% 8.60/4.61                  = ( Q @ K3 ) )
% 8.60/4.61             => ( ( ord_Least_nat @ P )
% 8.60/4.61                = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5813_Least__Suc,axiom,
% 8.60/4.61      ! [P: nat > $o,N: nat] :
% 8.60/4.61        ( ( P @ N )
% 8.60/4.61       => ( ~ ( P @ zero_zero_nat )
% 8.60/4.61         => ( ( ord_Least_nat @ P )
% 8.60/4.61            = ( suc
% 8.60/4.61              @ ( ord_Least_nat
% 8.60/4.61                @ ^ [M2: nat] : ( P @ ( suc @ M2 ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5814_Inf__nat__def,axiom,
% 8.60/4.61      ( complete_Inf_Inf_nat
% 8.60/4.61      = ( ^ [X5: set_nat] :
% 8.60/4.61            ( ord_Least_nat
% 8.60/4.61            @ ^ [N3: nat] : ( member_nat @ N3 @ X5 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5815_type__definition__integer,axiom,
% 8.60/4.61      type_d8366093980585677751er_int @ code_int_of_integer @ code_integer_of_int @ top_top_set_int ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5816_mset__set__upto__eq__mset__upto,axiom,
% 8.60/4.61      ! [N: nat] :
% 8.60/4.61        ( ( mset_set_nat @ ( set_ord_lessThan_nat @ N ) )
% 8.60/4.61        = ( mset_nat @ ( upt @ zero_zero_nat @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5817_filterlim__lessThan__at__top,axiom,
% 8.60/4.61      filter3212408913953519116et_nat @ set_ord_lessThan_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5818_filterlim__atMost__at__top,axiom,
% 8.60/4.61      filter3212408913953519116et_nat @ set_ord_atMost_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5819_bij__betw__Suc,axiom,
% 8.60/4.61      ! [M3: set_nat,N4: set_nat] :
% 8.60/4.61        ( ( bij_betw_nat_nat @ suc @ M3 @ N4 )
% 8.60/4.61        = ( ( image_nat_nat @ suc @ M3 )
% 8.60/4.61          = N4 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5820_Sup__int__def,axiom,
% 8.60/4.61      ( complete_Sup_Sup_int
% 8.60/4.61      = ( ^ [X5: set_int] :
% 8.60/4.61            ( the_int
% 8.60/4.61            @ ^ [X: int] :
% 8.60/4.61                ( ( member_int @ X @ X5 )
% 8.60/4.61                & ! [Y4: int] :
% 8.60/4.61                    ( ( member_int @ Y4 @ X5 )
% 8.60/4.61                   => ( ord_less_eq_int @ Y4 @ X ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5821_and__not__num_Opelims,axiom,
% 8.60/4.61      ! [X2: num,Xa: num,Y: option_num] :
% 8.60/4.61        ( ( ( bit_and_not_num @ X2 @ Xa )
% 8.60/4.61          = Y )
% 8.60/4.61       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X2 @ Xa ) )
% 8.60/4.61         => ( ( ( X2 = one )
% 8.60/4.61             => ( ( Xa = one )
% 8.60/4.61               => ( ( Y = none_num )
% 8.60/4.61                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 8.60/4.61           => ( ( ( X2 = one )
% 8.60/4.61               => ! [N2: num] :
% 8.60/4.61                    ( ( Xa
% 8.60/4.61                      = ( bit0 @ N2 ) )
% 8.60/4.61                   => ( ( Y
% 8.60/4.61                        = ( some_num @ one ) )
% 8.60/4.61                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 8.60/4.61             => ( ( ( X2 = one )
% 8.60/4.61                 => ! [N2: num] :
% 8.60/4.61                      ( ( Xa
% 8.60/4.61                        = ( bit1 @ N2 ) )
% 8.60/4.61                     => ( ( Y = none_num )
% 8.60/4.61                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 8.60/4.61               => ( ! [M4: num] :
% 8.60/4.61                      ( ( X2
% 8.60/4.61                        = ( bit0 @ M4 ) )
% 8.60/4.61                     => ( ( Xa = one )
% 8.60/4.61                       => ( ( Y
% 8.60/4.61                            = ( some_num @ ( bit0 @ M4 ) ) )
% 8.60/4.61                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 8.60/4.61                 => ( ! [M4: num] :
% 8.60/4.61                        ( ( X2
% 8.60/4.61                          = ( bit0 @ M4 ) )
% 8.60/4.61                       => ! [N2: num] :
% 8.60/4.61                            ( ( Xa
% 8.60/4.61                              = ( bit0 @ N2 ) )
% 8.60/4.61                           => ( ( Y
% 8.60/4.61                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 8.60/4.61                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 8.60/4.61                   => ( ! [M4: num] :
% 8.60/4.61                          ( ( X2
% 8.60/4.61                            = ( bit0 @ M4 ) )
% 8.60/4.61                         => ! [N2: num] :
% 8.60/4.61                              ( ( Xa
% 8.60/4.61                                = ( bit1 @ N2 ) )
% 8.60/4.61                             => ( ( Y
% 8.60/4.61                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 8.60/4.61                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 8.60/4.61                     => ( ! [M4: num] :
% 8.60/4.61                            ( ( X2
% 8.60/4.61                              = ( bit1 @ M4 ) )
% 8.60/4.61                           => ( ( Xa = one )
% 8.60/4.61                             => ( ( Y
% 8.60/4.61                                  = ( some_num @ ( bit0 @ M4 ) ) )
% 8.60/4.61                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 8.60/4.61                       => ( ! [M4: num] :
% 8.60/4.61                              ( ( X2
% 8.60/4.61                                = ( bit1 @ M4 ) )
% 8.60/4.61                             => ! [N2: num] :
% 8.60/4.61                                  ( ( Xa
% 8.60/4.61                                    = ( bit0 @ N2 ) )
% 8.60/4.61                                 => ( ( Y
% 8.60/4.61                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 8.60/4.61                                        @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 8.60/4.61                                        @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 8.60/4.61                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 8.60/4.61                         => ~ ! [M4: num] :
% 8.60/4.61                                ( ( X2
% 8.60/4.61                                  = ( bit1 @ M4 ) )
% 8.60/4.61                               => ! [N2: num] :
% 8.60/4.61                                    ( ( Xa
% 8.60/4.61                                      = ( bit1 @ N2 ) )
% 8.60/4.61                                   => ( ( Y
% 8.60/4.61                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 8.60/4.61                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5822_and__num_Opelims,axiom,
% 8.60/4.61      ! [X2: num,Xa: num,Y: option_num] :
% 8.60/4.61        ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa )
% 8.60/4.61          = Y )
% 8.60/4.61       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X2 @ Xa ) )
% 8.60/4.61         => ( ( ( X2 = one )
% 8.60/4.61             => ( ( Xa = one )
% 8.60/4.61               => ( ( Y
% 8.60/4.61                    = ( some_num @ one ) )
% 8.60/4.61                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 8.60/4.61           => ( ( ( X2 = one )
% 8.60/4.61               => ! [N2: num] :
% 8.60/4.61                    ( ( Xa
% 8.60/4.61                      = ( bit0 @ N2 ) )
% 8.60/4.61                   => ( ( Y = none_num )
% 8.60/4.61                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 8.60/4.61             => ( ( ( X2 = one )
% 8.60/4.61                 => ! [N2: num] :
% 8.60/4.61                      ( ( Xa
% 8.60/4.61                        = ( bit1 @ N2 ) )
% 8.60/4.61                     => ( ( Y
% 8.60/4.61                          = ( some_num @ one ) )
% 8.60/4.61                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 8.60/4.61               => ( ! [M4: num] :
% 8.60/4.61                      ( ( X2
% 8.60/4.61                        = ( bit0 @ M4 ) )
% 8.60/4.61                     => ( ( Xa = one )
% 8.60/4.61                       => ( ( Y = none_num )
% 8.60/4.61                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 8.60/4.61                 => ( ! [M4: num] :
% 8.60/4.61                        ( ( X2
% 8.60/4.61                          = ( bit0 @ M4 ) )
% 8.60/4.61                       => ! [N2: num] :
% 8.60/4.61                            ( ( Xa
% 8.60/4.61                              = ( bit0 @ N2 ) )
% 8.60/4.61                           => ( ( Y
% 8.60/4.61                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 8.60/4.61                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 8.60/4.61                   => ( ! [M4: num] :
% 8.60/4.61                          ( ( X2
% 8.60/4.61                            = ( bit0 @ M4 ) )
% 8.60/4.61                         => ! [N2: num] :
% 8.60/4.61                              ( ( Xa
% 8.60/4.61                                = ( bit1 @ N2 ) )
% 8.60/4.61                             => ( ( Y
% 8.60/4.61                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 8.60/4.61                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 8.60/4.61                     => ( ! [M4: num] :
% 8.60/4.61                            ( ( X2
% 8.60/4.61                              = ( bit1 @ M4 ) )
% 8.60/4.61                           => ( ( Xa = one )
% 8.60/4.61                             => ( ( Y
% 8.60/4.61                                  = ( some_num @ one ) )
% 8.60/4.61                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 8.60/4.61                       => ( ! [M4: num] :
% 8.60/4.61                              ( ( X2
% 8.60/4.61                                = ( bit1 @ M4 ) )
% 8.60/4.61                             => ! [N2: num] :
% 8.60/4.61                                  ( ( Xa
% 8.60/4.61                                    = ( bit0 @ N2 ) )
% 8.60/4.61                                 => ( ( Y
% 8.60/4.61                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 8.60/4.61                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 8.60/4.61                         => ~ ! [M4: num] :
% 8.60/4.61                                ( ( X2
% 8.60/4.61                                  = ( bit1 @ M4 ) )
% 8.60/4.61                               => ! [N2: num] :
% 8.60/4.61                                    ( ( Xa
% 8.60/4.61                                      = ( bit1 @ N2 ) )
% 8.60/4.61                                   => ( ( Y
% 8.60/4.61                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 8.60/4.61                                          @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 8.60/4.61                                          @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 8.60/4.61                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5823_int_Obi__total,axiom,
% 8.60/4.61      bi_tot896582865486249351at_int @ pcr_int ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5824_Domainp__cr__rat,axiom,
% 8.60/4.61      ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 8.60/4.61      = ( ^ [X: product_prod_int_int] :
% 8.60/4.61            ( ( product_snd_int_int @ X )
% 8.60/4.61           != zero_zero_int ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5825_eventually__sequentially__Suc,axiom,
% 8.60/4.61      ! [P: nat > $o] :
% 8.60/4.61        ( ( eventually_nat
% 8.60/4.61          @ ^ [I2: nat] : ( P @ ( suc @ I2 ) )
% 8.60/4.61          @ at_top_nat )
% 8.60/4.61        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5826_eventually__sequentially__seg,axiom,
% 8.60/4.61      ! [P: nat > $o,K: nat] :
% 8.60/4.61        ( ( eventually_nat
% 8.60/4.61          @ ^ [N3: nat] : ( P @ ( plus_plus_nat @ N3 @ K ) )
% 8.60/4.61          @ at_top_nat )
% 8.60/4.61        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5827_eventually__sequentially,axiom,
% 8.60/4.61      ! [P: nat > $o] :
% 8.60/4.61        ( ( eventually_nat @ P @ at_top_nat )
% 8.60/4.61        = ( ? [N8: nat] :
% 8.60/4.61            ! [N3: nat] :
% 8.60/4.61              ( ( ord_less_eq_nat @ N8 @ N3 )
% 8.60/4.61             => ( P @ N3 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5828_eventually__sequentiallyI,axiom,
% 8.60/4.61      ! [C: nat,P: nat > $o] :
% 8.60/4.61        ( ! [X3: nat] :
% 8.60/4.61            ( ( ord_less_eq_nat @ C @ X3 )
% 8.60/4.61           => ( P @ X3 ) )
% 8.60/4.61       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5829_le__sequentially,axiom,
% 8.60/4.61      ! [F4: filter_nat] :
% 8.60/4.61        ( ( ord_le2510731241096832064er_nat @ F4 @ at_top_nat )
% 8.60/4.61        = ( ! [N8: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N8 ) @ F4 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5830_eventually__False__sequentially,axiom,
% 8.60/4.61      ~ ( eventually_nat
% 8.60/4.61        @ ^ [N3: nat] : $false
% 8.60/4.61        @ at_top_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5831_int_Oright__total,axiom,
% 8.60/4.61      right_1157779049177982926at_int @ pcr_int ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5832_pair__lessI2,axiom,
% 8.60/4.61      ! [A: nat,B: nat,S: nat,T: nat] :
% 8.60/4.61        ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.61       => ( ( ord_less_nat @ S @ T )
% 8.60/4.61         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5833_pair__leqI2,axiom,
% 8.60/4.61      ! [A: nat,B: nat,S: nat,T: nat] :
% 8.60/4.61        ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.61       => ( ( ord_less_eq_nat @ S @ T )
% 8.60/4.61         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5834_euclidean__size__integer_Orep__eq,axiom,
% 8.60/4.61      ( euclid6377331345833325938nteger
% 8.60/4.61      = ( ^ [X: code_integer] : ( euclid4774559944035922753ze_int @ ( code_int_of_integer @ X ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5835_euclidean__size__integer__def,axiom,
% 8.60/4.61      ( euclid6377331345833325938nteger
% 8.60/4.61      = ( map_fu6539832666145259331at_nat @ code_int_of_integer @ id_nat @ euclid4774559944035922753ze_int ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5836_euclidean__size__integer_Oabs__eq,axiom,
% 8.60/4.61      ! [X2: int] :
% 8.60/4.61        ( ( euclid6377331345833325938nteger @ ( code_integer_of_int @ X2 ) )
% 8.60/4.61        = ( euclid4774559944035922753ze_int @ X2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5837_euclidean__size__natural_Orsp,axiom,
% 8.60/4.61      ( bNF_re5653821019739307937at_nat
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ euclid4777050414544973029ze_nat
% 8.60/4.61      @ euclid4777050414544973029ze_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5838_euclidean__size__integer_Orsp,axiom,
% 8.60/4.61      ( bNF_re3715656647883201625at_nat
% 8.60/4.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ euclid4774559944035922753ze_int
% 8.60/4.61      @ euclid4774559944035922753ze_int ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5839_division__segment__integer_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_integer] :
% 8.60/4.61        ( ( code_int_of_integer @ ( euclid6289375185220004616nteger @ X2 ) )
% 8.60/4.61        = ( euclid3395696857347342551nt_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5840_abs__division__segment,axiom,
% 8.60/4.61      ! [K: int] :
% 8.60/4.61        ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 8.60/4.61        = one_one_int ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5841_division__segment__integer_Orsp,axiom,
% 8.60/4.61      ( bNF_re4712519889275205905nt_int
% 8.60/4.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61      @ euclid3395696857347342551nt_int
% 8.60/4.61      @ euclid3395696857347342551nt_int ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5842_division__segment__natural_Orsp,axiom,
% 8.60/4.61      ( bNF_re5653821019739307937at_nat
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ euclid3398187327856392827nt_nat
% 8.60/4.61      @ euclid3398187327856392827nt_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5843_division__segment__nat__def,axiom,
% 8.60/4.61      ( euclid3398187327856392827nt_nat
% 8.60/4.61      = ( ^ [N3: nat] : one_one_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5844_division__segment__integer_Oabs__eq,axiom,
% 8.60/4.61      ! [X2: int] :
% 8.60/4.61        ( ( euclid6289375185220004616nteger @ ( code_integer_of_int @ X2 ) )
% 8.60/4.61        = ( code_integer_of_int @ ( euclid3395696857347342551nt_int @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5845_division__segment__eq__sgn,axiom,
% 8.60/4.61      ! [K: int] :
% 8.60/4.61        ( ( K != zero_zero_int )
% 8.60/4.61       => ( ( euclid3395696857347342551nt_int @ K )
% 8.60/4.61          = ( sgn_sgn_int @ K ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5846_division__segment__integer__def,axiom,
% 8.60/4.61      ( euclid6289375185220004616nteger
% 8.60/4.61      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ euclid3395696857347342551nt_int ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5847_division__segment__int__def,axiom,
% 8.60/4.61      ( euclid3395696857347342551nt_int
% 8.60/4.61      = ( ^ [K2: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5848_wf__int__ge__less__than2,axiom,
% 8.60/4.61      ! [D: int] : ( wf_int @ ( int_ge_less_than2 @ D ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5849_wf__int__ge__less__than,axiom,
% 8.60/4.61      ! [D: int] : ( wf_int @ ( int_ge_less_than @ D ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5850_wf__less,axiom,
% 8.60/4.61      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5851_num__of__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re6718328864250387230um_num @ code_pcr_integer
% 8.60/4.61      @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 8.60/4.61      @ ( comp_nat_num_int @ num_of_nat @ nat2 )
% 8.60/4.61      @ code_num_of_integer ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5852_euclidean__size__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ euclid4774559944035922753ze_int
% 8.60/4.61      @ euclid6377331345833325938nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5853_integer_Oleft__unique,axiom,
% 8.60/4.61      left_u6795595883297946906nteger @ code_pcr_integer ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5854_zero__integer_Otransfer,axiom,
% 8.60/4.61      code_pcr_integer @ zero_zero_int @ zero_z3403309356797280102nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5855_one__integer_Otransfer,axiom,
% 8.60/4.61      code_pcr_integer @ one_one_int @ one_one_Code_integer ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5856_integer_Obi__unique,axiom,
% 8.60/4.61      bi_uni8663861020805155098nteger @ code_pcr_integer ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5857_integer_Odomain,axiom,
% 8.60/4.61      ! [P: int > $o] :
% 8.60/4.61        ( ( ( domainp_int_int
% 8.60/4.61            @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.61          = P )
% 8.60/4.61       => ( ( domain452967906960104687nteger @ code_pcr_integer )
% 8.60/4.61          = P ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5858_integer_Obi__total,axiom,
% 8.60/4.61      bi_tot1331153423839324337nteger @ code_pcr_integer ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5859_flip__bit__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re4935368626670024657nteger
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 8.60/4.61      @ bit_se2159334234014336723it_int
% 8.60/4.61      @ bit_se1345352211410354436nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5860_push__bit__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re4935368626670024657nteger
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 8.60/4.61      @ bit_se545348938243370406it_int
% 8.60/4.61      @ bit_se7788150548672797655nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5861_drop__bit__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re4935368626670024657nteger
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 8.60/4.61      @ bit_se8568078237143864401it_int
% 8.60/4.61      @ bit_se3928097537394005634nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5862_xor__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se6526347334894502574or_int @ bit_se3222712562003087583nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5863_bit__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re4711666741709854504_nat_o @ code_pcr_integer
% 8.60/4.61      @ ^ [Y3: nat > $o,Z: nat > $o] : ( Y3 = Z )
% 8.60/4.61      @ bit_se1146084159140164899it_int
% 8.60/4.61      @ bit_se9216721137139052372nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5864_or__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se1409905431419307370or_int @ bit_se1080825931792720795nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5865_take__bit__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re4935368626670024657nteger
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 8.60/4.61      @ bit_se2923211474154528505it_int
% 8.60/4.61      @ bit_se1745604003318907178nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5866_not__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ bit_ri7919022796975470100ot_int @ bit_ri7632146776885996613nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5867_and__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ bit_se725231765392027082nd_int @ bit_se3949692690581998587nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5868_dup_Otransfer,axiom,
% 8.60/4.61      ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer
% 8.60/4.61      @ ^ [K2: int] : ( plus_plus_int @ K2 @ K2 )
% 8.60/4.61      @ code_dup ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5869_integer__of__nat_Otransfer,axiom,
% 8.60/4.61      ( bNF_re4153400068438556298nteger
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ code_pcr_integer
% 8.60/4.61      @ semiri1314217659103216013at_int
% 8.60/4.61      @ code_integer_of_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5870_less__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 8.60/4.61      @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 8.60/4.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.61      @ ord_less_int
% 8.60/4.61      @ ord_le6747313008572928689nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5871_times__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ times_times_int @ times_3573771949741848930nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5872_divide__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ divide_divide_int @ divide6298287555418463151nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5873_abs__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ abs_abs_int @ abs_abs_Code_integer ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5874_nat__of__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re2807294637932363402at_nat @ code_pcr_integer
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ nat2
% 8.60/4.61      @ code_nat_of_integer ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5875_modulo__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ modulo_modulo_int @ modulo364778990260209775nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5876_plus__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ plus_plus_int @ plus_p5714425477246183910nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5877_sgn__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ sgn_sgn_int @ sgn_sgn_Code_integer ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5878_integer_Orep__transfer,axiom,
% 8.60/4.61      ( bNF_re3804157879324367682nt_int @ code_pcr_integer
% 8.60/4.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61      @ ^ [X: int] : X
% 8.60/4.61      @ code_int_of_integer ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5879_integer_Oid__abs__transfer,axiom,
% 8.60/4.61      ( bNF_re982302072995117890nteger
% 8.60/4.61      @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61      @ code_pcr_integer
% 8.60/4.61      @ ^ [X: int] : X
% 8.60/4.61      @ code_integer_of_int ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5880_gcd__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ gcd_gcd_int @ gcd_gcd_Code_integer ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5881_minus__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ minus_minus_int @ minus_8373710615458151222nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5882_uminus__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ uminus_uminus_int @ uminus1351360451143612070nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5883_mask__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re4153400068438556298nteger
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ code_pcr_integer
% 8.60/4.61      @ bit_se2000444600071755411sk_int
% 8.60/4.61      @ bit_se2119862282449309892nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5884_unset__bit__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re4935368626670024657nteger
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 8.60/4.61      @ bit_se4203085406695923979it_int
% 8.60/4.61      @ bit_se8260200283734997820nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5885_set__bit__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re4935368626670024657nteger
% 8.60/4.61      @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61      @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer )
% 8.60/4.61      @ bit_se7879613467334960850it_int
% 8.60/4.61      @ bit_se2793503036327961859nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5886_integer_Oright__total,axiom,
% 8.60/4.61      right_7281159819619925802nteger @ code_pcr_integer ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5887_less__eq__integer_Otransfer,axiom,
% 8.60/4.61      ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 8.60/4.61      @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 8.60/4.61        @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 8.60/4.61      @ ord_less_eq_int
% 8.60/4.61      @ ord_le3102999989581377725nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5888_division__segment__integer_Otransfer,axiom,
% 8.60/4.61      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ euclid3395696857347342551nt_int @ euclid6289375185220004616nteger ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5889_sub_Otransfer,axiom,
% 8.60/4.61      ( bNF_re7876454716742015248nteger
% 8.60/4.61      @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 8.60/4.61      @ ( bNF_re6501075790457514782nteger
% 8.60/4.61        @ ^ [Y3: num,Z: num] : ( Y3 = Z )
% 8.60/4.61        @ code_pcr_integer )
% 8.60/4.61      @ ^ [M2: num,N3: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N3 ) )
% 8.60/4.61      @ code_sub ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5890_eventually__prod__sequentially,axiom,
% 8.60/4.61      ! [P: product_prod_nat_nat > $o] :
% 8.60/4.61        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 8.60/4.61        = ( ? [N8: nat] :
% 8.60/4.61            ! [M2: nat] :
% 8.60/4.61              ( ( ord_less_eq_nat @ N8 @ M2 )
% 8.60/4.61             => ! [N3: nat] :
% 8.60/4.61                  ( ( ord_less_eq_nat @ N8 @ N3 )
% 8.60/4.61                 => ( P @ ( product_Pair_nat_nat @ N3 @ M2 ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5891_UNIV__char__of__nat,axiom,
% 8.60/4.61      ( top_top_set_char
% 8.60/4.61      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5892_inj__on__char__of__nat,axiom,
% 8.60/4.61      inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5893_range__nat__of__char,axiom,
% 8.60/4.61      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 8.60/4.61      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5894_char_Osize_I2_J,axiom,
% 8.60/4.61      ! [X12: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X8: $o] :
% 8.60/4.61        ( ( size_size_char @ ( char2 @ X12 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X8 ) )
% 8.60/4.61        = zero_zero_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5895_integer__of__char__code,axiom,
% 8.60/4.61      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B6: $o,B7: $o] :
% 8.60/4.61        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B6 @ B7 ) )
% 8.60/4.61        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B7 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B6 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5896_char_Osize__gen,axiom,
% 8.60/4.61      ! [X12: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X8: $o] :
% 8.60/4.61        ( ( size_char @ ( char2 @ X12 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X8 ) )
% 8.60/4.61        = zero_zero_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5897_char__of__integer__code,axiom,
% 8.60/4.61      ( char_of_integer
% 8.60/4.61      = ( ^ [K2: code_integer] :
% 8.60/4.61            ( produc4188289175737317920o_char
% 8.60/4.61            @ ^ [Q0: code_integer,B02: $o] :
% 8.60/4.61                ( produc4188289175737317920o_char
% 8.60/4.61                @ ^ [Q1: code_integer,B12: $o] :
% 8.60/4.61                    ( produc4188289175737317920o_char
% 8.60/4.61                    @ ^ [Q22: code_integer,B23: $o] :
% 8.60/4.61                        ( produc4188289175737317920o_char
% 8.60/4.61                        @ ^ [Q32: code_integer,B33: $o] :
% 8.60/4.61                            ( produc4188289175737317920o_char
% 8.60/4.61                            @ ^ [Q42: code_integer,B43: $o] :
% 8.60/4.61                                ( produc4188289175737317920o_char
% 8.60/4.61                                @ ^ [Q52: code_integer,B53: $o] :
% 8.60/4.61                                    ( produc4188289175737317920o_char
% 8.60/4.61                                    @ ^ [Q62: code_integer,B62: $o] :
% 8.60/4.61                                        ( produc4188289175737317920o_char
% 8.60/4.61                                        @ ^ [Uu: code_integer] : ( char2 @ B02 @ B12 @ B23 @ B33 @ B43 @ B53 @ B62 )
% 8.60/4.61                                        @ ( code_bit_cut_integer @ Q62 ) )
% 8.60/4.61                                    @ ( code_bit_cut_integer @ Q52 ) )
% 8.60/4.61                                @ ( code_bit_cut_integer @ Q42 ) )
% 8.60/4.61                            @ ( code_bit_cut_integer @ Q32 ) )
% 8.60/4.61                        @ ( code_bit_cut_integer @ Q22 ) )
% 8.60/4.61                    @ ( code_bit_cut_integer @ Q1 ) )
% 8.60/4.61                @ ( code_bit_cut_integer @ Q0 ) )
% 8.60/4.61            @ ( code_bit_cut_integer @ K2 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5898_assert_H__def,axiom,
% 8.60/4.61      ( refine_Imp_assert
% 8.60/4.61      = ( ^ [P5: $o] : ( if_Hea8138950348631371857t_unit @ P5 @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( heap_T2927564422264180874t_unit @ ( cons_char @ ( char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false ) @ ( cons_char @ ( char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false ) @ nil_char ) ) ) ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5899_wait__def,axiom,
% 8.60/4.61      ( heap_Time_wait
% 8.60/4.61      = ( ^ [N3: nat] :
% 8.60/4.61            ( heap_T6183433275982383450t_unit
% 8.60/4.61            @ ^ [H3: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H3 @ N3 ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5900_unit__all__impI,axiom,
% 8.60/4.61      ! [P: product_unit > $o,Q: product_unit > $o] :
% 8.60/4.61        ( ( ( P @ product_Unity )
% 8.60/4.61         => ( Q @ product_Unity ) )
% 8.60/4.61       => ! [X4: product_unit] :
% 8.60/4.61            ( ( P @ X4 )
% 8.60/4.61           => ( Q @ X4 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5901_eq__sym__Unity__conv,axiom,
% 8.60/4.61      ! [X2: $o] :
% 8.60/4.61        ( ( X2
% 8.60/4.61          = ( product_Unity = product_Unity ) )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5902_refines__assert_H,axiom,
% 8.60/4.61      ! [Phi: $o] : ( refine451278484176762712t_unit @ ( heap_T4284346855313245393t_unit @ product_Unity ) @ ( refine_Imp_assert @ Phi ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5903_execute__assert_H,axiom,
% 8.60/4.61      ! [P: $o,H: heap_e7401611519738050253t_unit] :
% 8.60/4.61        ( ( P
% 8.60/4.61         => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H )
% 8.60/4.61            = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H @ zero_zero_nat ) ) ) ) )
% 8.60/4.61        & ( ~ P
% 8.60/4.61         => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H )
% 8.60/4.61            = none_P9117596204409417319it_nat ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5904_natural__zero__minus__one,axiom,
% 8.60/4.61      ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 8.60/4.61      = zero_z2226904508553997617atural ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5905_minus__shift__def,axiom,
% 8.60/4.61      ( minus_shift
% 8.60/4.61      = ( ^ [R2: code_natural,K2: code_natural,L2: code_natural] : ( if_Code_natural @ ( ord_le5570908160329646204atural @ K2 @ L2 ) @ ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ R2 @ K2 ) @ L2 ) @ ( minus_7197305767214868737atural @ K2 @ L2 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5906_next_Osimps,axiom,
% 8.60/4.61      ! [V: code_natural,W2: code_natural] :
% 8.60/4.61        ( ( next @ ( produc3574140220909816553atural @ V @ W2 ) )
% 8.60/4.61        = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5907_log_Oelims,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural,Y: code_natural] :
% 8.60/4.61        ( ( ( log @ X2 @ Xa )
% 8.60/4.61          = Y )
% 8.60/4.61       => ( ( ( ( ord_le1926595141338095240atural @ X2 @ one_one_Code_natural )
% 8.60/4.61              | ( ord_le5570908160329646204atural @ Xa @ X2 ) )
% 8.60/4.61           => ( Y = one_one_Code_natural ) )
% 8.60/4.61          & ( ~ ( ( ord_le1926595141338095240atural @ X2 @ one_one_Code_natural )
% 8.60/4.61                | ( ord_le5570908160329646204atural @ Xa @ X2 ) )
% 8.60/4.61           => ( Y
% 8.60/4.61              = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X2 @ ( divide5121882707175180666atural @ Xa @ X2 ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5908_log_Osimps,axiom,
% 8.60/4.61      ( log
% 8.60/4.61      = ( ^ [B2: code_natural,I2: code_natural] :
% 8.60/4.61            ( if_Code_natural
% 8.60/4.61            @ ( ( ord_le1926595141338095240atural @ B2 @ one_one_Code_natural )
% 8.60/4.61              | ( ord_le5570908160329646204atural @ I2 @ B2 ) )
% 8.60/4.61            @ one_one_Code_natural
% 8.60/4.61            @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B2 @ ( divide5121882707175180666atural @ I2 @ B2 ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5909_split__seed__def,axiom,
% 8.60/4.61      ( split_seed
% 8.60/4.61      = ( ^ [S4: produc7822875418678951345atural] :
% 8.60/4.61            ( produc8282080750456430313atural
% 8.60/4.61            @ ^ [V3: code_natural,W: code_natural] :
% 8.60/4.61                ( produc8282080750456430313atural
% 8.60/4.61                @ ^ [V5: code_natural,W4: code_natural] : ( produc4480994950612372183atural @ ( produc3574140220909816553atural @ ( inc_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ V3 ) @ W4 ) @ ( produc3574140220909816553atural @ V5 @ ( inc_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ W ) ) )
% 8.60/4.61                @ ( produc6591912806276919810atural @ ( next @ S4 ) ) )
% 8.60/4.61            @ S4 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5910_Random_Orange__def,axiom,
% 8.60/4.61      ( range
% 8.60/4.61      = ( ^ [K2: code_natural] :
% 8.60/4.61            ( produc5538323210962509403atural
% 8.60/4.61            @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K2 )
% 8.60/4.61              @ ^ [L2: code_natural] :
% 8.60/4.61                  ( produc5538323210962509403atural @ next
% 8.60/4.61                  @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V3 @ ( times_2397367101498566445atural @ L2 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 8.60/4.61              @ one_one_Code_natural )
% 8.60/4.61            @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V3 @ K2 ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5911_inc__shift__def,axiom,
% 8.60/4.61      ( inc_shift
% 8.60/4.61      = ( ^ [V3: code_natural,K2: code_natural] : ( if_Code_natural @ ( V3 = K2 ) @ one_one_Code_natural @ ( plus_p4538020629002901425atural @ K2 @ one_one_Code_natural ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5912_log_Opelims,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural,Y: code_natural] :
% 8.60/4.61        ( ( ( log @ X2 @ Xa )
% 8.60/4.61          = Y )
% 8.60/4.61       => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X2 @ Xa ) )
% 8.60/4.61         => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X2 @ one_one_Code_natural )
% 8.60/4.61                    | ( ord_le5570908160329646204atural @ Xa @ X2 ) )
% 8.60/4.61                 => ( Y = one_one_Code_natural ) )
% 8.60/4.61                & ( ~ ( ( ord_le1926595141338095240atural @ X2 @ one_one_Code_natural )
% 8.60/4.61                      | ( ord_le5570908160329646204atural @ Xa @ X2 ) )
% 8.60/4.61                 => ( Y
% 8.60/4.61                    = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X2 @ ( divide5121882707175180666atural @ Xa @ X2 ) ) ) ) ) )
% 8.60/4.61             => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X2 @ Xa ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5913_natural__of__nat__of__nat,axiom,
% 8.60/4.61      code_natural_of_nat = semiri3763490453095760265atural ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5914_divide__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( divide5121882707175180666atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( divide_divide_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5915_less__eq__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( ord_le1926595141338095240atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( ord_less_eq_nat @ Xa @ X2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5916_minus__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( minus_7197305767214868737atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( minus_minus_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5917_zero__natural__def,axiom,
% 8.60/4.61      ( zero_z2226904508553997617atural
% 8.60/4.61      = ( code_natural_of_nat @ zero_zero_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5918_one__natural__def,axiom,
% 8.60/4.61      ( one_one_Code_natural
% 8.60/4.61      = ( code_natural_of_nat @ one_one_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5919_euclidean__size__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [X2: nat] :
% 8.60/4.61        ( ( euclid5200926497590043453atural @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( euclid4777050414544973029ze_nat @ X2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5920_mask__natural__def,axiom,
% 8.60/4.61      ( bit_se943457434206027407atural
% 8.60/4.61      = ( map_fu4742413587575543474atural @ id_nat @ code_natural_of_nat @ bit_se2002935070580805687sk_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5921_drop__bit__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( bit_se2751692689150723149atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( bit_se8570568707652914677it_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5922_and__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( bit_se2773287842338716102atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( bit_se727722235901077358nd_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5923_bit__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [X2: nat] :
% 8.60/4.61        ( ( bit_se8040316288895769887atural @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( bit_se1148574629649215175it_nat @ X2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5924_take__bit__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( bit_se569199155075624693atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( bit_se2925701944663578781it_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5925_xor__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( bit_se2046307713759805098atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( bit_se6528837805403552850or_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5926_or__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( bit_se9127793120404214118atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( bit_se1412395901928357646or_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5927_push__bit__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( bit_se6611745700429515170atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( bit_se547839408752420682it_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5928_mask__natural_Oabs__eq,axiom,
% 8.60/4.61      ( bit_se943457434206027407atural
% 8.60/4.61      = ( ^ [X: nat] : ( code_natural_of_nat @ ( bit_se2002935070580805687sk_nat @ X ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5929_flip__bit__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( bit_se168947363167071951atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( bit_se2161824704523386999it_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5930_unset__bit__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( bit_se7083795435491715335atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( bit_se4205575877204974255it_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5931_set__bit__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( bit_se1617098188084679374atural @ Xa @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( bit_se7882103937844011126it_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5932_division__segment__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [X2: nat] :
% 8.60/4.61        ( ( euclid5112970336976722131atural @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( euclid3398187327856392827nt_nat @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5933_natural__of__nat__cases,axiom,
% 8.60/4.61      ! [X2: code_natural] :
% 8.60/4.61        ~ ! [Y2: nat] :
% 8.60/4.61            ( ( X2
% 8.60/4.61              = ( code_natural_of_nat @ Y2 ) )
% 8.60/4.61           => ~ ( member_nat @ Y2 @ top_top_set_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5934_natural__of__nat__induct,axiom,
% 8.60/4.61      ! [P: code_natural > $o,X2: code_natural] :
% 8.60/4.61        ( ! [Y2: nat] :
% 8.60/4.61            ( ( member_nat @ Y2 @ top_top_set_nat )
% 8.60/4.61           => ( P @ ( code_natural_of_nat @ Y2 ) ) )
% 8.60/4.61       => ( P @ X2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5935_natural__of__nat__inject,axiom,
% 8.60/4.61      ! [X2: nat,Y: nat] :
% 8.60/4.61        ( ( member_nat @ X2 @ top_top_set_nat )
% 8.60/4.61       => ( ( member_nat @ Y @ top_top_set_nat )
% 8.60/4.61         => ( ( ( code_natural_of_nat @ X2 )
% 8.60/4.61              = ( code_natural_of_nat @ Y ) )
% 8.60/4.61            = ( X2 = Y ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5936_less__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( ord_le5570908160329646204atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( ord_less_nat @ Xa @ X2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5937_plus__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( plus_p4538020629002901425atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( plus_plus_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5938_times__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( times_2397367101498566445atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( times_times_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5939_modulo__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [Xa: nat,X2: nat] :
% 8.60/4.61        ( ( modulo8411746178871703098atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( modulo_modulo_nat @ Xa @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5940_Nat_Oabs__eq,axiom,
% 8.60/4.61      ! [X2: int] :
% 8.60/4.61        ( ( code_Nat @ ( code_integer_of_int @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( nat2 @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5941_nat__of__natural__inverse,axiom,
% 8.60/4.61      ! [X2: code_natural] :
% 8.60/4.61        ( ( code_natural_of_nat @ ( code_nat_of_natural @ X2 ) )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5942_nat__of__natural__of__nat__inverse,axiom,
% 8.60/4.61      ! [N: nat] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( code_natural_of_nat @ N ) )
% 8.60/4.61        = N ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5943_natural__of__nat__of__natural__inverse,axiom,
% 8.60/4.61      ! [N: code_natural] :
% 8.60/4.61        ( ( code_natural_of_nat @ ( code_nat_of_natural @ N ) )
% 8.60/4.61        = N ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5944_nat__of__natural__min,axiom,
% 8.60/4.61      ! [K: code_natural,L: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( ord_min_Code_natural @ K @ L ) )
% 8.60/4.61        = ( ord_min_nat @ ( code_nat_of_natural @ K ) @ ( code_nat_of_natural @ L ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5945_nat__of__natural__max,axiom,
% 8.60/4.61      ! [K: code_natural,L: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( ord_max_Code_natural @ K @ L ) )
% 8.60/4.61        = ( ord_max_nat @ ( code_nat_of_natural @ K ) @ ( code_nat_of_natural @ L ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5946_nat__of__natural__of__nat,axiom,
% 8.60/4.61      ! [N: nat] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( semiri3763490453095760265atural @ N ) )
% 8.60/4.61        = N ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5947_of__nat__of__natural,axiom,
% 8.60/4.61      ! [N: code_natural] :
% 8.60/4.61        ( ( semiri3763490453095760265atural @ ( code_nat_of_natural @ N ) )
% 8.60/4.61        = N ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5948_zero__natural_Orep__eq,axiom,
% 8.60/4.61      ( ( code_nat_of_natural @ zero_z2226904508553997617atural )
% 8.60/4.61      = zero_zero_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5949_one__natural_Orep__eq,axiom,
% 8.60/4.61      ( ( code_nat_of_natural @ one_one_Code_natural )
% 8.60/4.61      = one_one_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5950_plus__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( plus_p4538020629002901425atural @ X2 @ Xa ) )
% 8.60/4.61        = ( plus_plus_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5951_minus__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( minus_7197305767214868737atural @ X2 @ Xa ) )
% 8.60/4.61        = ( minus_minus_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5952_nat__of__natural__numeral,axiom,
% 8.60/4.61      ! [K: num] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( numera5444537566228673987atural @ K ) )
% 8.60/4.61        = ( numeral_numeral_nat @ K ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5953_times__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( times_2397367101498566445atural @ X2 @ Xa ) )
% 8.60/4.61        = ( times_times_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5954_divide__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( divide5121882707175180666atural @ X2 @ Xa ) )
% 8.60/4.61        = ( divide_divide_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5955_modulo__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( modulo8411746178871703098atural @ X2 @ Xa ) )
% 8.60/4.61        = ( modulo_modulo_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5956_division__segment__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( euclid5112970336976722131atural @ X2 ) )
% 8.60/4.61        = ( euclid3398187327856392827nt_nat @ ( code_nat_of_natural @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5957_euclidean__size__natural_Orep__eq,axiom,
% 8.60/4.61      ( euclid5200926497590043453atural
% 8.60/4.61      = ( ^ [X: code_natural] : ( euclid4777050414544973029ze_nat @ ( code_nat_of_natural @ X ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5958_minus__natural__def,axiom,
% 8.60/4.61      ( minus_7197305767214868737atural
% 8.60/4.61      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ minus_minus_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5959_or__natural__def,axiom,
% 8.60/4.61      ( bit_se9127793120404214118atural
% 8.60/4.61      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se1412395901928357646or_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5960_xor__natural__def,axiom,
% 8.60/4.61      ( bit_se2046307713759805098atural
% 8.60/4.61      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se6528837805403552850or_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5961_and__natural__def,axiom,
% 8.60/4.61      ( bit_se2773287842338716102atural
% 8.60/4.61      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se727722235901077358nd_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5962_division__segment__natural__def,axiom,
% 8.60/4.61      ( euclid5112970336976722131atural
% 8.60/4.61      = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ euclid3398187327856392827nt_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5963_natural__of__nat__inverse,axiom,
% 8.60/4.61      ! [Y: nat] :
% 8.60/4.61        ( ( member_nat @ Y @ top_top_set_nat )
% 8.60/4.61       => ( ( code_nat_of_natural @ ( code_natural_of_nat @ Y ) )
% 8.60/4.61          = Y ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5964_type__definition__natural,axiom,
% 8.60/4.61      type_d4410041424927559462al_nat @ code_nat_of_natural @ code_natural_of_nat @ top_top_set_nat ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5965_plus__natural__def,axiom,
% 8.60/4.61      ( plus_p4538020629002901425atural
% 8.60/4.61      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ plus_plus_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5966_less__natural__def,axiom,
% 8.60/4.61      ( ord_le5570908160329646204atural
% 8.60/4.61      = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5967_less__natural_Orep__eq,axiom,
% 8.60/4.61      ( ord_le5570908160329646204atural
% 8.60/4.61      = ( ^ [X: code_natural,Xa4: code_natural] : ( ord_less_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5968_nat__of__natural__induct,axiom,
% 8.60/4.61      ! [Y: nat,P: nat > $o] :
% 8.60/4.61        ( ( member_nat @ Y @ top_top_set_nat )
% 8.60/4.61       => ( ! [X3: code_natural] : ( P @ ( code_nat_of_natural @ X3 ) )
% 8.60/4.61         => ( P @ Y ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5969_nat__of__natural__cases,axiom,
% 8.60/4.61      ! [Y: nat] :
% 8.60/4.61        ( ( member_nat @ Y @ top_top_set_nat )
% 8.60/4.61       => ~ ! [X3: code_natural] :
% 8.60/4.61              ( Y
% 8.60/4.61             != ( code_nat_of_natural @ X3 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5970_nat__of__natural,axiom,
% 8.60/4.61      ! [X2: code_natural] : ( member_nat @ ( code_nat_of_natural @ X2 ) @ top_top_set_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5971_drop__bit__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: nat,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se2751692689150723149atural @ X2 @ Xa ) )
% 8.60/4.61        = ( bit_se8570568707652914677it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5972_bit__natural_Orep__eq,axiom,
% 8.60/4.61      ( bit_se8040316288895769887atural
% 8.60/4.61      = ( ^ [X: code_natural] : ( bit_se1148574629649215175it_nat @ ( code_nat_of_natural @ X ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5973_or__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se9127793120404214118atural @ X2 @ Xa ) )
% 8.60/4.61        = ( bit_se1412395901928357646or_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5974_xor__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se2046307713759805098atural @ X2 @ Xa ) )
% 8.60/4.61        = ( bit_se6528837805403552850or_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5975_natural__eq__iff,axiom,
% 8.60/4.61      ( ( ^ [Y3: code_natural,Z: code_natural] : ( Y3 = Z ) )
% 8.60/4.61      = ( ^ [M2: code_natural,N3: code_natural] :
% 8.60/4.61            ( ( code_nat_of_natural @ M2 )
% 8.60/4.61            = ( code_nat_of_natural @ N3 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5976_natural__eqI,axiom,
% 8.60/4.61      ! [M: code_natural,N: code_natural] :
% 8.60/4.61        ( ( ( code_nat_of_natural @ M )
% 8.60/4.61          = ( code_nat_of_natural @ N ) )
% 8.60/4.61       => ( M = N ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5977_nat__of__natural__inject,axiom,
% 8.60/4.61      ! [X2: code_natural,Y: code_natural] :
% 8.60/4.61        ( ( ( code_nat_of_natural @ X2 )
% 8.60/4.61          = ( code_nat_of_natural @ Y ) )
% 8.60/4.61        = ( X2 = Y ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5978_take__bit__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: nat,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se569199155075624693atural @ X2 @ Xa ) )
% 8.60/4.61        = ( bit_se2925701944663578781it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5979_and__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se2773287842338716102atural @ X2 @ Xa ) )
% 8.60/4.61        = ( bit_se727722235901077358nd_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5980_mask__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: nat] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se943457434206027407atural @ X2 ) )
% 8.60/4.61        = ( bit_se2002935070580805687sk_nat @ X2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5981_push__bit__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: nat,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se6611745700429515170atural @ X2 @ Xa ) )
% 8.60/4.61        = ( bit_se547839408752420682it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5982_set__bit__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: nat,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se1617098188084679374atural @ X2 @ Xa ) )
% 8.60/4.61        = ( bit_se7882103937844011126it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5983_unset__bit__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: nat,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se7083795435491715335atural @ X2 @ Xa ) )
% 8.60/4.61        = ( bit_se4205575877204974255it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5984_flip__bit__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: nat,Xa: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( bit_se168947363167071951atural @ X2 @ Xa ) )
% 8.60/4.61        = ( bit_se2161824704523386999it_nat @ X2 @ ( code_nat_of_natural @ Xa ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5985_Nat_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_integer] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( code_Nat @ X2 ) )
% 8.60/4.61        = ( nat2 @ ( code_int_of_integer @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5986_euclidean__size__natural__def,axiom,
% 8.60/4.61      ( euclid5200926497590043453atural
% 8.60/4.61      = ( map_fu226235371393106610at_nat @ code_nat_of_natural @ id_nat @ euclid4777050414544973029ze_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5987_bit__natural__def,axiom,
% 8.60/4.61      ( bit_se8040316288895769887atural
% 8.60/4.61      = ( map_fu6244533035418998608_nat_o @ code_nat_of_natural @ id_nat_o @ bit_se1148574629649215175it_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5988_less__eq__natural_Orep__eq,axiom,
% 8.60/4.61      ( ord_le1926595141338095240atural
% 8.60/4.61      = ( ^ [X: code_natural,Xa4: code_natural] : ( ord_less_eq_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5989_times__natural__def,axiom,
% 8.60/4.61      ( times_2397367101498566445atural
% 8.60/4.61      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ times_times_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5990_divide__natural__def,axiom,
% 8.60/4.61      ( divide5121882707175180666atural
% 8.60/4.61      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ divide_divide_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5991_take__bit__natural__def,axiom,
% 8.60/4.61      ( bit_se569199155075624693atural
% 8.60/4.61      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se2925701944663578781it_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5992_push__bit__natural__def,axiom,
% 8.60/4.61      ( bit_se6611745700429515170atural
% 8.60/4.61      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se547839408752420682it_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5993_less__eq__natural__def,axiom,
% 8.60/4.61      ( ord_le1926595141338095240atural
% 8.60/4.61      = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_eq_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5994_modulo__natural__def,axiom,
% 8.60/4.61      ( modulo8411746178871703098atural
% 8.60/4.61      = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ modulo_modulo_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5995_drop__bit__natural__def,axiom,
% 8.60/4.61      ( bit_se2751692689150723149atural
% 8.60/4.61      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se8570568707652914677it_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5996_flip__bit__natural__def,axiom,
% 8.60/4.61      ( bit_se168947363167071951atural
% 8.60/4.61      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se2161824704523386999it_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5997_set__bit__natural__def,axiom,
% 8.60/4.61      ( bit_se1617098188084679374atural
% 8.60/4.61      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se7882103937844011126it_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5998_unset__bit__natural__def,axiom,
% 8.60/4.61      ( bit_se7083795435491715335atural
% 8.60/4.61      = ( map_fu6981160461238011112atural @ id_nat @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ bit_se4205575877204974255it_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_5999_natural__decr,axiom,
% 8.60/4.61      ! [N: code_natural] :
% 8.60/4.61        ( ( N != zero_z2226904508553997617atural )
% 8.60/4.61       => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6000_Nat__def,axiom,
% 8.60/4.61      ( code_Nat
% 8.60/4.61      = ( map_fu1051355602067684763atural @ code_int_of_integer @ code_natural_of_nat @ nat2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6001_integer__of__natural_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural] :
% 8.60/4.61        ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ X2 ) )
% 8.60/4.61        = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6002_int__of__integer__of__natural,axiom,
% 8.60/4.61      ! [N: code_natural] :
% 8.60/4.61        ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ N ) )
% 8.60/4.61        = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6003_integer__of__natural__of__nat,axiom,
% 8.60/4.61      ! [N: nat] :
% 8.60/4.61        ( ( code_i5400310926305786745atural @ ( semiri3763490453095760265atural @ N ) )
% 8.60/4.61        = ( semiri4939895301339042750nteger @ N ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6004_integer__of__natural__def,axiom,
% 8.60/4.61      ( code_i5400310926305786745atural
% 8.60/4.61      = ( map_fu2787874002554666395nteger @ code_nat_of_natural @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6005_integer__of__natural_Oabs__eq,axiom,
% 8.60/4.61      ! [X2: nat] :
% 8.60/4.61        ( ( code_i5400310926305786745atural @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6006_integer__of__natural__of__integer,axiom,
% 8.60/4.61      ! [K: code_integer] :
% 8.60/4.61        ( ( code_i5400310926305786745atural @ ( code_n4118661773612635043nteger @ K ) )
% 8.60/4.61        = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6007_natural__of__integer__def,axiom,
% 8.60/4.61      ( code_n4118661773612635043nteger
% 8.60/4.61      = ( map_fu1051355602067684763atural @ code_int_of_integer @ code_natural_of_nat @ nat2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6008_natural__of__integer__of__natural,axiom,
% 8.60/4.61      ! [N: code_natural] :
% 8.60/4.61        ( ( code_n4118661773612635043nteger @ ( code_i5400310926305786745atural @ N ) )
% 8.60/4.61        = N ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6009_natural__of__integer_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_integer] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( code_n4118661773612635043nteger @ X2 ) )
% 8.60/4.61        = ( nat2 @ ( code_int_of_integer @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6010_natural__of__integer_Oabs__eq,axiom,
% 8.60/4.61      ! [X2: int] :
% 8.60/4.61        ( ( code_n4118661773612635043nteger @ ( code_integer_of_int @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( nat2 @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6011_Code__Numeral_Osize__nat__def,axiom,
% 8.60/4.61      code_size_nat = code_nat_of_natural ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6012_Code__Numeral_OSuc__def,axiom,
% 8.60/4.61      ( code_Suc
% 8.60/4.61      = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ suc ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6013_natural_Oinject,axiom,
% 8.60/4.61      ! [Natural: code_natural,Natural2: code_natural] :
% 8.60/4.61        ( ( ( code_Suc @ Natural )
% 8.60/4.61          = ( code_Suc @ Natural2 ) )
% 8.60/4.61        = ( Natural = Natural2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6014_Suc_Orep__eq,axiom,
% 8.60/4.61      ! [X2: code_natural] :
% 8.60/4.61        ( ( code_nat_of_natural @ ( code_Suc @ X2 ) )
% 8.60/4.61        = ( suc @ ( code_nat_of_natural @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6015_natural_Odistinct_I2_J,axiom,
% 8.60/4.61      ! [Natural2: code_natural] :
% 8.60/4.61        ( ( code_Suc @ Natural2 )
% 8.60/4.61       != zero_z2226904508553997617atural ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6016_natural_Odistinct_I1_J,axiom,
% 8.60/4.61      ! [Natural2: code_natural] :
% 8.60/4.61        ( zero_z2226904508553997617atural
% 8.60/4.61       != ( code_Suc @ Natural2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6017_natural_Oexhaust,axiom,
% 8.60/4.61      ! [Y: code_natural] :
% 8.60/4.61        ( ( Y != zero_z2226904508553997617atural )
% 8.60/4.61       => ~ ! [Natural3: code_natural] :
% 8.60/4.61              ( Y
% 8.60/4.61             != ( code_Suc @ Natural3 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6018_Suc_Oabs__eq,axiom,
% 8.60/4.61      ! [X2: nat] :
% 8.60/4.61        ( ( code_Suc @ ( code_natural_of_nat @ X2 ) )
% 8.60/4.61        = ( code_natural_of_nat @ ( suc @ X2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6019_Suc__natural__minus__one,axiom,
% 8.60/4.61      ! [N: code_natural] :
% 8.60/4.61        ( ( minus_7197305767214868737atural @ ( code_Suc @ N ) @ one_one_Code_natural )
% 8.60/4.61        = N ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6020_prod__decode__triangle__add,axiom,
% 8.60/4.61      ! [K: nat,M: nat] :
% 8.60/4.61        ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) )
% 8.60/4.61        = ( nat_prod_decode_aux @ K @ M ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6021_prod__decode__def,axiom,
% 8.60/4.61      ( nat_prod_decode
% 8.60/4.61      = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6022_list__decode_Oelims,axiom,
% 8.60/4.61      ! [X2: nat,Y: list_nat] :
% 8.60/4.61        ( ( ( nat_list_decode @ X2 )
% 8.60/4.61          = Y )
% 8.60/4.61       => ( ( ( X2 = zero_zero_nat )
% 8.60/4.61           => ( Y != nil_nat ) )
% 8.60/4.61         => ~ ! [N2: nat] :
% 8.60/4.61                ( ( X2
% 8.60/4.61                  = ( suc @ N2 ) )
% 8.60/4.61               => ( Y
% 8.60/4.61                 != ( produc2761476792215241774st_nat
% 8.60/4.61                    @ ^ [X: nat,Y4: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y4 ) )
% 8.60/4.61                    @ ( nat_prod_decode @ N2 ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6023_list__decode_Osimps_I2_J,axiom,
% 8.60/4.61      ! [N: nat] :
% 8.60/4.61        ( ( nat_list_decode @ ( suc @ N ) )
% 8.60/4.61        = ( produc2761476792215241774st_nat
% 8.60/4.61          @ ^ [X: nat,Y4: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y4 ) )
% 8.60/4.61          @ ( nat_prod_decode @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6024_list__decode_Osimps_I1_J,axiom,
% 8.60/4.61      ( ( nat_list_decode @ zero_zero_nat )
% 8.60/4.61      = nil_nat ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6025_list__decode_Opelims,axiom,
% 8.60/4.61      ! [X2: nat,Y: list_nat] :
% 8.60/4.61        ( ( ( nat_list_decode @ X2 )
% 8.60/4.61          = Y )
% 8.60/4.61       => ( ( accp_nat @ nat_list_decode_rel @ X2 )
% 8.60/4.61         => ( ( ( X2 = zero_zero_nat )
% 8.60/4.61             => ( ( Y = nil_nat )
% 8.60/4.61               => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 8.60/4.61           => ~ ! [N2: nat] :
% 8.60/4.61                  ( ( X2
% 8.60/4.61                    = ( suc @ N2 ) )
% 8.60/4.61                 => ( ( Y
% 8.60/4.61                      = ( produc2761476792215241774st_nat
% 8.60/4.61                        @ ^ [X: nat,Y4: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y4 ) )
% 8.60/4.61                        @ ( nat_prod_decode @ N2 ) ) )
% 8.60/4.61                   => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6026_list__decode_Opsimps_I1_J,axiom,
% 8.60/4.61      ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 8.60/4.61     => ( ( nat_list_decode @ zero_zero_nat )
% 8.60/4.61        = nil_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6027_list__decode_Opinduct,axiom,
% 8.60/4.61      ! [A0: nat,P: nat > $o] :
% 8.60/4.61        ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 8.60/4.61       => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 8.60/4.61           => ( P @ zero_zero_nat ) )
% 8.60/4.61         => ( ! [N2: nat] :
% 8.60/4.61                ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 8.60/4.61               => ( ! [X4: nat,Y5: nat] :
% 8.60/4.61                      ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 8.60/4.61                        = ( nat_prod_decode @ N2 ) )
% 8.60/4.61                     => ( P @ Y5 ) )
% 8.60/4.61                 => ( P @ ( suc @ N2 ) ) ) )
% 8.60/4.61           => ( P @ A0 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6028_list__decode_Opsimps_I2_J,axiom,
% 8.60/4.61      ! [N: nat] :
% 8.60/4.61        ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 8.60/4.61       => ( ( nat_list_decode @ ( suc @ N ) )
% 8.60/4.61          = ( produc2761476792215241774st_nat
% 8.60/4.61            @ ^ [X: nat,Y4: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y4 ) )
% 8.60/4.61            @ ( nat_prod_decode @ N ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6029_Code__Numeral_Osub__code_I4_J,axiom,
% 8.60/4.61      ! [N: num] :
% 8.60/4.61        ( ( code_sub @ one @ ( bit0 @ N ) )
% 8.60/4.61        = ( code_Neg @ ( bitM @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6030_less__eq__integer__code_I9_J,axiom,
% 8.60/4.61      ! [K: num,L: num] :
% 8.60/4.61        ( ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 8.60/4.61        = ( ord_less_eq_num @ L @ K ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6031_less__eq__integer__code_I3_J,axiom,
% 8.60/4.61      ! [L: num] :
% 8.60/4.61        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6032_less__eq__integer__code_I7_J,axiom,
% 8.60/4.61      ! [K: num] : ( ord_le3102999989581377725nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6033_minus__integer__code_I6_J,axiom,
% 8.60/4.61      ! [M: num,N: num] :
% 8.60/4.61        ( ( minus_8373710615458151222nteger @ ( code_Neg @ M ) @ ( code_Neg @ N ) )
% 8.60/4.61        = ( code_sub @ N @ M ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6034_Code__Numeral_Odup__code_I3_J,axiom,
% 8.60/4.61      ! [N: num] :
% 8.60/4.61        ( ( code_dup @ ( code_Neg @ N ) )
% 8.60/4.61        = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6035_less__integer__code_I9_J,axiom,
% 8.60/4.61      ! [K: num,L: num] :
% 8.60/4.61        ( ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 8.60/4.61        = ( ord_less_num @ L @ K ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6036_plus__integer__code_I6_J,axiom,
% 8.60/4.61      ! [M: num,N: num] :
% 8.60/4.61        ( ( plus_p5714425477246183910nteger @ ( code_Neg @ M ) @ ( code_Neg @ N ) )
% 8.60/4.61        = ( code_Neg @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6037_less__integer__code_I7_J,axiom,
% 8.60/4.61      ! [K: num] : ( ord_le6747313008572928689nteger @ ( code_Neg @ K ) @ zero_z3403309356797280102nteger ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6038_less__integer__code_I3_J,axiom,
% 8.60/4.61      ! [L: num] :
% 8.60/4.61        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( code_Neg @ L ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6039_divmod__abs__code_I2_J,axiom,
% 8.60/4.61      ! [K: num,L: num] :
% 8.60/4.61        ( ( code_divmod_abs @ ( code_Neg @ K ) @ ( code_Neg @ L ) )
% 8.60/4.61        = ( unique3479559517661332726nteger @ K @ L ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6040_Code__Numeral_Osub__code_I5_J,axiom,
% 8.60/4.61      ! [N: num] :
% 8.60/4.61        ( ( code_sub @ one @ ( bit1 @ N ) )
% 8.60/4.61        = ( code_Neg @ ( bit0 @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6041_Gcd__int__set__eq__fold,axiom,
% 8.60/4.61      ! [Xs: list_int] :
% 8.60/4.61        ( ( gcd_Gcd_int @ ( set_int2 @ Xs ) )
% 8.60/4.61        = ( fold_int_int @ gcd_gcd_int @ Xs @ zero_zero_int ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6042_int_Oid__abs__transfer,axiom,
% 8.60/4.61      ( bNF_re7934895593101944656at_int
% 8.60/4.61      @ ( basic_5328504652464829177at_nat
% 8.60/4.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61        @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.61      @ pcr_int
% 8.60/4.61      @ ^ [X: product_prod_nat_nat] : X
% 8.60/4.61      @ abs_Integ ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6043_rat_Odomain,axiom,
% 8.60/4.61      ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 8.60/4.61      = ( ^ [X: product_prod_int_int] :
% 8.60/4.61          ? [Y4: product_prod_int_int] :
% 8.60/4.61            ( ( basic_4387203522000727145nt_int
% 8.60/4.61              @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61              @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61              @ X
% 8.60/4.61              @ Y4 )
% 8.60/4.61            & ( ratrel @ Y4 @ Y4 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6044_rat_Odomain__par,axiom,
% 8.60/4.61      ! [DR1: int > $o,DR2: int > $o,P22: product_prod_int_int > $o] :
% 8.60/4.61        ( ( ( domainp_int_int
% 8.60/4.61            @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.61          = DR1 )
% 8.60/4.61       => ( ( ( domainp_int_int
% 8.60/4.61              @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.61            = DR2 )
% 8.60/4.61         => ( ( bNF_re8699439704749558557nt_o_o
% 8.60/4.61              @ ( basic_4387203522000727145nt_int
% 8.60/4.61                @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61                @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.61              @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 8.60/4.61              @ P22
% 8.60/4.61              @ ^ [X: product_prod_int_int] : ( ratrel @ X @ X ) )
% 8.60/4.61           => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 8.60/4.61              = ( inf_in3604695632404883862_int_o @ ( basic_1567116559311922317nt_int @ DR1 @ DR2 ) @ P22 ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6045_rat_Odomain__par__left__total,axiom,
% 8.60/4.61      ! [P2: product_prod_int_int > $o] :
% 8.60/4.61        ( ( left_t3131394472396969446nt_int
% 8.60/4.61          @ ( basic_4387203522000727145nt_int
% 8.60/4.61            @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61            @ ^ [Y3: int,Z: int] : ( Y3 = Z ) ) )
% 8.60/4.61       => ( ( bNF_re8699439704749558557nt_o_o
% 8.60/4.61            @ ( basic_4387203522000727145nt_int
% 8.60/4.61              @ ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61              @ ^ [Y3: int,Z: int] : ( Y3 = Z ) )
% 8.60/4.61            @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 8.60/4.61            @ P2
% 8.60/4.61            @ ^ [X: product_prod_int_int] : ( ratrel @ X @ X ) )
% 8.60/4.61         => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 8.60/4.61            = P2 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6046_Gcd__nat__set__eq__fold,axiom,
% 8.60/4.61      ! [Xs: list_nat] :
% 8.60/4.61        ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs ) )
% 8.60/4.61        = ( fold_nat_nat @ gcd_gcd_nat @ Xs @ zero_zero_nat ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6047_Abs__rat__cases,axiom,
% 8.60/4.61      ! [X2: rat] :
% 8.60/4.61        ~ ! [Y2: set_Pr958786334691620121nt_int] :
% 8.60/4.61            ( ( X2
% 8.60/4.61              = ( abs_rat @ Y2 ) )
% 8.60/4.61           => ~ ( member2340774599025711042nt_int @ Y2
% 8.60/4.61                @ ( collec5210948495886036740nt_int
% 8.60/4.61                  @ ^ [C4: set_Pr958786334691620121nt_int] :
% 8.60/4.61                    ? [X: product_prod_int_int] :
% 8.60/4.61                      ( ( ratrel @ X @ X )
% 8.60/4.61                      & ( C4
% 8.60/4.61                        = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6048_Abs__rat__induct,axiom,
% 8.60/4.61      ! [P: rat > $o,X2: rat] :
% 8.60/4.61        ( ! [Y2: set_Pr958786334691620121nt_int] :
% 8.60/4.61            ( ( member2340774599025711042nt_int @ Y2
% 8.60/4.61              @ ( collec5210948495886036740nt_int
% 8.60/4.61                @ ^ [C4: set_Pr958786334691620121nt_int] :
% 8.60/4.61                  ? [X: product_prod_int_int] :
% 8.60/4.61                    ( ( ratrel @ X @ X )
% 8.60/4.61                    & ( C4
% 8.60/4.61                      = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 8.60/4.61           => ( P @ ( abs_rat @ Y2 ) ) )
% 8.60/4.61       => ( P @ X2 ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6049_int_Odomain,axiom,
% 8.60/4.61      ! [DR1: nat > $o,DR2: nat > $o] :
% 8.60/4.61        ( ( ( domainp_nat_nat
% 8.60/4.61            @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.61          = DR1 )
% 8.60/4.61       => ( ( ( domainp_nat_nat
% 8.60/4.61              @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.61            = DR2 )
% 8.60/4.61         => ( ( domain7287725470393535433at_int @ pcr_int )
% 8.60/4.61            = ( basic_570253317919918037at_nat @ DR1 @ DR2 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6050_Abs__rat__inject,axiom,
% 8.60/4.61      ! [X2: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
% 8.60/4.61        ( ( member2340774599025711042nt_int @ X2
% 8.60/4.61          @ ( collec5210948495886036740nt_int
% 8.60/4.61            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 8.60/4.61              ? [X: product_prod_int_int] :
% 8.60/4.61                ( ( ratrel @ X @ X )
% 8.60/4.61                & ( C4
% 8.60/4.61                  = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 8.60/4.61       => ( ( member2340774599025711042nt_int @ Y
% 8.60/4.61            @ ( collec5210948495886036740nt_int
% 8.60/4.61              @ ^ [C4: set_Pr958786334691620121nt_int] :
% 8.60/4.61                ? [X: product_prod_int_int] :
% 8.60/4.61                  ( ( ratrel @ X @ X )
% 8.60/4.61                  & ( C4
% 8.60/4.61                    = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 8.60/4.61         => ( ( ( abs_rat @ X2 )
% 8.60/4.61              = ( abs_rat @ Y ) )
% 8.60/4.61            = ( X2 = Y ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6051_Abs__rat__inverse,axiom,
% 8.60/4.61      ! [Y: set_Pr958786334691620121nt_int] :
% 8.60/4.61        ( ( member2340774599025711042nt_int @ Y
% 8.60/4.61          @ ( collec5210948495886036740nt_int
% 8.60/4.61            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 8.60/4.61              ? [X: product_prod_int_int] :
% 8.60/4.61                ( ( ratrel @ X @ X )
% 8.60/4.61                & ( C4
% 8.60/4.61                  = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 8.60/4.61       => ( ( rep_rat @ ( abs_rat @ Y ) )
% 8.60/4.61          = Y ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6052_type__definition__rat,axiom,
% 8.60/4.61      ( type_d8554052265237484179nt_int @ rep_rat @ abs_rat
% 8.60/4.61      @ ( collec5210948495886036740nt_int
% 8.60/4.61        @ ^ [C4: set_Pr958786334691620121nt_int] :
% 8.60/4.61          ? [X: product_prod_int_int] :
% 8.60/4.61            ( ( ratrel @ X @ X )
% 8.60/4.61            & ( C4
% 8.60/4.61              = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6053_Rep__rat,axiom,
% 8.60/4.61      ! [X2: rat] :
% 8.60/4.61        ( member2340774599025711042nt_int @ ( rep_rat @ X2 )
% 8.60/4.61        @ ( collec5210948495886036740nt_int
% 8.60/4.61          @ ^ [C4: set_Pr958786334691620121nt_int] :
% 8.60/4.61            ? [X: product_prod_int_int] :
% 8.60/4.61              ( ( ratrel @ X @ X )
% 8.60/4.61              & ( C4
% 8.60/4.61                = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6054_Rep__rat__cases,axiom,
% 8.60/4.61      ! [Y: set_Pr958786334691620121nt_int] :
% 8.60/4.61        ( ( member2340774599025711042nt_int @ Y
% 8.60/4.61          @ ( collec5210948495886036740nt_int
% 8.60/4.61            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 8.60/4.61              ? [X: product_prod_int_int] :
% 8.60/4.61                ( ( ratrel @ X @ X )
% 8.60/4.61                & ( C4
% 8.60/4.61                  = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 8.60/4.61       => ~ ! [X3: rat] :
% 8.60/4.61              ( Y
% 8.60/4.61             != ( rep_rat @ X3 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6055_Rep__rat__induct,axiom,
% 8.60/4.61      ! [Y: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 8.60/4.61        ( ( member2340774599025711042nt_int @ Y
% 8.60/4.61          @ ( collec5210948495886036740nt_int
% 8.60/4.61            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 8.60/4.61              ? [X: product_prod_int_int] :
% 8.60/4.61                ( ( ratrel @ X @ X )
% 8.60/4.61                & ( C4
% 8.60/4.61                  = ( collec213857154873943460nt_int @ ( ratrel @ X ) ) ) ) ) )
% 8.60/4.61       => ( ! [X3: rat] : ( P @ ( rep_rat @ X3 ) )
% 8.60/4.61         => ( P @ Y ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6056_pcr__int__def,axiom,
% 8.60/4.61      ( pcr_int
% 8.60/4.61      = ( relcom8911704206367525917at_int
% 8.60/4.61        @ ( basic_5328504652464829177at_nat
% 8.60/4.61          @ ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 8.60/4.61          @ ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
% 8.60/4.61        @ cr_int ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6057_int_Opcr__cr__eq,axiom,
% 8.60/4.61      pcr_int = cr_int ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6058_cr__int__def,axiom,
% 8.60/4.61      ( cr_int
% 8.60/4.61      = ( ^ [X: product_prod_nat_nat] :
% 8.60/4.61            ( ^ [Y3: int,Z: int] : ( Y3 = Z )
% 8.60/4.61            @ ( abs_Integ @ X ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6059_Quotient__int,axiom,
% 8.60/4.61      quotie1194848508323700631at_int @ intrel @ abs_Integ @ rep_Integ @ cr_int ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6060_lcm__code__integer,axiom,
% 8.60/4.61      ( gcd_lcm_Code_integer
% 8.60/4.61      = ( ^ [A2: code_integer,B2: code_integer] : ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B2 ) ) @ ( gcd_gcd_Code_integer @ A2 @ B2 ) ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6061_lcm__0__iff__nat,axiom,
% 8.60/4.61      ! [M: nat,N: nat] :
% 8.60/4.61        ( ( ( gcd_lcm_nat @ M @ N )
% 8.60/4.61          = zero_zero_nat )
% 8.60/4.61        = ( ( M = zero_zero_nat )
% 8.60/4.61          | ( N = zero_zero_nat ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6062_lcm__0__iff__int,axiom,
% 8.60/4.61      ! [M: int,N: int] :
% 8.60/4.61        ( ( ( gcd_lcm_int @ M @ N )
% 8.60/4.61          = zero_zero_int )
% 8.60/4.61        = ( ( M = zero_zero_int )
% 8.60/4.61          | ( N = zero_zero_int ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6063_lcm__proj2__if__dvd__nat,axiom,
% 8.60/4.61      ! [X2: nat,Y: nat] :
% 8.60/4.61        ( ( dvd_dvd_nat @ X2 @ Y )
% 8.60/4.61       => ( ( gcd_lcm_nat @ X2 @ Y )
% 8.60/4.61          = Y ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6064_lcm__proj1__if__dvd__nat,axiom,
% 8.60/4.61      ! [X2: nat,Y: nat] :
% 8.60/4.61        ( ( dvd_dvd_nat @ X2 @ Y )
% 8.60/4.61       => ( ( gcd_lcm_nat @ Y @ X2 )
% 8.60/4.61          = Y ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6065_lcm__proj2__iff__nat,axiom,
% 8.60/4.61      ! [M: nat,N: nat] :
% 8.60/4.61        ( ( ( gcd_lcm_nat @ M @ N )
% 8.60/4.61          = N )
% 8.60/4.61        = ( dvd_dvd_nat @ M @ N ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6066_lcm__proj1__iff__nat,axiom,
% 8.60/4.61      ! [M: nat,N: nat] :
% 8.60/4.61        ( ( ( gcd_lcm_nat @ M @ N )
% 8.60/4.61          = M )
% 8.60/4.61        = ( dvd_dvd_nat @ N @ M ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6067_lcm__int__int__eq,axiom,
% 8.60/4.61      ! [M: nat,N: nat] :
% 8.60/4.61        ( ( gcd_lcm_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.60/4.61        = ( semiri1314217659103216013at_int @ ( gcd_lcm_nat @ M @ N ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6068_abs__lcm__int,axiom,
% 8.60/4.61      ! [I: int,J: int] :
% 8.60/4.61        ( ( abs_abs_int @ ( gcd_lcm_int @ I @ J ) )
% 8.60/4.61        = ( gcd_lcm_int @ I @ J ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6069_lcm__abs1__int,axiom,
% 8.60/4.61      ! [X2: int,Y: int] :
% 8.60/4.61        ( ( gcd_lcm_int @ ( abs_abs_int @ X2 ) @ Y )
% 8.60/4.61        = ( gcd_lcm_int @ X2 @ Y ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(fact_6070_lcm__abs2__int,axiom,
% 8.60/4.61      ! [X2: int,Y: int] :
% 8.60/4.61        ( ( gcd_lcm_int @ X2 @ ( abs_abs_int @ Y ) )
% 8.60/4.61        = ( gcd_lcm_int @ X2 @ Y ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 8.60/4.61      ! [X2: int,Y: int] :
% 8.60/4.61        ( ( if_int @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 8.60/4.61      ! [X2: int,Y: int] :
% 8.60/4.61        ( ( if_int @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 8.60/4.61      ! [X2: nat,Y: nat] :
% 8.60/4.61        ( ( if_nat @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 8.60/4.61      ! [X2: nat,Y: nat] :
% 8.60/4.61        ( ( if_nat @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 8.60/4.61      ! [X2: num,Y: num] :
% 8.60/4.61        ( ( if_num @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 8.60/4.61      ! [X2: num,Y: num] :
% 8.60/4.61        ( ( if_num @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 8.60/4.61      ! [X2: rat,Y: rat] :
% 8.60/4.61        ( ( if_rat @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 8.60/4.61      ! [X2: rat,Y: rat] :
% 8.60/4.61        ( ( if_rat @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_fChoice_1_1_fChoice_001t__Int__Oint_T,axiom,
% 8.60/4.61      ! [P: int > $o] :
% 8.60/4.61        ( ( P @ ( fChoice_int @ P ) )
% 8.60/4.61        = ( ? [X5: int] : ( P @ X5 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_fChoice_1_1_fChoice_001t__Nat__Onat_T,axiom,
% 8.60/4.61      ! [P: nat > $o] :
% 8.60/4.61        ( ( P @ ( fChoice_nat @ P ) )
% 8.60/4.61        = ( ? [X5: nat] : ( P @ X5 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 8.60/4.61      ! [X2: code_integer,Y: code_integer] :
% 8.60/4.61        ( ( if_Code_integer @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 8.60/4.61      ! [X2: code_integer,Y: code_integer] :
% 8.60/4.61        ( ( if_Code_integer @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 8.60/4.61      ! [X2: code_natural,Y: code_natural] :
% 8.60/4.61        ( ( if_Code_natural @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 8.60/4.61      ! [X2: code_natural,Y: code_natural] :
% 8.60/4.61        ( ( if_Code_natural @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 8.60/4.61      ! [X2: set_int,Y: set_int] :
% 8.60/4.61        ( ( if_set_int @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 8.60/4.61      ! [X2: set_int,Y: set_int] :
% 8.60/4.61        ( ( if_set_int @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 8.60/4.61      ! [X2: list_int,Y: list_int] :
% 8.60/4.61        ( ( if_list_int @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 8.60/4.61      ! [X2: list_int,Y: list_int] :
% 8.60/4.61        ( ( if_list_int @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_fChoice_1_1_fChoice_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 8.60/4.61      ! [P: set_nat > $o] :
% 8.60/4.61        ( ( P @ ( fChoice_set_nat @ P ) )
% 8.60/4.61        = ( ? [X5: set_nat] : ( P @ X5 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 8.60/4.61      ! [X2: option_num,Y: option_num] :
% 8.60/4.61        ( ( if_option_num @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 8.60/4.61      ! [X2: option_num,Y: option_num] :
% 8.60/4.61        ( ( if_option_num @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_Itf__a_J_T,axiom,
% 8.60/4.61      ! [X2: heap_Time_Heap_a,Y: heap_Time_Heap_a] :
% 8.60/4.61        ( ( if_Heap_Time_Heap_a @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_Itf__a_J_T,axiom,
% 8.60/4.61      ! [X2: heap_Time_Heap_a,Y: heap_Time_Heap_a] :
% 8.60/4.61        ( ( if_Heap_Time_Heap_a @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.60/4.61      ! [X2: product_prod_int_int,Y: product_prod_int_int] :
% 8.60/4.61        ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.60/4.61      ! [X2: product_prod_int_int,Y: product_prod_int_int] :
% 8.60/4.61        ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.60/4.61      ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.60/4.61        ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.60/4.61      ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.60/4.61        ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_T,axiom,
% 8.60/4.61      ! [X2: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 8.60/4.61        ( ( if_Hea8138950348631371857t_unit @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_T,axiom,
% 8.60/4.61      ! [X2: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
% 8.60/4.61        ( ( if_Hea8138950348631371857t_unit @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_fChoice_1_1_fChoice_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.60/4.61      ! [P: product_prod_nat_nat > $o] :
% 8.60/4.61        ( ( P @ ( fChoic6978938873391328853at_nat @ P ) )
% 8.60/4.61        = ( ? [X5: product_prod_nat_nat] : ( P @ X5 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 8.60/4.61      ! [X2: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 8.60/4.61        ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 8.60/4.61      ! [X2: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 8.60/4.61        ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_fChoice_1_1_fChoice_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 8.60/4.61      ! [P: set_Pr958786334691620121nt_int > $o] :
% 8.60/4.61        ( ( P @ ( fChoic2749331249758569069nt_int @ P ) )
% 8.60/4.61        = ( ? [X5: set_Pr958786334691620121nt_int] : ( P @ X5 ) ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.60/4.61      ! [P: $o] :
% 8.60/4.61        ( ( P = $true )
% 8.60/4.61        | ( P = $false ) ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.60/4.61      ! [X2: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 8.60/4.61        ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y )
% 8.60/4.61        = Y ) ).
% 8.60/4.61  
% 8.60/4.61  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.60/4.61      ! [X2: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 8.60/4.61        ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y )
% 8.60/4.61        = X2 ) ).
% 8.60/4.61  
% 8.60/4.61  thf(conj_0,conjecture,
% 8.60/4.61      ( ord_less_eq_nat
% 8.60/4.61      @ ( time_time_a
% 8.60/4.61        @ ( heap_T757603679106148408unit_a @ ( refine_Imp_assert @ p )
% 8.60/4.61          @ ^ [Uu: product_unit] : m )
% 8.60/4.61        @ h )
% 8.60/4.61      @ t ) ).
% 8.60/4.61  ------------------------
% 8.60/5.00  % (31295)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_31173 for (2996ds/4Mi)
% 8.60/5.00  % (31298)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_31173 for (2996ds/2Mi)
% 8.60/5.00  % (31299)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_31173 for (2996ds/275Mi)
% 8.60/5.00  % (31296)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_31173 for (2996ds/27Mi)
% 8.60/5.00  % (31294)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31173 for (2996ds/183Mi)
% 8.60/5.00  % (31300)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31173 for (2996ds/18Mi)
% 8.60/5.00  % (31297)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31173 for (2996ds/2Mi)
% 8.60/5.00  % (31298)Instruction limit reached!
% 8.60/5.00  % (31298)------------------------------
% 8.60/5.00  % (31298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/5.00  % (31298)Termination reason: Unknown
% 8.60/5.00  % (31298)Termination phase: shuffling
% 8.60/5.00  
% 8.60/5.00  % (31298)Memory used [KB]: 7931
% 8.60/5.00  % (31298)Time elapsed: 0.004 s
% 8.60/5.00  % (31298)Instructions burned: 2 (million)
% 8.60/5.00  % (31298)------------------------------
% 8.60/5.00  % (31298)------------------------------
% 8.60/5.00  % (31297)Instruction limit reached!
% 8.60/5.00  % (31297)------------------------------
% 8.60/5.00  % (31297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/5.00  % (31297)Termination reason: Unknown
% 8.60/5.00  % (31297)Termination phase: shuffling
% 8.60/5.00  
% 8.60/5.00  % (31297)Memory used [KB]: 7931
% 8.60/5.00  % (31297)Time elapsed: 0.003 s
% 8.60/5.00  % (31297)Instructions burned: 2 (million)
% 8.60/5.00  % (31297)------------------------------
% 8.60/5.00  % (31297)------------------------------
% 8.60/5.00  % (31295)Instruction limit reached!
% 8.60/5.00  % (31295)------------------------------
% 8.60/5.00  % (31295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/5.00  % (31295)Termination reason: Unknown
% 8.60/5.00  % (31295)Termination phase: shuffling
% 8.60/5.00  
% 8.60/5.00  % (31295)Memory used [KB]: 8059
% 8.60/5.00  % (31295)Time elapsed: 0.006 s
% 8.60/5.00  % (31295)Instructions burned: 4 (million)
% 8.60/5.00  % (31295)------------------------------
% 8.60/5.00  % (31295)------------------------------
% 8.60/5.01  % (31300)Instruction limit reached!
% 8.60/5.01  % (31300)------------------------------
% 8.60/5.01  % (31300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/5.01  % (31300)Termination reason: Unknown
% 8.60/5.01  % (31300)Termination phase: shuffling
% 8.60/5.01  
% 8.60/5.01  % (31300)Memory used [KB]: 8571
% 8.60/5.01  % (31300)Time elapsed: 0.015 s
% 8.60/5.01  % (31300)Instructions burned: 19 (million)
% 8.60/5.01  % (31300)------------------------------
% 8.60/5.01  % (31300)------------------------------
% 8.60/5.02  % (31296)Instruction limit reached!
% 8.60/5.02  % (31296)------------------------------
% 8.60/5.02  % (31296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/5.02  % (31296)Termination reason: Unknown
% 8.60/5.02  % (31296)Termination phase: shuffling
% 8.60/5.02  
% 8.60/5.02  % (31296)Memory used [KB]: 8699
% 8.60/5.02  % (31296)Time elapsed: 0.020 s
% 8.60/5.02  % (31296)Instructions burned: 27 (million)
% 8.60/5.02  % (31296)------------------------------
% 8.60/5.02  % (31296)------------------------------
% 8.60/5.02  % (31302)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_31173 for (2996ds/37Mi)
% 8.60/5.02  % (31303)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_31173 for (2996ds/15Mi)
% 8.60/5.02  % (31301)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31173 for (2996ds/3Mi)
% 8.60/5.02  % (31301)Instruction limit reached!
% 8.60/5.02  % (31301)------------------------------
% 8.60/5.02  % (31301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/5.02  % (31301)Termination reason: Unknown
% 8.60/5.02  % (31301)Termination phase: shuffling
% 8.60/5.02  
% 8.60/5.02  % (31301)Memory used [KB]: 8059
% 8.60/5.02  % (31301)Time elapsed: 0.004 s
% 8.60/5.03  % (31301)Instructions burned: 3 (million)
% 8.60/5.03  % (31301)------------------------------
% 8.60/5.03  % (31301)------------------------------
% 9.15/5.03  % (31304)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_31173 for (2996ds/3Mi)
% 9.15/5.03  % (31303)Instruction limit reached!
% 9.15/5.03  % (31303)------------------------------
% 9.15/5.03  % (31303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.03  % (31303)Termination reason: Unknown
% 9.15/5.03  % (31303)Termination phase: shuffling
% 9.15/5.03  
% 9.15/5.03  % (31303)Memory used [KB]: 8571
% 9.15/5.03  % (31303)Time elapsed: 0.014 s
% 9.15/5.03  % (31303)Instructions burned: 15 (million)
% 9.15/5.03  % (31303)------------------------------
% 9.15/5.03  % (31303)------------------------------
% 9.15/5.03  % (31304)Instruction limit reached!
% 9.15/5.03  % (31304)------------------------------
% 9.15/5.03  % (31304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.03  % (31304)Termination reason: Unknown
% 9.15/5.03  % (31304)Termination phase: shuffling
% 9.15/5.03  
% 9.15/5.03  % (31304)Memory used [KB]: 7931
% 9.15/5.03  % (31304)Time elapsed: 0.004 s
% 9.15/5.03  % (31304)Instructions burned: 3 (million)
% 9.15/5.03  % (31304)------------------------------
% 9.15/5.03  % (31304)------------------------------
% 9.15/5.04  % (31305)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_31173 for (2995ds/1041Mi)
% 9.15/5.04  % (31306)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31173 for (2995ds/7Mi)
% 9.15/5.04  % (31302)Instruction limit reached!
% 9.15/5.04  % (31302)------------------------------
% 9.15/5.04  % (31302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.04  % (31302)Termination reason: Unknown
% 9.15/5.04  % (31302)Termination phase: shuffling
% 9.15/5.04  
% 9.15/5.04  % (31302)Memory used [KB]: 8955
% 9.15/5.04  % (31302)Time elapsed: 0.025 s
% 9.15/5.04  % (31302)Instructions burned: 38 (million)
% 9.15/5.04  % (31302)------------------------------
% 9.15/5.04  % (31302)------------------------------
% 9.15/5.05  % (31306)Instruction limit reached!
% 9.15/5.05  % (31306)------------------------------
% 9.15/5.05  % (31306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.05  % (31306)Termination reason: Unknown
% 9.15/5.05  % (31306)Termination phase: shuffling
% 9.15/5.05  
% 9.15/5.05  % (31306)Memory used [KB]: 8443
% 9.15/5.05  % (31306)Time elapsed: 0.009 s
% 9.15/5.05  % (31306)Instructions burned: 7 (million)
% 9.15/5.05  % (31306)------------------------------
% 9.15/5.05  % (31306)------------------------------
% 9.15/5.05  % (31307)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31173 for (2995ds/16Mi)
% 9.15/5.05  % (31308)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_31173 for (2995ds/3Mi)
% 9.15/5.05  % (31308)Instruction limit reached!
% 9.15/5.05  % (31308)------------------------------
% 9.15/5.05  % (31308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.05  % (31308)Termination reason: Unknown
% 9.15/5.05  % (31308)Termination phase: shuffling
% 9.15/5.05  
% 9.15/5.05  % (31308)Memory used [KB]: 7931
% 9.15/5.05  % (31308)Time elapsed: 0.004 s
% 9.15/5.05  % (31308)Instructions burned: 3 (million)
% 9.15/5.05  % (31308)------------------------------
% 9.15/5.05  % (31308)------------------------------
% 9.15/5.06  % (31309)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_31173 for (2995ds/3Mi)
% 9.15/5.06  % (31307)Instruction limit reached!
% 9.15/5.06  % (31307)------------------------------
% 9.15/5.06  % (31307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.06  % (31309)Instruction limit reached!
% 9.15/5.06  % (31309)------------------------------
% 9.15/5.06  % (31309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.06  % (31309)Termination reason: Unknown
% 9.15/5.06  % (31309)Termination phase: shuffling
% 9.15/5.06  
% 9.15/5.06  % (31309)Memory used [KB]: 7931
% 9.15/5.06  % (31309)Time elapsed: 0.004 s
% 9.15/5.06  % (31309)Instructions burned: 3 (million)
% 9.15/5.06  % (31309)------------------------------
% 9.15/5.06  % (31309)------------------------------
% 9.15/5.06  % (31307)Termination reason: Unknown
% 9.15/5.06  % (31307)Termination phase: shuffling
% 9.15/5.06  
% 9.15/5.06  % (31307)Memory used [KB]: 8571
% 9.15/5.06  % (31307)Time elapsed: 0.015 s
% 9.15/5.06  % (31307)Instructions burned: 16 (million)
% 9.15/5.06  % (31307)------------------------------
% 9.15/5.06  % (31307)------------------------------
% 9.15/5.07  % (31310)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31173 for (2995ds/7Mi)
% 9.15/5.07  % (31311)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31173 for (2995ds/3Mi)
% 9.15/5.07  % (31311)Instruction limit reached!
% 9.15/5.07  % (31311)------------------------------
% 9.15/5.07  % (31311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.07  % (31311)Termination reason: Unknown
% 9.15/5.07  % (31311)Termination phase: shuffling
% 9.15/5.07  
% 9.15/5.07  % (31311)Memory used [KB]: 8059
% 9.15/5.07  % (31311)Time elapsed: 0.005 s
% 9.15/5.07  % (31311)Instructions burned: 3 (million)
% 9.15/5.07  % (31311)------------------------------
% 9.15/5.07  % (31311)------------------------------
% 9.15/5.07  % (31310)Instruction limit reached!
% 9.15/5.07  % (31310)------------------------------
% 9.15/5.07  % (31310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.07  % (31310)Termination reason: Unknown
% 9.15/5.07  % (31310)Termination phase: shuffling
% 9.15/5.07  
% 9.15/5.07  % (31310)Memory used [KB]: 8315
% 9.15/5.07  % (31310)Time elapsed: 0.009 s
% 9.15/5.07  % (31310)Instructions burned: 7 (million)
% 9.15/5.07  % (31310)------------------------------
% 9.15/5.07  % (31310)------------------------------
% 9.15/5.08  % (31313)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31173 for (2995ds/18Mi)
% 9.15/5.08  % (31312)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31173 for (2995ds/4Mi)
% 9.15/5.09  % (31312)Instruction limit reached!
% 9.15/5.09  % (31312)------------------------------
% 9.15/5.09  % (31312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.09  % (31312)Termination reason: Unknown
% 9.15/5.09  % (31312)Termination phase: shuffling
% 9.15/5.09  
% 9.15/5.09  % (31312)Memory used [KB]: 8059
% 9.15/5.09  % (31312)Time elapsed: 0.006 s
% 9.15/5.09  % (31312)Instructions burned: 4 (million)
% 9.15/5.09  % (31312)------------------------------
% 9.15/5.09  % (31312)------------------------------
% 9.15/5.09  % (31314)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31173 for (2995ds/710Mi)
% 9.15/5.09  % (31315)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31173 for (2995ds/6Mi)
% 9.15/5.10  % (31313)Instruction limit reached!
% 9.15/5.10  % (31313)------------------------------
% 9.15/5.10  % (31313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.10  % (31313)Termination reason: Unknown
% 9.15/5.10  % (31313)Termination phase: shuffling
% 9.15/5.10  
% 9.15/5.10  % (31313)Memory used [KB]: 8571
% 9.15/5.10  % (31313)Time elapsed: 0.016 s
% 9.15/5.10  % (31313)Instructions burned: 18 (million)
% 9.15/5.10  % (31313)------------------------------
% 9.15/5.10  % (31313)------------------------------
% 9.15/5.10  % (31315)Instruction limit reached!
% 9.15/5.10  % (31315)------------------------------
% 9.15/5.10  % (31315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.10  % (31315)Termination reason: Unknown
% 9.15/5.10  % (31315)Termination phase: shuffling
% 9.15/5.10  
% 9.15/5.10  % (31315)Memory used [KB]: 8187
% 9.15/5.10  % (31315)Time elapsed: 0.008 s
% 9.15/5.10  % (31315)Instructions burned: 6 (million)
% 9.15/5.10  % (31315)------------------------------
% 9.15/5.10  % (31315)------------------------------
% 9.15/5.10  % (31294)Instruction limit reached!
% 9.15/5.10  % (31294)------------------------------
% 9.15/5.10  % (31294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.10  % (31294)Termination reason: Unknown
% 9.15/5.10  % (31294)Termination phase: shuffling
% 9.15/5.10  
% 9.15/5.10  % (31294)Memory used [KB]: 11001
% 9.15/5.10  % (31294)Time elapsed: 0.101 s
% 9.15/5.10  % (31294)Instructions burned: 183 (million)
% 9.15/5.10  % (31294)------------------------------
% 9.15/5.10  % (31294)------------------------------
% 9.15/5.10  % (31316)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_31173 for (2995ds/902Mi)
% 9.15/5.11  % (31317)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_31173 for (2995ds/21Mi)
% 9.15/5.12  % (31318)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31173 for (2995ds/5Mi)
% 9.15/5.12  % (31319)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_31173 for (2995ds/6Mi)
% 9.15/5.12  % (31318)Instruction limit reached!
% 9.15/5.12  % (31318)------------------------------
% 9.15/5.12  % (31318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.12  % (31318)Termination reason: Unknown
% 9.15/5.12  % (31318)Termination phase: shuffling
% 9.15/5.12  
% 9.15/5.12  % (31318)Memory used [KB]: 8187
% 9.15/5.12  % (31318)Time elapsed: 0.006 s
% 9.15/5.12  % (31318)Instructions burned: 5 (million)
% 9.15/5.12  % (31318)------------------------------
% 9.15/5.12  % (31318)------------------------------
% 9.15/5.12  % (31319)Instruction limit reached!
% 9.15/5.12  % (31319)------------------------------
% 9.15/5.12  % (31319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/5.12  % (31319)Termination reason: Unknown
% 9.15/5.12  % (31319)Termination phase: shuffling
% 9.15/5.12  
% 9.15/5.12  % (31319)Memory used [KB]: 8315
% 9.15/5.12  % (31319)Time elapsed: 0.009 s
% 9.15/5.12  % (31319)Instructions burned: 6 (million)
% 9.15/5.12  % (31319)------------------------------
% 9.15/5.12  % (31319)------------------------------
% 9.71/5.13  % (31317)Instruction limit reached!
% 9.71/5.13  % (31317)------------------------------
% 9.71/5.13  % (31317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/5.13  % (31317)Termination reason: Unknown
% 9.71/5.13  % (31317)Termination phase: shuffling
% 9.71/5.13  
% 9.71/5.13  % (31317)Memory used [KB]: 8571
% 9.71/5.13  % (31317)Time elapsed: 0.018 s
% 9.71/5.13  % (31317)Instructions burned: 21 (million)
% 9.71/5.13  % (31317)------------------------------
% 9.71/5.13  % (31317)------------------------------
% 9.71/5.14  % (31320)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31173 for (2994ds/377Mi)
% 9.71/5.14  % (31321)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_31173 for (2994ds/779Mi)
% 9.71/5.15  % (31299)Instruction limit reached!
% 9.71/5.15  % (31299)------------------------------
% 9.71/5.15  % (31299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/5.15  % (31322)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_31173 for (2994ds/19Mi)
% 9.71/5.15  % (31299)Termination reason: Unknown
% 9.71/5.15  % (31299)Termination phase: shuffling
% 9.71/5.15  
% 9.71/5.15  % (31299)Memory used [KB]: 12281
% 9.71/5.15  % (31299)Time elapsed: 0.149 s
% 9.71/5.15  % (31299)Instructions burned: 275 (million)
% 9.71/5.15  % (31299)------------------------------
% 9.71/5.15  % (31299)------------------------------
% 9.71/5.16  % (31322)Instruction limit reached!
% 9.71/5.16  % (31322)------------------------------
% 9.71/5.16  % (31322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/5.16  % (31322)Termination reason: Unknown
% 9.71/5.16  % (31322)Termination phase: shuffling
% 9.71/5.16  
% 9.71/5.16  % (31322)Memory used [KB]: 8571
% 9.71/5.16  % (31322)Time elapsed: 0.016 s
% 9.71/5.16  % (31322)Instructions burned: 20 (million)
% 9.71/5.16  % (31322)------------------------------
% 9.71/5.16  % (31322)------------------------------
% 9.71/5.17  % (31323)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31173 for (2994ds/879Mi)
% 9.71/5.18  % (31324)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31173 for (2994ds/17Mi)
% 9.71/5.19  % (31324)Instruction limit reached!
% 9.71/5.19  % (31324)------------------------------
% 9.71/5.19  % (31324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/5.19  % (31324)Termination reason: Unknown
% 9.71/5.19  % (31324)Termination phase: shuffling
% 9.71/5.19  
% 9.71/5.19  % (31324)Memory used [KB]: 8571
% 9.71/5.19  % (31324)Time elapsed: 0.016 s
% 9.71/5.19  % (31324)Instructions burned: 18 (million)
% 9.71/5.19  % (31324)------------------------------
% 9.71/5.19  % (31324)------------------------------
% 9.84/5.21  % (31325)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31173 for (2994ds/3Mi)
% 9.84/5.22  % (31325)Instruction limit reached!
% 9.84/5.22  % (31325)------------------------------
% 9.84/5.22  % (31325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/5.22  % (31325)Termination reason: Unknown
% 9.84/5.22  % (31325)Termination phase: shuffling
% 9.84/5.22  
% 9.84/5.22  % (31325)Memory used [KB]: 8059
% 9.84/5.22  % (31325)Time elapsed: 0.005 s
% 9.84/5.22  % (31325)Instructions burned: 3 (million)
% 9.84/5.22  % (31325)------------------------------
% 9.84/5.22  % (31325)------------------------------
% 9.84/5.23  % (31326)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_31173 for (2993ds/30Mi)
% 9.84/5.25  % (31326)Instruction limit reached!
% 9.84/5.25  % (31326)------------------------------
% 9.84/5.25  % (31326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/5.25  % (31326)Termination reason: Unknown
% 9.84/5.25  % (31326)Termination phase: shuffling
% 9.84/5.25  
% 9.84/5.25  % (31326)Memory used [KB]: 8699
% 9.84/5.25  % (31326)Time elapsed: 0.022 s
% 9.84/5.25  % (31326)Instructions burned: 30 (million)
% 9.84/5.25  % (31326)------------------------------
% 9.84/5.25  % (31326)------------------------------
% 9.84/5.27  % (31327)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_31173 for (2993ds/127Mi)
% 9.91/5.34  % (31320)Instruction limit reached!
% 9.91/5.34  % (31320)------------------------------
% 9.91/5.34  % (31320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/5.34  % (31320)Termination reason: Unknown
% 9.91/5.34  % (31320)Termination phase: shuffling
% 9.91/5.34  
% 9.91/5.34  % (31320)Memory used [KB]: 14583
% 9.91/5.34  % (31320)Time elapsed: 0.203 s
% 9.91/5.34  % (31320)Instructions burned: 377 (million)
% 9.91/5.34  % (31320)------------------------------
% 9.91/5.34  % (31320)------------------------------
% 9.91/5.34  % (31327)Instruction limit reached!
% 9.91/5.34  % (31327)------------------------------
% 9.91/5.34  % (31327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/5.34  % (31327)Termination reason: Unknown
% 9.91/5.34  % (31327)Termination phase: shuffling
% 9.91/5.34  
% 9.91/5.34  % (31327)Memory used [KB]: 10234
% 9.91/5.34  % (31327)Time elapsed: 0.072 s
% 9.91/5.34  % (31327)Instructions burned: 127 (million)
% 9.91/5.34  % (31327)------------------------------
% 9.91/5.34  % (31327)------------------------------
% 9.91/5.36  % (31328)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_31173 for (2992ds/100Mi)
% 9.91/5.36  % (31329)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_31173 for (2992ds/3Mi)
% 9.91/5.36  % (31329)Instruction limit reached!
% 9.91/5.36  % (31329)------------------------------
% 9.91/5.36  % (31329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/5.36  % (31329)Termination reason: Unknown
% 9.91/5.36  % (31329)Termination phase: shuffling
% 9.91/5.36  
% 9.91/5.36  % (31329)Memory used [KB]: 8059
% 9.91/5.36  % (31329)Time elapsed: 0.005 s
% 9.91/5.36  % (31329)Instructions burned: 3 (million)
% 9.91/5.36  % (31329)------------------------------
% 9.91/5.36  % (31329)------------------------------
% 9.91/5.38  % (31330)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_31173 for (2992ds/20Mi)
% 9.91/5.39  % (31330)Instruction limit reached!
% 9.91/5.39  % (31330)------------------------------
% 9.91/5.39  % (31330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/5.39  % (31330)Termination reason: Unknown
% 9.91/5.39  % (31330)Termination phase: shuffling
% 9.91/5.39  
% 9.91/5.39  % (31330)Memory used [KB]: 8699
% 9.91/5.40  % (31330)Time elapsed: 0.017 s
% 9.91/5.40  % (31330)Instructions burned: 21 (million)
% 9.91/5.40  % (31330)------------------------------
% 9.91/5.40  % (31330)------------------------------
% 10.23/5.41  % (31328)Instruction limit reached!
% 10.23/5.41  % (31328)------------------------------
% 10.23/5.41  % (31328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/5.41  % (31328)Termination reason: Unknown
% 10.23/5.41  % (31328)Termination phase: shuffling
% 10.23/5.41  
% 10.23/5.41  % (31328)Memory used [KB]: 9850
% 10.23/5.41  % (31328)Time elapsed: 0.053 s
% 10.23/5.41  % (31328)Instructions burned: 100 (million)
% 10.23/5.41  % (31328)------------------------------
% 10.23/5.41  % (31328)------------------------------
% 10.23/5.41  % (31331)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_31173 for (2992ds/86Mi)
% 10.23/5.43  % (31332)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_31173 for (2992ds/107Mi)
% 10.23/5.45  % (31314)Instruction limit reached!
% 10.23/5.45  % (31314)------------------------------
% 10.23/5.45  % (31314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/5.45  % (31314)Termination reason: Unknown
% 10.23/5.45  % (31314)Termination phase: SInE selection
% 10.23/5.45  
% 10.23/5.45  % (31314)Memory used [KB]: 14711
% 10.23/5.45  % (31314)Time elapsed: 0.362 s
% 10.23/5.45  % (31314)Instructions burned: 710 (million)
% 10.23/5.45  % (31314)------------------------------
% 10.23/5.45  % (31314)------------------------------
% 10.23/5.46  % (31331)Instruction limit reached!
% 10.23/5.46  % (31331)------------------------------
% 10.23/5.46  % (31331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/5.46  % (31331)Termination reason: Unknown
% 10.23/5.46  % (31331)Termination phase: shuffling
% 10.23/5.46  
% 10.23/5.46  % (31331)Memory used [KB]: 9594
% 10.23/5.46  % (31331)Time elapsed: 0.050 s
% 10.23/5.46  % (31331)Instructions burned: 87 (million)
% 10.23/5.46  % (31331)------------------------------
% 10.23/5.46  % (31331)------------------------------
% 10.23/5.47  % (31333)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_31173 for (2991ds/39Mi)
% 10.23/5.48  % (31334)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_31173 for (2991ds/448Mi)
% 10.23/5.49  % (31332)Instruction limit reached!
% 10.23/5.49  % (31332)------------------------------
% 10.23/5.49  % (31332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/5.49  % (31332)Termination reason: Unknown
% 10.23/5.49  % (31332)Termination phase: shuffling
% 10.23/5.49  
% 10.23/5.49  % (31332)Memory used [KB]: 9978
% 10.23/5.49  % (31332)Time elapsed: 0.062 s
% 10.23/5.49  % (31332)Instructions burned: 107 (million)
% 10.23/5.49  % (31332)------------------------------
% 10.23/5.49  % (31332)------------------------------
% 10.23/5.49  % (31333)Instruction limit reached!
% 10.23/5.49  % (31333)------------------------------
% 10.23/5.49  % (31333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.23/5.49  % (31333)Termination reason: Unknown
% 10.23/5.49  % (31333)Termination phase: shuffling
% 10.23/5.49  
% 10.23/5.49  % (31333)Memory used [KB]: 8955
% 10.23/5.49  % (31333)Time elapsed: 0.025 s
% 10.23/5.49  % (31333)Instructions burned: 39 (million)
% 10.23/5.49  % (31333)------------------------------
% 10.23/5.49  % (31333)------------------------------
% 10.90/5.51  % (31335)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_31173 for (2991ds/46Mi)
% 10.90/5.51  % (31336)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_31173 for (2991ds/98Mi)
% 10.90/5.52  % (31321)Instruction limit reached!
% 10.90/5.52  % (31321)------------------------------
% 10.90/5.52  % (31321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/5.52  % (31321)Termination reason: Unknown
% 10.90/5.52  % (31321)Termination phase: shuffling
% 10.90/5.52  
% 10.90/5.52  % (31321)Memory used [KB]: 22387
% 10.90/5.52  % (31321)Time elapsed: 0.380 s
% 10.90/5.52  % (31321)Instructions burned: 780 (million)
% 10.90/5.52  % (31321)------------------------------
% 10.90/5.52  % (31321)------------------------------
% 10.90/5.53  % (31305)Instruction limit reached!
% 10.90/5.53  % (31305)------------------------------
% 10.90/5.53  % (31305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/5.53  % (31305)Termination reason: Unknown
% 10.90/5.53  % (31305)Termination phase: Property scanning
% 10.90/5.53  
% 10.90/5.53  % (31305)Memory used [KB]: 23155
% 10.90/5.53  % (31305)Time elapsed: 0.501 s
% 10.90/5.53  % (31305)Instructions burned: 1042 (million)
% 10.90/5.53  % (31305)------------------------------
% 10.90/5.53  % (31305)------------------------------
% 10.90/5.54  % (31335)Instruction limit reached!
% 10.90/5.54  % (31335)------------------------------
% 10.90/5.54  % (31335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/5.54  % (31335)Termination reason: Unknown
% 10.90/5.54  % (31335)Termination phase: shuffling
% 10.90/5.54  
% 10.90/5.54  % (31335)Memory used [KB]: 9083
% 10.90/5.54  % (31335)Time elapsed: 0.030 s
% 10.90/5.54  % (31335)Instructions burned: 47 (million)
% 10.90/5.54  % (31335)------------------------------
% 10.90/5.54  % (31335)------------------------------
% 10.90/5.54  % (31337)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_31173 for (2990ds/507Mi)
% 10.90/5.55  % (31338)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_31173 for (2990ds/149Mi)
% 10.90/5.55  % (31339)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_31173 for (2990ds/39Mi)
% 10.90/5.56  % (31336)Instruction limit reached!
% 10.90/5.56  % (31336)------------------------------
% 10.90/5.56  % (31336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/5.56  % (31336)Termination reason: Unknown
% 10.90/5.56  % (31336)Termination phase: shuffling
% 10.90/5.56  
% 10.90/5.56  % (31336)Memory used [KB]: 9850
% 10.90/5.56  % (31336)Time elapsed: 0.054 s
% 10.90/5.56  % (31336)Instructions burned: 99 (million)
% 10.90/5.56  % (31336)------------------------------
% 10.90/5.56  % (31336)------------------------------
% 10.90/5.57  % (31316)Instruction limit reached!
% 10.90/5.57  % (31316)------------------------------
% 10.90/5.57  % (31316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/5.57  % (31316)Termination reason: Unknown
% 10.90/5.57  % (31316)Termination phase: Property scanning
% 10.90/5.57  
% 10.90/5.57  % (31316)Memory used [KB]: 21492
% 10.90/5.57  % (31316)Time elapsed: 0.471 s
% 10.90/5.57  % (31316)Instructions burned: 903 (million)
% 10.90/5.57  % (31316)------------------------------
% 10.90/5.57  % (31316)------------------------------
% 10.90/5.58  % (31339)Instruction limit reached!
% 10.90/5.58  % (31339)------------------------------
% 10.90/5.58  % (31339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/5.58  % (31339)Termination reason: Unknown
% 10.90/5.58  % (31339)Termination phase: shuffling
% 10.90/5.58  
% 10.90/5.58  % (31339)Memory used [KB]: 8955
% 10.90/5.58  % (31339)Time elapsed: 0.026 s
% 10.90/5.58  % (31339)Instructions burned: 39 (million)
% 10.90/5.58  % (31339)------------------------------
% 10.90/5.58  % (31339)------------------------------
% 10.90/5.58  % (31340)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_31173 for (2990ds/6Mi)
% 10.90/5.59  % (31340)Instruction limit reached!
% 10.90/5.59  % (31340)------------------------------
% 10.90/5.59  % (31340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.90/5.59  % (31340)Termination reason: Unknown
% 10.90/5.59  % (31340)Termination phase: shuffling
% 10.90/5.59  
% 10.90/5.59  % (31340)Memory used [KB]: 8187
% 10.90/5.59  % (31340)Time elapsed: 0.008 s
% 10.90/5.59  % (31340)Instructions burned: 6 (million)
% 10.90/5.59  % (31340)------------------------------
% 10.90/5.59  % (31340)------------------------------
% 10.90/5.59  % (31341)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_31173 for (2990ds/1087Mi)
% 10.90/5.60  % (31342)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_31173 for (2990ds/47Mi)
% 12.48/5.61  % (31343)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_31173 for (2990ds/44Mi)
% 12.48/5.61  % (31323)Instruction limit reached!
% 12.48/5.61  % (31323)------------------------------
% 12.48/5.61  % (31323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.48/5.61  % (31323)Termination reason: Unknown
% 12.48/5.61  % (31323)Termination phase: SInE selection
% 12.48/5.61  
% 12.48/5.61  % (31323)Memory used [KB]: 14839
% 12.48/5.61  % (31323)Time elapsed: 0.446 s
% 12.48/5.61  % (31323)Instructions burned: 879 (million)
% 12.48/5.61  % (31323)------------------------------
% 12.48/5.61  % (31323)------------------------------
% 12.48/5.62  % (31342)Instruction limit reached!
% 12.48/5.62  % (31342)------------------------------
% 12.48/5.62  % (31342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.48/5.62  % (31342)Termination reason: Unknown
% 12.48/5.62  % (31342)Termination phase: shuffling
% 12.48/5.62  
% 12.48/5.62  % (31342)Memory used [KB]: 9083
% 12.48/5.62  % (31342)Time elapsed: 0.031 s
% 12.48/5.62  % (31342)Instructions burned: 48 (million)
% 12.48/5.62  % (31342)------------------------------
% 12.48/5.62  % (31342)------------------------------
% 12.48/5.63  % (31344)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_31173 for (2989ds/432Mi)
% 12.48/5.63  % (31343)Instruction limit reached!
% 12.48/5.63  % (31343)------------------------------
% 12.48/5.63  % (31343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.48/5.63  % (31343)Termination reason: Unknown
% 12.48/5.63  % (31343)Termination phase: shuffling
% 12.48/5.63  
% 12.48/5.63  % (31343)Memory used [KB]: 8955
% 12.48/5.63  % (31343)Time elapsed: 0.027 s
% 12.48/5.63  % (31343)Instructions burned: 44 (million)
% 12.48/5.63  % (31343)------------------------------
% 12.48/5.63  % (31343)------------------------------
% 12.48/5.63  % (31338)Instruction limit reached!
% 12.48/5.63  % (31338)------------------------------
% 12.48/5.63  % (31338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.48/5.63  % (31338)Termination reason: Unknown
% 12.48/5.63  % (31338)Termination phase: shuffling
% 12.48/5.63  
% 12.48/5.63  % (31338)Memory used [KB]: 10490
% 12.48/5.63  % (31338)Time elapsed: 0.082 s
% 12.48/5.63  % (31338)Instructions burned: 149 (million)
% 12.48/5.63  % (31338)------------------------------
% 12.48/5.63  % (31338)------------------------------
% 12.48/5.64  % (31345)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_31173 for (2989ds/62Mi)
% 12.48/5.65  % (31346)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_31173 for (2989ds/31Mi)
% 12.48/5.65  % (31347)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_31173 for (2989ds/96Mi)
% 12.48/5.67  % (31346)Instruction limit reached!
% 12.48/5.67  % (31346)------------------------------
% 12.48/5.67  % (31346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.48/5.67  % (31346)Termination reason: Unknown
% 12.48/5.67  % (31346)Termination phase: shuffling
% 12.48/5.67  
% 12.48/5.67  % (31346)Memory used [KB]: 8827
% 12.48/5.67  % (31346)Time elapsed: 0.023 s
% 12.48/5.67  % (31346)Instructions burned: 32 (million)
% 12.48/5.67  % (31346)------------------------------
% 12.48/5.67  % (31346)------------------------------
% 12.48/5.68  % (31345)Instruction limit reached!
% 12.48/5.68  % (31345)------------------------------
% 12.48/5.68  % (31345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.48/5.68  % (31345)Termination reason: Unknown
% 12.48/5.68  % (31345)Termination phase: shuffling
% 12.48/5.68  
% 12.48/5.68  % (31345)Memory used [KB]: 9338
% 12.48/5.68  % (31345)Time elapsed: 0.035 s
% 12.48/5.68  % (31345)Instructions burned: 63 (million)
% 12.48/5.68  % (31345)------------------------------
% 12.48/5.68  % (31345)------------------------------
% 12.48/5.69  % (31348)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_31173 for (2989ds/453Mi)
% 12.48/5.69  % (31349)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_31173 for (2989ds/71Mi)
% 13.22/5.70  % (31334)Instruction limit reached!
% 13.22/5.70  % (31334)------------------------------
% 13.22/5.70  % (31334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/5.70  % (31334)Termination reason: Unknown
% 13.22/5.70  % (31334)Termination phase: shuffling
% 13.22/5.70  
% 13.22/5.70  % (31334)Memory used [KB]: 17782
% 13.22/5.70  % (31334)Time elapsed: 0.222 s
% 13.22/5.70  % (31334)Instructions burned: 449 (million)
% 13.22/5.70  % (31334)------------------------------
% 13.22/5.70  % (31334)------------------------------
% 13.22/5.70  % (31347)Instruction limit reached!
% 13.22/5.70  % (31347)------------------------------
% 13.22/5.70  % (31347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/5.70  % (31347)Termination reason: Unknown
% 13.22/5.70  % (31347)Termination phase: shuffling
% 13.22/5.70  
% 13.22/5.70  % (31347)Memory used [KB]: 9850
% 13.22/5.70  % (31347)Time elapsed: 0.055 s
% 13.22/5.70  % (31347)Instructions burned: 96 (million)
% 13.22/5.70  % (31347)------------------------------
% 13.22/5.70  % (31347)------------------------------
% 13.22/5.72  % (31350)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_31173 for (2989ds/83Mi)
% 13.22/5.72  % (31351)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_31173 for (2989ds/11Mi)
% 13.22/5.73  % (31351)Instruction limit reached!
% 13.22/5.73  % (31351)------------------------------
% 13.22/5.73  % (31351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/5.73  % (31351)Termination reason: Unknown
% 13.22/5.73  % (31351)Termination phase: shuffling
% 13.22/5.73  
% 13.22/5.73  % (31351)Memory used [KB]: 8443
% 13.22/5.73  % (31351)Time elapsed: 0.012 s
% 13.22/5.73  % (31351)Instructions burned: 12 (million)
% 13.22/5.73  % (31351)------------------------------
% 13.22/5.73  % (31351)------------------------------
% 13.22/5.73  % (31349)Instruction limit reached!
% 13.22/5.73  % (31349)------------------------------
% 13.22/5.73  % (31349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/5.73  % (31349)Termination reason: Unknown
% 13.22/5.73  % (31349)Termination phase: shuffling
% 13.22/5.73  
% 13.22/5.73  % (31349)Memory used [KB]: 9338
% 13.22/5.73  % (31349)Time elapsed: 0.042 s
% 13.22/5.73  % (31349)Instructions burned: 71 (million)
% 13.22/5.73  % (31349)------------------------------
% 13.22/5.73  % (31349)------------------------------
% 13.22/5.75  % (31352)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_31173 for (2988ds/41Mi)
% 13.22/5.75  % (31353)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31173 for (2988ds/6Mi)
% 13.22/5.76  % (31353)Instruction limit reached!
% 13.22/5.76  % (31353)------------------------------
% 13.22/5.76  % (31353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/5.76  % (31353)Termination reason: Unknown
% 13.22/5.76  % (31353)Termination phase: shuffling
% 13.22/5.76  
% 13.22/5.76  % (31353)Memory used [KB]: 8315
% 13.22/5.76  % (31353)Time elapsed: 0.009 s
% 13.22/5.76  % (31353)Instructions burned: 6 (million)
% 13.22/5.76  % (31353)------------------------------
% 13.22/5.76  % (31353)------------------------------
% 13.22/5.77  % (31350)Instruction limit reached!
% 13.22/5.77  % (31350)------------------------------
% 13.22/5.77  % (31350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/5.77  % (31350)Termination reason: Unknown
% 13.22/5.77  % (31350)Termination phase: shuffling
% 13.22/5.77  
% 13.22/5.77  % (31350)Memory used [KB]: 9594
% 13.22/5.77  % (31350)Time elapsed: 0.048 s
% 13.22/5.77  % (31350)Instructions burned: 83 (million)
% 13.22/5.77  % (31350)------------------------------
% 13.22/5.77  % (31350)------------------------------
% 13.22/5.77  % (31352)Instruction limit reached!
% 13.22/5.77  % (31352)------------------------------
% 13.22/5.77  % (31352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/5.77  % (31352)Termination reason: Unknown
% 13.22/5.77  % (31352)Termination phase: shuffling
% 13.22/5.77  
% 13.22/5.77  % (31352)Memory used [KB]: 8955
% 13.22/5.77  % (31352)Time elapsed: 0.026 s
% 13.22/5.77  % (31352)Instructions burned: 42 (million)
% 13.22/5.77  % (31352)------------------------------
% 13.22/5.77  % (31352)------------------------------
% 13.22/5.78  % (31354)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_31173 for (2988ds/150Mi)
% 13.22/5.78  % (31355)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_31173 for (2988ds/343Mi)
% 13.22/5.79  % (31356)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_31173 for (2988ds/109Mi)
% 13.76/5.80  % (31337)Instruction limit reached!
% 13.76/5.80  % (31337)------------------------------
% 13.76/5.80  % (31337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/5.80  % (31337)Termination reason: Unknown
% 13.76/5.80  % (31337)Termination phase: shuffling
% 13.76/5.80  
% 13.76/5.80  % (31337)Memory used [KB]: 16119
% 13.76/5.80  % (31337)Time elapsed: 0.265 s
% 13.76/5.80  % (31337)Instructions burned: 508 (million)
% 13.76/5.80  % (31337)------------------------------
% 13.76/5.80  % (31337)------------------------------
% 13.76/5.82  % (31357)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_31173 for (2988ds/253Mi)
% 13.76/5.84  % (31344)Instruction limit reached!
% 13.76/5.84  % (31344)------------------------------
% 13.76/5.84  % (31344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/5.84  % (31344)Termination reason: Unknown
% 13.76/5.84  % (31344)Termination phase: shuffling
% 13.76/5.84  
% 13.76/5.84  % (31344)Memory used [KB]: 17526
% 13.76/5.84  % (31344)Time elapsed: 0.209 s
% 13.76/5.84  % (31344)Instructions burned: 432 (million)
% 13.76/5.84  % (31344)------------------------------
% 13.76/5.84  % (31344)------------------------------
% 13.76/5.85  % (31356)Instruction limit reached!
% 13.76/5.85  % (31356)------------------------------
% 13.76/5.85  % (31356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/5.85  % (31356)Termination reason: Unknown
% 13.76/5.85  % (31356)Termination phase: shuffling
% 13.76/5.85  
% 13.76/5.85  % (31356)Memory used [KB]: 9978
% 13.76/5.85  % (31356)Time elapsed: 0.063 s
% 13.76/5.85  % (31356)Instructions burned: 109 (million)
% 13.76/5.85  % (31356)------------------------------
% 13.76/5.85  % (31356)------------------------------
% 13.76/5.86  % (31358)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_31173 for (2987ds/140Mi)
% 13.76/5.86  % (31354)Instruction limit reached!
% 13.76/5.86  % (31354)------------------------------
% 13.76/5.86  % (31354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/5.86  % (31354)Termination reason: Unknown
% 13.76/5.86  % (31354)Termination phase: shuffling
% 13.76/5.86  
% 13.76/5.86  % (31354)Memory used [KB]: 10490
% 13.76/5.86  % (31354)Time elapsed: 0.083 s
% 13.76/5.86  % (31354)Instructions burned: 151 (million)
% 13.76/5.86  % (31354)------------------------------
% 13.76/5.86  % (31354)------------------------------
% 13.76/5.87  % (31359)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_31173 for (2987ds/614Mi)
% 13.76/5.88  % (31360)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_31173 for (2987ds/202Mi)
% 14.44/5.91  % (31348)Instruction limit reached!
% 14.44/5.91  % (31348)------------------------------
% 14.44/5.91  % (31348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/5.91  % (31348)Termination reason: Unknown
% 14.44/5.91  % (31348)Termination phase: shuffling
% 14.44/5.91  
% 14.44/5.91  % (31348)Memory used [KB]: 17910
% 14.44/5.91  % (31348)Time elapsed: 0.221 s
% 14.44/5.91  % (31348)Instructions burned: 454 (million)
% 14.44/5.91  % (31348)------------------------------
% 14.44/5.91  % (31348)------------------------------
% 14.44/5.93  % (31361)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_31173 for (2987ds/339Mi)
% 14.44/5.93  % (31358)Instruction limit reached!
% 14.44/5.93  % (31358)------------------------------
% 14.44/5.93  % (31358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/5.93  % (31358)Termination reason: Unknown
% 14.44/5.93  % (31358)Termination phase: shuffling
% 14.44/5.93  
% 14.44/5.93  % (31358)Memory used [KB]: 10362
% 14.44/5.93  % (31358)Time elapsed: 0.077 s
% 14.44/5.93  % (31358)Instructions burned: 141 (million)
% 14.44/5.93  % (31358)------------------------------
% 14.44/5.93  % (31358)------------------------------
% 14.44/5.95  % (31362)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_31173 for (2986ds/283Mi)
% 14.44/5.96  % (31357)Instruction limit reached!
% 14.44/5.96  % (31357)------------------------------
% 14.44/5.96  % (31357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/5.96  % (31357)Termination reason: Unknown
% 14.44/5.96  % (31357)Termination phase: shuffling
% 14.44/5.96  
% 14.44/5.96  % (31357)Memory used [KB]: 12025
% 14.44/5.96  % (31357)Time elapsed: 0.139 s
% 14.44/5.96  % (31357)Instructions burned: 254 (million)
% 14.44/5.96  % (31357)------------------------------
% 14.44/5.96  % (31357)------------------------------
% 14.44/5.97  % (31355)Instruction limit reached!
% 14.44/5.97  % (31355)------------------------------
% 14.44/5.97  % (31355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/5.97  % (31355)Termination reason: Unknown
% 14.44/5.97  % (31355)Termination phase: shuffling
% 14.44/5.97  
% 14.44/5.97  % (31355)Memory used [KB]: 14072
% 14.44/5.97  % (31355)Time elapsed: 0.183 s
% 14.44/5.97  % (31355)Instructions burned: 344 (million)
% 14.44/5.97  % (31355)------------------------------
% 14.44/5.97  % (31355)------------------------------
% 14.44/5.98  % (31363)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_31173 for (2986ds/134Mi)
% 14.44/5.98  % (31364)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_31173 for (2986ds/298Mi)
% 14.44/5.98  % (31360)Instruction limit reached!
% 14.44/5.98  % (31360)------------------------------
% 14.44/5.98  % (31360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/5.98  % (31360)Termination reason: Unknown
% 14.44/5.98  % (31360)Termination phase: shuffling
% 14.44/5.98  
% 14.44/5.98  % (31360)Memory used [KB]: 11257
% 14.44/5.98  % (31360)Time elapsed: 0.111 s
% 14.44/5.98  % (31360)Instructions burned: 203 (million)
% 14.44/5.98  % (31360)------------------------------
% 14.44/5.98  % (31360)------------------------------
% 14.44/6.00  % (31365)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_31173 for (2986ds/192Mi)
% 16.17/6.05  % (31363)Instruction limit reached!
% 16.17/6.05  % (31363)------------------------------
% 16.17/6.05  % (31363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.17/6.05  % (31363)Termination reason: Unknown
% 16.17/6.05  % (31363)Termination phase: shuffling
% 16.17/6.05  
% 16.17/6.05  % (31363)Memory used [KB]: 10362
% 16.17/6.05  % (31363)Time elapsed: 0.074 s
% 16.17/6.05  % (31363)Instructions burned: 134 (million)
% 16.17/6.05  % (31363)------------------------------
% 16.17/6.05  % (31363)------------------------------
% 16.17/6.07  % (31366)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_31173 for (2985ds/258Mi)
% 16.17/6.09  % (31362)Instruction limit reached!
% 16.17/6.09  % (31362)------------------------------
% 16.17/6.09  % (31362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.17/6.09  % (31362)Termination reason: Unknown
% 16.17/6.09  % (31362)Termination phase: shuffling
% 16.17/6.09  
% 16.17/6.09  % (31362)Memory used [KB]: 13560
% 16.17/6.09  % (31362)Time elapsed: 0.138 s
% 16.17/6.09  % (31362)Instructions burned: 283 (million)
% 16.17/6.09  % (31362)------------------------------
% 16.17/6.09  % (31362)------------------------------
% 16.17/6.10  % (31367)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_31173 for (2985ds/90Mi)
% 16.17/6.11  % (31365)Instruction limit reached!
% 16.17/6.11  % (31365)------------------------------
% 16.17/6.11  % (31365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.17/6.11  % (31365)Termination reason: Unknown
% 16.17/6.11  % (31365)Termination phase: shuffling
% 16.17/6.11  
% 16.17/6.11  % (31365)Memory used [KB]: 11129
% 16.17/6.11  % (31365)Time elapsed: 0.105 s
% 16.17/6.11  % (31365)Instructions burned: 193 (million)
% 16.17/6.11  % (31365)------------------------------
% 16.17/6.11  % (31365)------------------------------
% 16.17/6.12  % (31361)Instruction limit reached!
% 16.17/6.12  % (31361)------------------------------
% 16.17/6.12  % (31361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.17/6.12  % (31361)Termination reason: Unknown
% 16.17/6.12  % (31361)Termination phase: shuffling
% 16.17/6.12  
% 16.17/6.12  % (31361)Memory used [KB]: 14072
% 16.17/6.12  % (31361)Time elapsed: 0.183 s
% 16.17/6.12  % (31361)Instructions burned: 339 (million)
% 16.17/6.12  % (31361)------------------------------
% 16.17/6.12  % (31361)------------------------------
% 16.17/6.12  % (31368)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_31173 for (2984ds/231Mi)
% 16.77/6.13  % (31364)Instruction limit reached!
% 16.77/6.13  % (31364)------------------------------
% 16.77/6.13  % (31364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.77/6.13  % (31364)Termination reason: Unknown
% 16.77/6.13  % (31364)Termination phase: shuffling
% 16.77/6.13  
% 16.77/6.13  % (31364)Memory used [KB]: 13560
% 16.77/6.13  % (31364)Time elapsed: 0.147 s
% 16.77/6.13  % (31364)Instructions burned: 299 (million)
% 16.77/6.13  % (31364)------------------------------
% 16.77/6.13  % (31364)------------------------------
% 16.77/6.13  % (31369)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_31173 for (2984ds/458Mi)
% 16.77/6.15  % (31341)Instruction limit reached!
% 16.77/6.15  % (31341)------------------------------
% 16.77/6.15  % (31341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.77/6.15  % (31341)Termination reason: Unknown
% 16.77/6.15  % (31341)Termination phase: Saturation
% 16.77/6.15  
% 16.77/6.15  % (31341)Memory used [KB]: 20468
% 16.77/6.15  % (31341)Time elapsed: 0.577 s
% 16.77/6.15  % (31341)Instructions burned: 1087 (million)
% 16.77/6.15  % (31341)------------------------------
% 16.77/6.15  % (31341)------------------------------
% 16.77/6.15  % (31370)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_31173 for (2984ds/31Mi)
% 16.77/6.16  % (31367)Instruction limit reached!
% 16.77/6.16  % (31367)------------------------------
% 16.77/6.16  % (31367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.77/6.16  % (31367)Termination reason: Unknown
% 16.77/6.16  % (31367)Termination phase: shuffling
% 16.77/6.16  
% 16.77/6.16  % (31367)Memory used [KB]: 9722
% 16.77/6.16  % (31367)Time elapsed: 0.052 s
% 16.77/6.16  % (31367)Instructions burned: 91 (million)
% 16.77/6.16  % (31367)------------------------------
% 16.77/6.16  % (31367)------------------------------
% 16.77/6.17  % (31371)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_31173 for (2984ds/297Mi)
% 16.77/6.17  % (31370)Instruction limit reached!
% 16.77/6.17  % (31370)------------------------------
% 16.77/6.17  % (31370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.77/6.17  % (31370)Termination reason: Unknown
% 16.77/6.17  % (31370)Termination phase: shuffling
% 16.77/6.17  
% 16.77/6.17  % (31370)Memory used [KB]: 8827
% 16.77/6.17  % (31370)Time elapsed: 0.022 s
% 16.77/6.17  % (31370)Instructions burned: 32 (million)
% 16.77/6.17  % (31370)------------------------------
% 16.77/6.17  % (31370)------------------------------
% 16.77/6.17  % (31372)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_31173 for (2984ds/987Mi)
% 16.77/6.18  % (31359)Instruction limit reached!
% 16.77/6.18  % (31359)------------------------------
% 16.77/6.18  % (31359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.77/6.18  % (31359)Termination reason: Unknown
% 16.77/6.18  % (31359)Termination phase: Property scanning
% 16.77/6.18  
% 16.77/6.18  % (31359)Memory used [KB]: 14583
% 16.77/6.18  % (31359)Time elapsed: 0.312 s
% 16.77/6.18  % (31359)Instructions burned: 615 (million)
% 16.77/6.18  % (31359)------------------------------
% 16.77/6.18  % (31359)------------------------------
% 16.77/6.19  % (31373)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_31173 for (2984ds/182Mi)
% 16.99/6.20  % (31374)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_31173 for (2984ds/182Mi)
% 16.99/6.21  % (31366)Instruction limit reached!
% 16.99/6.21  % (31366)------------------------------
% 16.99/6.21  % (31366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.99/6.21  % (31366)Termination reason: Unknown
% 16.99/6.21  % (31366)Termination phase: shuffling
% 16.99/6.21  
% 16.99/6.21  % (31366)Memory used [KB]: 13048
% 16.99/6.21  % (31366)Time elapsed: 0.141 s
% 16.99/6.21  % (31366)Instructions burned: 259 (million)
% 16.99/6.21  % (31366)------------------------------
% 16.99/6.21  % (31366)------------------------------
% 16.99/6.23  % (31375)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_31173 for (2983ds/154Mi)
% 16.99/6.24  % (31368)Instruction limit reached!
% 16.99/6.24  % (31368)------------------------------
% 16.99/6.24  % (31368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.99/6.24  % (31368)Termination reason: Unknown
% 16.99/6.24  % (31368)Termination phase: shuffling
% 16.99/6.24  
% 16.99/6.24  % (31368)Memory used [KB]: 12792
% 16.99/6.24  % (31368)Time elapsed: 0.114 s
% 16.99/6.24  % (31368)Instructions burned: 231 (million)
% 16.99/6.24  % (31368)------------------------------
% 16.99/6.24  % (31368)------------------------------
% 16.99/6.26  % (31376)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_31173 for (2983ds/79Mi)
% 16.99/6.28  % (31373)Instruction limit reached!
% 16.99/6.28  % (31373)------------------------------
% 16.99/6.28  % (31373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.99/6.28  % (31373)Termination reason: Unknown
% 16.99/6.28  % (31373)Termination phase: shuffling
% 16.99/6.28  
% 16.99/6.28  % (31373)Memory used [KB]: 11001
% 16.99/6.28  % (31373)Time elapsed: 0.098 s
% 16.99/6.28  % (31373)Instructions burned: 182 (million)
% 16.99/6.28  % (31373)------------------------------
% 16.99/6.28  % (31373)------------------------------
% 17.40/6.30  % (31374)Instruction limit reached!
% 17.40/6.30  % (31374)------------------------------
% 17.40/6.30  % (31374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/6.30  % (31374)Termination reason: Unknown
% 17.40/6.30  % (31374)Termination phase: shuffling
% 17.40/6.30  
% 17.40/6.30  % (31374)Memory used [KB]: 11129
% 17.40/6.30  % (31374)Time elapsed: 0.102 s
% 17.40/6.30  % (31374)Instructions burned: 183 (million)
% 17.40/6.30  % (31374)------------------------------
% 17.40/6.30  % (31374)------------------------------
% 17.40/6.30  % (31376)Instruction limit reached!
% 17.40/6.30  % (31376)------------------------------
% 17.40/6.30  % (31376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/6.30  % (31376)Termination reason: Unknown
% 17.40/6.30  % (31376)Termination phase: shuffling
% 17.40/6.30  
% 17.40/6.30  % (31376)Memory used [KB]: 9594
% 17.40/6.30  % (31376)Time elapsed: 0.047 s
% 17.40/6.30  % (31376)Instructions burned: 80 (million)
% 17.40/6.30  % (31376)------------------------------
% 17.40/6.30  % (31376)------------------------------
% 17.40/6.30  % (31377)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_31173 for (2983ds/216Mi)
% 17.40/6.31  % (31375)Instruction limit reached!
% 17.40/6.31  % (31375)------------------------------
% 17.40/6.31  % (31375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/6.31  % (31375)Termination reason: Unknown
% 17.40/6.31  % (31375)Termination phase: shuffling
% 17.40/6.31  
% 17.40/6.31  % (31375)Memory used [KB]: 11641
% 17.40/6.31  % (31375)Time elapsed: 0.079 s
% 17.40/6.31  % (31375)Instructions burned: 154 (million)
% 17.40/6.31  % (31375)------------------------------
% 17.40/6.31  % (31375)------------------------------
% 17.40/6.31  % (31371)Instruction limit reached!
% 17.40/6.31  % (31371)------------------------------
% 17.40/6.31  % (31371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/6.31  % (31371)Termination reason: Unknown
% 17.40/6.31  % (31371)Termination phase: shuffling
% 17.40/6.31  
% 17.40/6.31  % (31371)Memory used [KB]: 13560
% 17.40/6.31  % (31371)Time elapsed: 0.148 s
% 17.40/6.31  % (31371)Instructions burned: 297 (million)
% 17.40/6.31  % (31371)------------------------------
% 17.40/6.31  % (31371)------------------------------
% 17.40/6.32  % (31378)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_31173 for (2983ds/114Mi)
% 17.40/6.32  % (31379)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_31173 for (2983ds/922Mi)
% 17.40/6.32  % (31380)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_31173 for (2983ds/182Mi)
% 17.40/6.33  % (31381)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_31173 for (2983ds/164Mi)
% 17.40/6.37  % (31369)Instruction limit reached!
% 17.40/6.37  % (31369)------------------------------
% 17.40/6.37  % (31369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/6.37  % (31369)Termination reason: Unknown
% 17.40/6.37  % (31369)Termination phase: Property scanning
% 17.40/6.37  
% 17.40/6.37  % (31369)Memory used [KB]: 14583
% 17.40/6.37  % (31369)Time elapsed: 0.238 s
% 17.40/6.37  % (31369)Instructions burned: 458 (million)
% 17.40/6.37  % (31369)------------------------------
% 17.40/6.37  % (31369)------------------------------
% 17.40/6.38  % (31378)Instruction limit reached!
% 17.40/6.38  % (31378)------------------------------
% 17.40/6.38  % (31378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/6.38  % (31378)Termination reason: Unknown
% 17.40/6.38  % (31378)Termination phase: shuffling
% 17.40/6.38  
% 17.40/6.38  % (31378)Memory used [KB]: 10106
% 17.40/6.38  % (31378)Time elapsed: 0.065 s
% 17.40/6.38  % (31378)Instructions burned: 114 (million)
% 17.40/6.38  % (31378)------------------------------
% 17.40/6.38  % (31378)------------------------------
% 17.40/6.39  % (31382)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_31173 for (2982ds/50Mi)
% 18.18/6.40  % (31383)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_31173 for (2982ds/368Mi)
% 18.18/6.41  % (31377)Instruction limit reached!
% 18.18/6.41  % (31377)------------------------------
% 18.18/6.41  % (31377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.18/6.41  % (31377)Termination reason: Unknown
% 18.18/6.41  % (31377)Termination phase: shuffling
% 18.18/6.41  
% 18.18/6.41  % (31377)Memory used [KB]: 12537
% 18.18/6.41  % (31377)Time elapsed: 0.106 s
% 18.18/6.41  % (31377)Instructions burned: 216 (million)
% 18.18/6.41  % (31377)------------------------------
% 18.18/6.41  % (31377)------------------------------
% 18.18/6.41  % (31381)Instruction limit reached!
% 18.18/6.41  % (31381)------------------------------
% 18.18/6.41  % (31381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.18/6.41  % (31381)Termination reason: Unknown
% 18.18/6.41  % (31381)Termination phase: shuffling
% 18.18/6.41  
% 18.18/6.41  % (31381)Memory used [KB]: 11769
% 18.18/6.41  % (31381)Time elapsed: 0.085 s
% 18.18/6.41  % (31381)Instructions burned: 165 (million)
% 18.18/6.41  % (31381)------------------------------
% 18.18/6.41  % (31381)------------------------------
% 18.18/6.41  % (31380)Instruction limit reached!
% 18.18/6.41  % (31380)------------------------------
% 18.18/6.41  % (31380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.18/6.41  % (31380)Termination reason: Unknown
% 18.18/6.41  % (31380)Termination phase: shuffling
% 18.18/6.41  
% 18.18/6.41  % (31380)Memory used [KB]: 12025
% 18.18/6.41  % (31380)Time elapsed: 0.092 s
% 18.18/6.41  % (31380)Instructions burned: 183 (million)
% 18.18/6.41  % (31380)------------------------------
% 18.18/6.41  % (31380)------------------------------
% 18.18/6.42  % (31382)Instruction limit reached!
% 18.18/6.42  % (31382)------------------------------
% 18.18/6.42  % (31382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.18/6.42  % (31382)Termination reason: Unknown
% 18.18/6.42  % (31382)Termination phase: shuffling
% 18.18/6.42  
% 18.18/6.42  % (31382)Memory used [KB]: 9083
% 18.18/6.42  % (31382)Time elapsed: 0.031 s
% 18.18/6.42  % (31382)Instructions burned: 51 (million)
% 18.18/6.42  % (31382)------------------------------
% 18.18/6.42  % (31382)------------------------------
% 18.18/6.42  % (31384)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_31173 for (2982ds/1021Mi)
% 18.18/6.43  % (31385)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_31173 for (2982ds/267Mi)
% 18.18/6.43  % (31386)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_31173 for (2982ds/204Mi)
% 18.18/6.44  % (31387)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_31173 for (2982ds/26Mi)
% 18.18/6.45  % (31387)Instruction limit reached!
% 18.18/6.45  % (31387)------------------------------
% 18.18/6.45  % (31387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.18/6.45  % (31387)Termination reason: Unknown
% 18.18/6.45  % (31387)Termination phase: shuffling
% 18.18/6.45  
% 18.18/6.45  % (31387)Memory used [KB]: 8699
% 18.18/6.45  % (31387)Time elapsed: 0.019 s
% 18.18/6.45  % (31387)Instructions burned: 26 (million)
% 18.18/6.45  % (31387)------------------------------
% 18.18/6.45  % (31387)------------------------------
% 18.18/6.47  % (31388)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_31173 for (2981ds/53Mi)
% 18.59/6.50  % (31388)Instruction limit reached!
% 18.59/6.50  % (31388)------------------------------
% 18.59/6.50  % (31388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/6.50  % (31388)Termination reason: Unknown
% 18.59/6.50  % (31388)Termination phase: shuffling
% 18.59/6.50  
% 18.59/6.50  % (31388)Memory used [KB]: 9210
% 18.59/6.50  % (31388)Time elapsed: 0.032 s
% 18.59/6.50  % (31388)Instructions burned: 54 (million)
% 18.59/6.50  % (31388)------------------------------
% 18.59/6.50  % (31388)------------------------------
% 18.59/6.52  % (31389)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_31173 for (2981ds/4436Mi)
% 18.59/6.54  % (31386)Instruction limit reached!
% 18.59/6.54  % (31386)------------------------------
% 18.59/6.54  % (31386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/6.54  % (31386)Termination reason: Unknown
% 18.59/6.54  % (31386)Termination phase: shuffling
% 18.59/6.54  
% 18.59/6.54  % (31386)Memory used [KB]: 11129
% 18.59/6.54  % (31386)Time elapsed: 0.110 s
% 18.59/6.54  % (31386)Instructions burned: 204 (million)
% 18.59/6.54  % (31386)------------------------------
% 18.59/6.54  % (31386)------------------------------
% 18.59/6.56  % (31390)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_31173 for (2980ds/1539Mi)
% 18.59/6.56  % (31385)Instruction limit reached!
% 18.59/6.56  % (31385)------------------------------
% 18.59/6.56  % (31385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/6.56  % (31385)Termination reason: Unknown
% 18.59/6.56  % (31385)Termination phase: shuffling
% 18.59/6.56  
% 18.59/6.56  % (31385)Memory used [KB]: 13304
% 18.59/6.56  % (31385)Time elapsed: 0.134 s
% 18.59/6.56  % (31385)Instructions burned: 268 (million)
% 18.59/6.56  % (31385)------------------------------
% 18.59/6.56  % (31385)------------------------------
% 18.59/6.58  % (31391)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_31173 for (2980ds/408Mi)
% 18.59/6.59  % (31383)Instruction limit reached!
% 18.59/6.59  % (31383)------------------------------
% 18.59/6.59  % (31383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/6.59  % (31383)Termination reason: Unknown
% 18.59/6.59  % (31383)Termination phase: shuffling
% 18.59/6.59  
% 18.59/6.59  % (31383)Memory used [KB]: 14456
% 18.59/6.59  % (31383)Time elapsed: 0.197 s
% 18.59/6.59  % (31383)Instructions burned: 368 (million)
% 18.59/6.59  % (31383)------------------------------
% 18.59/6.59  % (31383)------------------------------
% 18.92/6.61  % (31392)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_31173 for (2980ds/5205Mi)
% 18.92/6.67  % (31372)Instruction limit reached!
% 18.92/6.67  % (31372)------------------------------
% 18.92/6.67  % (31372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.92/6.67  % (31372)Termination reason: Unknown
% 18.92/6.67  % (31372)Termination phase: Property scanning
% 18.92/6.67  
% 18.92/6.67  % (31372)Memory used [KB]: 23155
% 18.92/6.67  % (31372)Time elapsed: 0.496 s
% 18.92/6.67  % (31372)Instructions burned: 988 (million)
% 18.92/6.67  % (31372)------------------------------
% 18.92/6.67  % (31372)------------------------------
% 18.92/6.69  % (31393)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_31173 for (2979ds/1913Mi)
% 19.65/6.80  % (31391)Instruction limit reached!
% 19.65/6.80  % (31391)------------------------------
% 19.65/6.80  % (31391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.65/6.80  % (31391)Termination reason: Unknown
% 19.65/6.80  % (31391)Termination phase: Property scanning
% 19.65/6.80  
% 19.65/6.80  % (31391)Memory used [KB]: 14711
% 19.65/6.80  % (31391)Time elapsed: 0.217 s
% 19.65/6.80  % (31391)Instructions burned: 408 (million)
% 19.65/6.80  % (31391)------------------------------
% 19.65/6.80  % (31391)------------------------------
% 19.65/6.81  % (31379)Instruction limit reached!
% 19.65/6.81  % (31379)------------------------------
% 19.65/6.81  % (31379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.65/6.81  % (31379)Termination reason: Unknown
% 19.65/6.81  % (31379)Termination phase: Saturation
% 19.65/6.81  
% 19.65/6.81  % (31379)Memory used [KB]: 20084
% 19.65/6.81  % (31379)Time elapsed: 0.493 s
% 19.65/6.81  % (31379)Instructions burned: 922 (million)
% 19.65/6.81  % (31379)------------------------------
% 19.65/6.81  % (31379)------------------------------
% 19.65/6.82  % (31394)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_31173 for (2978ds/4350Mi)
% 19.65/6.83  % (31395)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_31173 for (2977ds/68Mi)
% 19.65/6.87  % (31395)Instruction limit reached!
% 19.65/6.87  % (31395)------------------------------
% 19.65/6.87  % (31395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.65/6.87  % (31395)Termination reason: Unknown
% 19.65/6.87  % (31395)Termination phase: shuffling
% 19.65/6.87  
% 19.65/6.87  % (31395)Memory used [KB]: 9338
% 19.65/6.87  % (31395)Time elapsed: 0.040 s
% 19.65/6.87  % (31395)Instructions burned: 68 (million)
% 19.65/6.87  % (31395)------------------------------
% 19.65/6.87  % (31395)------------------------------
% 19.65/6.89  % (31396)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_31173 for (2977ds/358Mi)
% 20.46/7.01  % (31384)Instruction limit reached!
% 20.46/7.01  % (31384)------------------------------
% 20.46/7.01  % (31384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.46/7.01  % (31384)Termination reason: Unknown
% 20.46/7.01  % (31384)Termination phase: Property scanning
% 20.46/7.01  
% 20.46/7.01  % (31384)Memory used [KB]: 22515
% 20.46/7.01  % (31384)Time elapsed: 0.591 s
% 20.46/7.01  % (31384)Instructions burned: 1022 (million)
% 20.46/7.01  % (31384)------------------------------
% 20.46/7.01  % (31384)------------------------------
% 20.46/7.03  % (31397)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_31173 for (2975ds/31Mi)
% 23.18/7.05  % (31397)Instruction limit reached!
% 23.18/7.05  % (31397)------------------------------
% 23.18/7.05  % (31397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.18/7.05  % (31397)Termination reason: Unknown
% 23.18/7.05  % (31397)Termination phase: shuffling
% 23.18/7.05  
% 23.18/7.05  % (31397)Memory used [KB]: 8827
% 23.18/7.05  % (31397)Time elapsed: 0.022 s
% 23.18/7.05  % (31397)Instructions burned: 31 (million)
% 23.18/7.05  % (31397)------------------------------
% 23.18/7.05  % (31397)------------------------------
% 23.18/7.07  % (31398)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_31173 for (2975ds/279Mi)
% 23.18/7.09  % (31396)Instruction limit reached!
% 23.18/7.09  % (31396)------------------------------
% 23.18/7.09  % (31396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.18/7.09  % (31396)Termination reason: Unknown
% 23.18/7.09  % (31396)Termination phase: shuffling
% 23.18/7.09  
% 23.18/7.09  % (31396)Memory used [KB]: 14328
% 23.18/7.09  % (31396)Time elapsed: 0.206 s
% 23.18/7.09  % (31396)Instructions burned: 359 (million)
% 23.18/7.09  % (31396)------------------------------
% 23.18/7.09  % (31396)------------------------------
% 23.18/7.11  % (31399)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_31173 for (2975ds/258Mi)
% 24.13/7.21  % (31398)Instruction limit reached!
% 24.13/7.21  % (31398)------------------------------
% 24.13/7.21  % (31398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/7.21  % (31398)Termination reason: Unknown
% 24.13/7.21  % (31398)Termination phase: shuffling
% 24.13/7.21  
% 24.13/7.21  % (31398)Memory used [KB]: 13432
% 24.13/7.21  % (31398)Time elapsed: 0.138 s
% 24.13/7.21  % (31398)Instructions burned: 280 (million)
% 24.13/7.21  % (31398)------------------------------
% 24.13/7.21  % (31398)------------------------------
% 24.13/7.23  % (31400)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_31173 for (2973ds/26Mi)
% 24.13/7.24  % (31399)Instruction limit reached!
% 24.13/7.24  % (31399)------------------------------
% 24.13/7.24  % (31399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/7.24  % (31399)Termination reason: Unknown
% 24.13/7.24  % (31399)Termination phase: shuffling
% 24.13/7.24  
% 24.13/7.24  % (31399)Memory used [KB]: 12920
% 24.13/7.24  % (31399)Time elapsed: 0.132 s
% 24.13/7.24  % (31399)Instructions burned: 259 (million)
% 24.13/7.24  % (31399)------------------------------
% 24.13/7.24  % (31399)------------------------------
% 24.13/7.24  % (31400)Instruction limit reached!
% 24.13/7.24  % (31400)------------------------------
% 24.13/7.24  % (31400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/7.24  % (31400)Termination reason: Unknown
% 24.13/7.24  % (31400)Termination phase: shuffling
% 24.13/7.24  
% 24.13/7.24  % (31400)Memory used [KB]: 8699
% 24.13/7.24  % (31400)Time elapsed: 0.019 s
% 24.13/7.24  % (31400)Instructions burned: 27 (million)
% 24.13/7.24  % (31400)------------------------------
% 24.13/7.24  % (31400)------------------------------
% 24.13/7.26  % (31401)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_31173 for (2973ds/995Mi)
% 24.13/7.26  % (31402)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_31173 for (2973ds/373Mi)
% 24.97/7.30  % (31390)Instruction limit reached!
% 24.97/7.30  % (31390)------------------------------
% 24.97/7.30  % (31390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.97/7.30  % (31390)Termination reason: Unknown
% 24.97/7.30  % (31390)Termination phase: Function definition elimination
% 24.97/7.30  
% 24.97/7.30  % (31390)Memory used [KB]: 20980
% 24.97/7.30  % (31390)Time elapsed: 0.743 s
% 24.97/7.30  % (31390)Instructions burned: 1540 (million)
% 24.97/7.30  % (31390)------------------------------
% 24.97/7.30  % (31390)------------------------------
% 24.97/7.32  % (31403)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_31173 for (2973ds/253Mi)
% 25.35/7.40  % (31394)First to succeed.
% 25.35/7.41  % (31394)Refutation found. Thanks to Tanya!
% 25.35/7.41  % SZS status Theorem for DTF2THF_31173
% 25.35/7.41  % SZS output start Proof for DTF2THF_31173
% 25.35/7.41  thf(type_def_5, type, rat: $tType).
% 25.35/7.41  thf(type_def_6, type, int: $tType).
% 25.35/7.41  thf(type_def_8, type, nat: $tType).
% 25.35/7.41  thf(type_def_9, type, heap_T5660665574680485309rray_o: $tType).
% 25.35/7.41  thf(type_def_10, type, heap_T1346037964561226099ay_int: $tType).
% 25.35/7.41  thf(type_def_11, type, heap_T3836121109492952855ay_nat: $tType).
% 25.35/7.41  thf(type_def_12, type, array_Product_unit: $tType).
% 25.35/7.41  thf(type_def_13, type, heap_T5738788834812785303t_unit: $tType).
% 25.35/7.41  thf(type_def_14, type, list_o: $tType).
% 25.35/7.41  thf(type_def_15, type, list_int: $tType).
% 25.35/7.41  thf(type_def_16, type, list_nat: $tType).
% 25.35/7.41  thf(type_def_17, type, set_Pr1261947904930325089at_nat: $tType).
% 25.35/7.41  thf(type_def_18, type, code_integer: $tType).
% 25.35/7.41  thf(type_def_19, type, num: $tType).
% 25.35/7.41  thf(type_def_20, type, product_prod_int_int: $tType).
% 25.35/7.41  thf(type_def_21, type, product_prod_nat_nat: $tType).
% 25.35/7.41  thf(type_def_22, type, code_natural: $tType).
% 25.35/7.41  thf(type_def_23, type, option_num: $tType).
% 25.35/7.41  thf(type_def_24, type, product_prod_num_num: $tType).
% 25.35/7.41  thf(type_def_25, type, produc6271795597528267376eger_o: $tType).
% 25.35/7.41  thf(type_def_26, type, produc8923325533196201883nteger: $tType).
% 25.35/7.41  thf(type_def_27, type, set_nat: $tType).
% 25.35/7.41  thf(type_def_28, type, set_set_nat: $tType).
% 25.35/7.41  thf(type_def_29, type, set_int: $tType).
% 25.35/7.41  thf(type_def_30, type, filter_nat: $tType).
% 25.35/7.41  thf(type_def_31, type, filter1242075044329608583at_nat: $tType).
% 25.35/7.41  thf(type_def_32, type, filter_set_nat: $tType).
% 25.35/7.41  thf(type_def_33, type, set_list_nat: $tType).
% 25.35/7.41  thf(type_def_34, type, set_Product_unit: $tType).
% 25.35/7.41  thf(type_def_35, type, set_Code_integer: $tType).
% 25.35/7.41  thf(type_def_36, type, char: $tType).
% 25.35/7.41  thf(type_def_37, type, set_Pr8693737435421807431at_nat: $tType).
% 25.35/7.41  thf(type_def_38, type, heap_e7401611519738050253t_unit: $tType).
% 25.35/7.41  thf(type_def_39, type, option8956607266484857688it_nat: $tType).
% 25.35/7.41  thf(type_def_40, type, product_unit: $tType).
% 25.35/7.41  thf(type_def_41, type, heap_Time_Heap_a: $tType).
% 25.35/7.41  thf(type_def_42, type, a: $tType).
% 25.35/7.41  thf(type_def_43, type, list_char: $tType).
% 25.35/7.41  thf(type_def_44, type, set_Pr958786334691620121nt_int: $tType).
% 25.35/7.41  thf(type_def_45, type, set_rat: $tType).
% 25.35/7.41  thf(type_def_46, type, list_num: $tType).
% 25.35/7.41  thf(type_def_47, type, list_rat: $tType).
% 25.35/7.41  thf(type_def_48, type, list_Code_integer: $tType).
% 25.35/7.41  thf(type_def_49, type, multiset_nat: $tType).
% 25.35/7.41  thf(type_def_50, type, produc8664842809031399944it_nat: $tType).
% 25.35/7.41  thf(type_def_51, type, set_char: $tType).
% 25.35/7.41  thf(type_def_52, type, produc7822875418678951345atural: $tType).
% 25.35/7.41  thf(type_def_53, type, produc5835291356934675326atural: $tType).
% 25.35/7.41  thf(type_def_54, type, produc6653097349344004940it_nat: $tType).
% 25.35/7.41  thf(type_def_55, type, product_prod_nat_num: $tType).
% 25.35/7.41  thf(type_def_56, type, produc6756470014200349799atural: $tType).
% 25.35/7.41  thf(type_def_57, type, produc859450856879609959at_nat: $tType).
% 25.35/7.41  thf(type_def_58, type, ref_Product_unit: $tType).
% 25.35/7.41  thf(type_def_59, type, set_se6260736226359567993nt_int: $tType).
% 25.35/7.41  thf(func_def_0, type, produc6756470014200349799atural: $tType).
% 25.35/7.41  thf(func_def_1, type, option8956607266484857688it_nat: $tType).
% 25.35/7.41  thf(func_def_2, type, set_Pr8693737435421807431at_nat: $tType).
% 25.35/7.41  thf(func_def_3, type, produc8664842809031399944it_nat: $tType).
% 25.35/7.41  thf(func_def_4, type, produc5835291356934675326atural: $tType).
% 25.35/7.41  thf(func_def_5, type, produc859450856879609959at_nat: $tType).
% 25.35/7.41  thf(func_def_6, type, produc6653097349344004940it_nat: $tType).
% 25.35/7.41  thf(func_def_7, type, set_se6260736226359567993nt_int: $tType).
% 25.35/7.41  thf(func_def_8, type, produc7822875418678951345atural: $tType).
% 25.35/7.41  thf(func_def_9, type, produc8923325533196201883nteger: $tType).
% 25.35/7.41  thf(func_def_10, type, filter1242075044329608583at_nat: $tType).
% 25.35/7.41  thf(func_def_11, type, set_Pr1261947904930325089at_nat: $tType).
% 25.35/7.41  thf(func_def_12, type, set_Pr958786334691620121nt_int: $tType).
% 25.35/7.41  thf(func_def_13, type, heap_T3836121109492952855ay_nat: $tType).
% 25.35/7.41  thf(func_def_14, type, heap_T1346037964561226099ay_int: $tType).
% 25.35/7.41  thf(func_def_15, type, produc6271795597528267376eger_o: $tType).
% 25.35/7.41  thf(func_def_16, type, heap_T5738788834812785303t_unit: $tType).
% 25.35/7.41  thf(func_def_17, type, heap_T5660665574680485309rray_o: $tType).
% 25.35/7.41  thf(func_def_18, type, heap_e7401611519738050253t_unit: $tType).
% 25.35/7.41  thf(func_def_19, type, product_prod_num_num: $tType).
% 25.35/7.41  thf(func_def_20, type, product_prod_nat_num: $tType).
% 25.35/7.41  thf(func_def_21, type, product_prod_nat_nat: $tType).
% 25.35/7.41  thf(func_def_22, type, product_prod_int_int: $tType).
% 25.35/7.41  thf(func_def_23, type, filter_set_nat: $tType).
% 25.35/7.41  thf(func_def_24, type, set_list_nat: $tType).
% 25.35/7.41  thf(func_def_25, type, list_Code_integer: $tType).
% 25.35/7.41  thf(func_def_26, type, set_set_nat: $tType).
% 25.35/7.41  thf(func_def_27, type, set_Code_integer: $tType).
% 25.35/7.41  thf(func_def_28, type, array_Product_unit: $tType).
% 25.35/7.41  thf(func_def_29, type, ref_Product_unit: $tType).
% 25.35/7.41  thf(func_def_30, type, set_Product_unit: $tType).
% 25.35/7.41  thf(func_def_31, type, heap_Time_Heap_a: $tType).
% 25.35/7.41  thf(func_def_32, type, multiset_nat: $tType).
% 25.35/7.41  thf(func_def_33, type, option_num: $tType).
% 25.35/7.41  thf(func_def_34, type, list_char: $tType).
% 25.35/7.41  thf(func_def_35, type, filter_nat: $tType).
% 25.35/7.41  thf(func_def_36, type, set_char: $tType).
% 25.35/7.41  thf(func_def_37, type, list_rat: $tType).
% 25.35/7.41  thf(func_def_38, type, list_num: $tType).
% 25.35/7.41  thf(func_def_39, type, list_nat: $tType).
% 25.35/7.41  thf(func_def_40, type, list_int: $tType).
% 25.35/7.41  thf(func_def_41, type, set_rat: $tType).
% 25.35/7.41  thf(func_def_42, type, set_nat: $tType).
% 25.35/7.41  thf(func_def_43, type, set_int: $tType).
% 25.35/7.41  thf(func_def_44, type, code_natural: $tType).
% 25.35/7.41  thf(func_def_45, type, code_integer: $tType).
% 25.35/7.41  thf(func_def_46, type, product_unit: $tType).
% 25.35/7.41  thf(func_def_47, type, list_o: $tType).
% 25.35/7.41  thf(func_def_48, type, char: $tType).
% 25.35/7.41  thf(func_def_49, type, rat: $tType).
% 25.35/7.41  thf(func_def_50, type, num: $tType).
% 25.35/7.41  thf(func_def_51, type, nat: $tType).
% 25.35/7.41  thf(func_def_52, type, int: $tType).
% 25.35/7.41  thf(func_def_53, type, a: $tType).
% 25.35/7.41  thf(func_def_54, type, archim2889992004027027881ng_rat: rat > int).
% 25.35/7.41  thf(func_def_55, type, archim3151403230148437115or_rat: rat > int).
% 25.35/7.41  thf(func_def_56, type, archimedean_frac_rat: rat > rat).
% 25.35/7.41  thf(func_def_57, type, array_make_o: nat > (nat > $o) > heap_T5660665574680485309rray_o).
% 25.35/7.41  thf(func_def_58, type, array_make_int: nat > (nat > int) > heap_T1346037964561226099ay_int).
% 25.35/7.41  thf(func_def_59, type, array_make_nat: nat > (nat > nat) > heap_T3836121109492952855ay_nat).
% 25.35/7.41  thf(func_def_60, type, array_7872002506669749220t_unit: array_Product_unit > nat > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_61, type, array_of_list_o: list_o > heap_T5660665574680485309rray_o).
% 25.35/7.41  thf(func_def_62, type, array_of_list_int: list_int > heap_T1346037964561226099ay_int).
% 25.35/7.41  thf(func_def_63, type, array_of_list_nat: list_nat > heap_T3836121109492952855ay_nat).
% 25.35/7.41  thf(func_def_64, type, bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat).
% 25.35/7.41  thf(func_def_65, type, bNF_re6321650412969554871eger_o: (int > code_integer > $o) > ((int > $o) > (code_integer > $o) > $o) > (int > int > $o) > (code_integer > code_integer > $o) > $o).
% 25.35/7.41  thf(func_def_66, type, bNF_re398004352372739002nteger: (int > code_integer > $o) > ((int > int) > (code_integer > code_integer) > $o) > (int > int > int) > (code_integer > code_integer > code_integer) > $o).
% 25.35/7.41  thf(func_def_67, type, bNF_re4711666741709854504_nat_o: (int > code_integer > $o) > ((nat > $o) > (nat > $o) > $o) > (int > nat > $o) > (code_integer > nat > $o) > $o).
% 25.35/7.41  thf(func_def_68, type, bNF_re6574881592172037608er_o_o: (int > code_integer > $o) > ($o > $o > $o) > (int > $o) > (code_integer > $o) > $o).
% 25.35/7.41  thf(func_def_69, type, bNF_re3379532845092657523nteger: (int > code_integer > $o) > (int > code_integer > $o) > (int > int) > (code_integer > code_integer) > $o).
% 25.35/7.41  thf(func_def_70, type, bNF_re3804157879324367682nt_int: (int > code_integer > $o) > (int > int > $o) > (int > int) > (code_integer > int) > $o).
% 25.35/7.41  thf(func_def_71, type, bNF_re2807294637932363402at_nat: (int > code_integer > $o) > (nat > nat > $o) > (int > nat) > (code_integer > nat) > $o).
% 25.35/7.41  thf(func_def_72, type, bNF_re6718328864250387230um_num: (int > code_integer > $o) > (num > num > $o) > (int > num) > (code_integer > num) > $o).
% 25.35/7.41  thf(func_def_73, type, bNF_re3403563459893282935_int_o: (int > int > $o) > ((int > $o) > (int > $o) > $o) > (int > int > $o) > (int > int > $o) > $o).
% 25.35/7.41  thf(func_def_74, type, bNF_re711492959462206631nt_int: (int > int > $o) > ((int > int) > (int > int) > $o) > (int > int > int) > (int > int > int) > $o).
% 25.35/7.41  thf(func_def_75, type, bNF_re157797125943740599nt_int: (int > int > $o) > ((int > product_prod_int_int) > (int > product_prod_int_int) > $o) > (int > int > product_prod_int_int) > (int > int > product_prod_int_int) > $o).
% 25.35/7.41  thf(func_def_76, type, bNF_re3461391660133120880nt_rat: (int > int > $o) > ((int > product_prod_int_int) > (int > rat) > $o) > (int > int > product_prod_int_int) > (int > int > rat) > $o).
% 25.35/7.41  thf(func_def_77, type, bNF_re3376528473927230327_nat_o: (int > int > $o) > ((nat > $o) > (nat > $o) > $o) > (int > nat > $o) > (int > nat > $o) > $o).
% 25.35/7.41  thf(func_def_78, type, bNF_re5089333283451836215nt_o_o: (int > int > $o) > ($o > $o > $o) > (int > $o) > (int > $o) > $o).
% 25.35/7.41  thf(func_def_79, type, bNF_re982302072995117890nteger: (int > int > $o) > (int > code_integer > $o) > (int > int) > (int > code_integer) > $o).
% 25.35/7.41  thf(func_def_80, type, bNF_re4712519889275205905nt_int: (int > int > $o) > (int > int > $o) > (int > int) > (int > int) > $o).
% 25.35/7.41  thf(func_def_81, type, bNF_re3715656647883201625at_nat: (int > int > $o) > (nat > nat > $o) > (int > nat) > (int > nat) > $o).
% 25.35/7.41  thf(func_def_82, type, bNF_re7626690874201225453um_num: (int > int > $o) > (num > num > $o) > (int > num) > (int > num) > $o).
% 25.35/7.41  thf(func_def_83, type, bNF_re6250860962936578807nt_int: (int > int > $o) > (product_prod_int_int > product_prod_int_int > $o) > (int > product_prod_int_int) > (int > product_prod_int_int) > $o).
% 25.35/7.41  thf(func_def_84, type, bNF_re2214769303045360666nt_rat: (int > int > $o) > (product_prod_int_int > rat > $o) > (int > product_prod_int_int) > (int > rat) > $o).
% 25.35/7.41  thf(func_def_85, type, bNF_re4935368626670024657nteger: (nat > nat > $o) > ((int > int) > (code_integer > code_integer) > $o) > (nat > int > int) > (nat > code_integer > code_integer) > $o).
% 25.35/7.41  thf(func_def_86, type, bNF_re4785983289428654063nt_int: (nat > nat > $o) > ((int > int) > (int > int) > $o) > (nat > int > int) > (nat > int > int) > $o).
% 25.35/7.41  thf(func_def_87, type, bNF_re578469030762574527_nat_o: (nat > nat > $o) > ((nat > $o) > (nat > $o) > $o) > (nat > nat > $o) > (nat > nat > $o) > $o).
% 25.35/7.41  thf(func_def_88, type, bNF_re1345281282404953727at_nat: (nat > nat > $o) > ((nat > nat) > (nat > nat) > $o) > (nat > nat > nat) > (nat > nat > nat) > $o).
% 25.35/7.41  thf(func_def_89, type, bNF_re4705727531993890431at_o_o: (nat > nat > $o) > ($o > $o > $o) > (nat > $o) > (nat > $o) > $o).
% 25.35/7.41  thf(func_def_90, type, bNF_re4153400068438556298nteger: (nat > nat > $o) > (int > code_integer > $o) > (nat > int) > (nat > code_integer) > $o).
% 25.35/7.41  thf(func_def_91, type, bNF_re6650684261131312217nt_int: (nat > nat > $o) > (int > int > $o) > (nat > int) > (nat > int) > $o).
% 25.35/7.41  thf(func_def_92, type, bNF_re5653821019739307937at_nat: (nat > nat > $o) > (nat > nat > $o) > (nat > nat) > (nat > nat) > $o).
% 25.35/7.41  thf(func_def_93, type, bNF_re6830278522597306478at_int: (nat > nat > $o) > (product_prod_nat_nat > int > $o) > (nat > product_prod_nat_nat) > (nat > int) > $o).
% 25.35/7.41  thf(func_def_94, type, bNF_re7876454716742015248nteger: (num > num > $o) > ((num > int) > (num > code_integer) > $o) > (num > num > int) > (num > num > code_integer) > $o).
% 25.35/7.41  thf(func_def_95, type, bNF_re8402795839162346335um_int: (num > num > $o) > ((num > int) > (num > int) > $o) > (num > num > int) > (num > num > int) > $o).
% 25.35/7.41  thf(func_def_96, type, bNF_re6501075790457514782nteger: (num > num > $o) > (int > code_integer > $o) > (num > int) > (num > code_integer) > $o).
% 25.35/7.41  thf(func_def_97, type, bNF_re1822329894187522285nt_int: (num > num > $o) > (int > int > $o) > (num > int) > (num > int) > $o).
% 25.35/7.41  thf(func_def_98, type, bNF_re5228765855967844073nt_int: (product_prod_int_int > product_prod_int_int > $o) > ((product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > $o) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > $o).
% 25.35/7.41  thf(func_def_99, type, bNF_re8699439704749558557nt_o_o: (product_prod_int_int > product_prod_int_int > $o) > ($o > $o > $o) > (product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 25.35/7.41  thf(func_def_100, type, bNF_re7145576690424134365nt_int: (product_prod_int_int > product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > $o).
% 25.35/7.41  thf(func_def_101, type, bNF_re7627151682743391978at_rat: (product_prod_int_int > rat > $o) > ((product_prod_int_int > product_prod_int_int) > (rat > rat) > $o) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > (rat > rat > rat) > $o).
% 25.35/7.41  thf(func_def_102, type, bNF_re1494630372529172596at_o_o: (product_prod_int_int > rat > $o) > ($o > $o > $o) > (product_prod_int_int > $o) > (rat > $o) > $o).
% 25.35/7.41  thf(func_def_103, type, bNF_re8279943556446156061nt_rat: (product_prod_int_int > rat > $o) > (product_prod_int_int > rat > $o) > (product_prod_int_int > product_prod_int_int) > (rat > rat) > $o).
% 25.35/7.41  thf(func_def_104, type, bNF_re717283939379294677_int_o: (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (int > int > $o) > $o).
% 25.35/7.41  thf(func_def_105, type, bNF_re7408651293131936558nt_int: (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (int > int > int) > $o).
% 25.35/7.41  thf(func_def_106, type, bNF_re6644619430987730960nt_o_o: (product_prod_nat_nat > int > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (int > $o) > $o).
% 25.35/7.41  thf(func_def_107, type, bNF_re4555766996558763186at_nat: (product_prod_nat_nat > int > $o) > (nat > nat > $o) > (product_prod_nat_nat > nat) > (int > nat) > $o).
% 25.35/7.41  thf(func_def_108, type, bNF_re7400052026677387805at_int: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o).
% 25.35/7.41  thf(func_def_109, type, bNF_re4202695980764964119_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 25.35/7.41  thf(func_def_110, type, bNF_re3099431351363272937at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > $o) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > $o).
% 25.35/7.41  thf(func_def_111, type, bNF_re3666534408544137501at_o_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o).
% 25.35/7.41  thf(func_def_112, type, bNF_re8246922863344978751at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > (nat > nat > $o) > (product_prod_nat_nat > nat) > (product_prod_nat_nat > nat) > $o).
% 25.35/7.41  thf(func_def_113, type, bNF_re7934895593101944656at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > int) > $o).
% 25.35/7.41  thf(func_def_114, type, bNF_re2241393799969408733at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > $o).
% 25.35/7.41  thf(func_def_115, type, basic_1567116559311922317nt_int: (int > $o) > (int > $o) > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_116, type, basic_570253317919918037at_nat: (nat > $o) > (nat > $o) > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_117, type, basic_4387203522000727145nt_int: (int > int > $o) > (int > int > $o) > product_prod_int_int > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_118, type, basic_5328504652464829177at_nat: (nat > nat > $o) > (nat > nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_119, type, binomial: nat > nat > nat).
% 25.35/7.41  thf(func_def_120, type, gbinom8545251970709558553nteger: code_integer > nat > code_integer).
% 25.35/7.41  thf(func_def_121, type, gbinom7368847122466276068atural: code_natural > nat > code_natural).
% 25.35/7.41  thf(func_def_122, type, gbinomial_int: int > nat > int).
% 25.35/7.41  thf(func_def_123, type, gbinomial_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_124, type, gbinomial_rat: rat > nat > rat).
% 25.35/7.41  thf(func_def_125, type, bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_126, type, bit_and_not_num: num > num > option_num).
% 25.35/7.41  thf(func_def_127, type, bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o).
% 25.35/7.41  thf(func_def_128, type, bit_concat_bit: nat > int > int > int).
% 25.35/7.41  thf(func_def_129, type, bit_or_not_num_neg: num > num > num).
% 25.35/7.41  thf(func_def_130, type, bit_ri7632146776885996613nteger: code_integer > code_integer).
% 25.35/7.41  thf(func_def_131, type, bit_ri7919022796975470100ot_int: int > int).
% 25.35/7.41  thf(func_def_132, type, bit_ri631733984087533419it_int: nat > int > int).
% 25.35/7.41  thf(func_def_133, type, bit_se3949692690581998587nteger: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_134, type, bit_se2773287842338716102atural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_135, type, bit_se725231765392027082nd_int: int > int > int).
% 25.35/7.41  thf(func_def_136, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_137, type, bit_se3928097537394005634nteger: nat > code_integer > code_integer).
% 25.35/7.41  thf(func_def_138, type, bit_se2751692689150723149atural: nat > code_natural > code_natural).
% 25.35/7.41  thf(func_def_139, type, bit_se8568078237143864401it_int: nat > int > int).
% 25.35/7.41  thf(func_def_140, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_141, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 25.35/7.41  thf(func_def_142, type, bit_se168947363167071951atural: nat > code_natural > code_natural).
% 25.35/7.41  thf(func_def_143, type, bit_se2159334234014336723it_int: nat > int > int).
% 25.35/7.41  thf(func_def_144, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_145, type, bit_se2119862282449309892nteger: nat > code_integer).
% 25.35/7.41  thf(func_def_146, type, bit_se943457434206027407atural: nat > code_natural).
% 25.35/7.41  thf(func_def_147, type, bit_se2000444600071755411sk_int: nat > int).
% 25.35/7.41  thf(func_def_148, type, bit_se2002935070580805687sk_nat: nat > nat).
% 25.35/7.41  thf(func_def_149, type, bit_se1080825931792720795nteger: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_150, type, bit_se9127793120404214118atural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_151, type, bit_se1409905431419307370or_int: int > int > int).
% 25.35/7.41  thf(func_def_152, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_153, type, bit_se7788150548672797655nteger: nat > code_integer > code_integer).
% 25.35/7.41  thf(func_def_154, type, bit_se6611745700429515170atural: nat > code_natural > code_natural).
% 25.35/7.41  thf(func_def_155, type, bit_se545348938243370406it_int: nat > int > int).
% 25.35/7.41  thf(func_def_156, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_157, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 25.35/7.41  thf(func_def_158, type, bit_se1617098188084679374atural: nat > code_natural > code_natural).
% 25.35/7.41  thf(func_def_159, type, bit_se7879613467334960850it_int: nat > int > int).
% 25.35/7.41  thf(func_def_160, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_161, type, bit_se1745604003318907178nteger: nat > code_integer > code_integer).
% 25.35/7.41  thf(func_def_162, type, bit_se569199155075624693atural: nat > code_natural > code_natural).
% 25.35/7.41  thf(func_def_163, type, bit_se2923211474154528505it_int: nat > int > int).
% 25.35/7.41  thf(func_def_164, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_165, type, bit_se8260200283734997820nteger: nat > code_integer > code_integer).
% 25.35/7.41  thf(func_def_166, type, bit_se7083795435491715335atural: nat > code_natural > code_natural).
% 25.35/7.41  thf(func_def_167, type, bit_se4203085406695923979it_int: nat > int > int).
% 25.35/7.41  thf(func_def_168, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_169, type, bit_se3222712562003087583nteger: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_170, type, bit_se2046307713759805098atural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_171, type, bit_se6526347334894502574or_int: int > int > int).
% 25.35/7.41  thf(func_def_172, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_173, type, bit_se9216721137139052372nteger: code_integer > nat > $o).
% 25.35/7.41  thf(func_def_174, type, bit_se8040316288895769887atural: code_natural > nat > $o).
% 25.35/7.41  thf(func_def_175, type, bit_se1146084159140164899it_int: int > nat > $o).
% 25.35/7.41  thf(func_def_176, type, bit_se1148574629649215175it_nat: nat > nat > $o).
% 25.35/7.41  thf(func_def_177, type, bit_take_bit_num: nat > num > option_num).
% 25.35/7.41  thf(func_def_178, type, bit_un7362597486090784418nd_num: num > num > option_num).
% 25.35/7.41  thf(func_def_179, type, bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o).
% 25.35/7.41  thf(func_def_180, type, code_Nat: code_integer > code_natural).
% 25.35/7.41  thf(func_def_181, type, code_Neg: num > code_integer).
% 25.35/7.41  thf(func_def_182, type, code_Suc: code_natural > code_natural).
% 25.35/7.41  thf(func_def_183, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 25.35/7.41  thf(func_def_184, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_185, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_186, type, code_dup: code_integer > code_integer).
% 25.35/7.41  thf(func_def_187, type, code_int_of_integer: code_integer > int).
% 25.35/7.41  thf(func_def_188, type, code_integer_of_int: int > code_integer).
% 25.35/7.41  thf(func_def_189, type, code_integer_of_nat: nat > code_integer).
% 25.35/7.41  thf(func_def_190, type, code_i5400310926305786745atural: code_natural > code_integer).
% 25.35/7.41  thf(func_def_191, type, code_integer_of_num: num > code_integer).
% 25.35/7.41  thf(func_def_192, type, code_nat_of_integer: code_integer > nat).
% 25.35/7.41  thf(func_def_193, type, code_nat_of_natural: code_natural > nat).
% 25.35/7.41  thf(func_def_194, type, code_natural_of_nat: nat > code_natural).
% 25.35/7.41  thf(func_def_195, type, code_n4118661773612635043nteger: code_integer > code_natural).
% 25.35/7.41  thf(func_def_196, type, code_negative: num > code_integer).
% 25.35/7.41  thf(func_def_197, type, code_num_of_integer: code_integer > num).
% 25.35/7.41  thf(func_def_198, type, code_pcr_integer: int > code_integer > $o).
% 25.35/7.41  thf(func_def_199, type, code_positive: num > code_integer).
% 25.35/7.41  thf(func_def_200, type, code_size_nat: code_natural > nat).
% 25.35/7.41  thf(func_def_201, type, code_sub: num > num > code_integer).
% 25.35/7.41  thf(func_def_202, type, complete_Inf_Inf_nat: set_nat > nat).
% 25.35/7.41  thf(func_def_203, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 25.35/7.41  thf(func_def_204, type, complete_Sup_Sup_int: set_int > int).
% 25.35/7.41  thf(func_def_205, type, complete_Sup_Sup_nat: set_nat > nat).
% 25.35/7.41  thf(func_def_206, type, comple7399068483239264473et_nat: set_set_nat > set_nat).
% 25.35/7.41  thf(func_def_207, type, adjust_div: product_prod_int_int > int).
% 25.35/7.41  thf(func_def_208, type, adjust_mod: int > int > int).
% 25.35/7.41  thf(func_def_209, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_210, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_211, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_212, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 25.35/7.41  thf(func_def_213, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_214, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_215, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 25.35/7.41  thf(func_def_216, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_217, type, euclid6377331345833325938nteger: code_integer > nat).
% 25.35/7.41  thf(func_def_218, type, euclid5200926497590043453atural: code_natural > nat).
% 25.35/7.41  thf(func_def_219, type, euclid4774559944035922753ze_int: int > nat).
% 25.35/7.41  thf(func_def_220, type, euclid4777050414544973029ze_nat: nat > nat).
% 25.35/7.41  thf(func_def_221, type, euclid6289375185220004616nteger: code_integer > code_integer).
% 25.35/7.41  thf(func_def_222, type, euclid5112970336976722131atural: code_natural > code_natural).
% 25.35/7.41  thf(func_def_223, type, euclid3395696857347342551nt_int: int > int).
% 25.35/7.41  thf(func_def_224, type, euclid3398187327856392827nt_nat: nat > nat).
% 25.35/7.41  thf(func_def_225, type, comm_s8582702949713902594nteger: code_integer > nat > code_integer).
% 25.35/7.41  thf(func_def_226, type, comm_s7406298101470620109atural: code_natural > nat > code_natural).
% 25.35/7.41  thf(func_def_227, type, comm_s4660882817536571857er_int: int > nat > int).
% 25.35/7.41  thf(func_def_228, type, comm_s4663373288045622133er_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_229, type, comm_s4028243227959126397er_rat: rat > nat > rat).
% 25.35/7.41  thf(func_def_230, type, semiri3624122377584611663nteger: nat > code_integer).
% 25.35/7.41  thf(func_def_231, type, semiri2447717529341329178atural: nat > code_natural).
% 25.35/7.41  thf(func_def_232, type, semiri1406184849735516958ct_int: nat > int).
% 25.35/7.41  thf(func_def_233, type, semiri1408675320244567234ct_nat: nat > nat).
% 25.35/7.41  thf(func_def_234, type, semiri773545260158071498ct_rat: nat > rat).
% 25.35/7.41  thf(func_def_235, type, inverse_inverse_rat: rat > rat).
% 25.35/7.41  thf(func_def_236, type, at_top_nat: filter_nat).
% 25.35/7.41  thf(func_def_237, type, eventually_nat: (nat > $o) > filter_nat > $o).
% 25.35/7.41  thf(func_def_238, type, eventu1038000079068216329at_nat: (product_prod_nat_nat > $o) > filter1242075044329608583at_nat > $o).
% 25.35/7.41  thf(func_def_239, type, filter3212408913953519116et_nat: (nat > set_nat) > filter_set_nat > filter_nat > $o).
% 25.35/7.41  thf(func_def_240, type, finite3254316476582989077op_nat: set_nat > filter_set_nat).
% 25.35/7.41  thf(func_def_241, type, prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat).
% 25.35/7.41  thf(func_def_242, type, finite_card_int: set_int > nat).
% 25.35/7.41  thf(func_def_243, type, finite_card_list_nat: set_list_nat > nat).
% 25.35/7.41  thf(func_def_244, type, finite_card_nat: set_nat > nat).
% 25.35/7.41  thf(func_def_245, type, finite410649719033368117t_unit: set_Product_unit > nat).
% 25.35/7.41  thf(func_def_246, type, finite_card_set_nat: set_set_nat > nat).
% 25.35/7.41  thf(func_def_247, type, finite6017078050557962740nteger: set_Code_integer > $o).
% 25.35/7.41  thf(func_def_248, type, finite_finite_int: set_int > $o).
% 25.35/7.41  thf(func_def_249, type, finite_finite_nat: set_nat > $o).
% 25.35/7.41  thf(func_def_250, type, bij_betw_nat_nat: (nat > nat) > set_nat > set_nat > $o).
% 25.35/7.41  thf(func_def_251, type, comp_C8797469213163452608nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_252, type, comp_C1593894019821074884nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_253, type, comp_C3531382070062128313er_num: (code_integer > code_integer) > (num > code_integer) > num > code_integer).
% 25.35/7.41  thf(func_def_254, type, comp_int_nat_int: (int > nat) > (int > int) > int > nat).
% 25.35/7.41  thf(func_def_255, type, comp_nat_num_int: (nat > num) > (int > nat) > int > num).
% 25.35/7.41  thf(func_def_256, type, id_nat_o: (nat > $o) > nat > $o).
% 25.35/7.41  thf(func_def_257, type, id_o: $o > $o).
% 25.35/7.41  thf(func_def_258, type, id_int: int > int).
% 25.35/7.41  thf(func_def_259, type, id_nat: nat > nat).
% 25.35/7.41  thf(func_def_260, type, id_num: num > num).
% 25.35/7.41  thf(func_def_261, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 25.35/7.41  thf(func_def_262, type, inj_on_nat_char: (nat > char) > set_nat > $o).
% 25.35/7.41  thf(func_def_263, type, map_fu2496120808607739376eger_o: (code_integer > int) > ((int > $o) > code_integer > $o) > (int > int > $o) > code_integer > code_integer > $o).
% 25.35/7.41  thf(func_def_264, type, map_fu8272188784021352819nteger: (code_integer > int) > ((int > int) > code_integer > code_integer) > (int > int > int) > code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_265, type, map_fu186220595405829473_nat_o: (code_integer > int) > ((nat > $o) > nat > $o) > (int > nat > $o) > code_integer > nat > $o).
% 25.35/7.41  thf(func_def_266, type, map_fu6957801986076833569nt_o_o: (code_integer > int) > ($o > $o) > (int > $o) > code_integer > $o).
% 25.35/7.41  thf(func_def_267, type, map_fu2599414010547811884nteger: (code_integer > int) > (int > code_integer) > (int > int) > code_integer > code_integer).
% 25.35/7.41  thf(func_def_268, type, map_fu1051355602067684763atural: (code_integer > int) > (nat > code_natural) > (int > nat) > code_integer > code_natural).
% 25.35/7.41  thf(func_def_269, type, map_fu6539832666145259331at_nat: (code_integer > int) > (nat > nat) > (int > nat) > code_integer > nat).
% 25.35/7.41  thf(func_def_270, type, map_fu1227494855608507351um_num: (code_integer > int) > (num > num) > (int > num) > code_integer > num).
% 25.35/7.41  thf(func_def_271, type, map_fu6256889081107267320ural_o: (code_natural > nat) > ((nat > $o) > code_natural > $o) > (nat > nat > $o) > code_natural > code_natural > $o).
% 25.35/7.41  thf(func_def_272, type, map_fu6244533035418998608_nat_o: (code_natural > nat) > ((nat > $o) > nat > $o) > (nat > nat > $o) > code_natural > nat > $o).
% 25.35/7.41  thf(func_def_273, type, map_fu6549440983881763648atural: (code_natural > nat) > ((nat > nat) > code_natural > code_natural) > (nat > nat > nat) > code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_274, type, map_fu4892316939951275536at_o_o: (code_natural > nat) > ($o > $o) > (nat > $o) > code_natural > $o).
% 25.35/7.41  thf(func_def_275, type, map_fu2787874002554666395nteger: (code_natural > nat) > (int > code_integer) > (nat > int) > code_natural > code_integer).
% 25.35/7.41  thf(func_def_276, type, map_fu1239815594074539274atural: (code_natural > nat) > (nat > code_natural) > (nat > nat) > code_natural > code_natural).
% 25.35/7.41  thf(func_def_277, type, map_fu226235371393106610at_nat: (code_natural > nat) > (nat > nat) > (nat > nat) > code_natural > nat).
% 25.35/7.41  thf(func_def_278, type, map_fu7831380289885515383nt_rat: (int > int) > ((int > product_prod_int_int) > int > rat) > (int > int > product_prod_int_int) > int > int > rat).
% 25.35/7.41  thf(func_def_279, type, map_fu3424225382358772769nt_rat: (int > int) > (product_prod_int_int > rat) > (int > product_prod_int_int) > int > rat).
% 25.35/7.41  thf(func_def_280, 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 > $o).
% 25.35/7.41  thf(func_def_281, type, map_fu4960017516451851995nt_int: (int > product_prod_nat_nat) > ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > int > int > int).
% 25.35/7.41  thf(func_def_282, type, map_fu4826362097070443709at_o_o: (int > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > int > $o).
% 25.35/7.41  thf(func_def_283, type, map_fu2345160673673942751at_nat: (int > product_prod_nat_nat) > (nat > nat) > (product_prod_nat_nat > nat) > int > nat).
% 25.35/7.41  thf(func_def_284, type, map_fu3667384564859982768at_int: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > int > int).
% 25.35/7.41  thf(func_def_285, type, map_fu8224359078269604234nteger: (nat > nat) > ((int > int) > code_integer > code_integer) > (nat > int > int) > nat > code_integer > code_integer).
% 25.35/7.41  thf(func_def_286, type, map_fu6981160461238011112atural: (nat > nat) > ((nat > nat) > code_natural > code_natural) > (nat > nat > nat) > nat > code_natural > code_natural).
% 25.35/7.41  thf(func_def_287, type, map_fu6290471996055670595nteger: (nat > nat) > (int > code_integer) > (nat > int) > nat > code_integer).
% 25.35/7.41  thf(func_def_288, type, map_fu4742413587575543474atural: (nat > nat) > (nat > code_natural) > (nat > nat) > nat > code_natural).
% 25.35/7.41  thf(func_def_289, type, map_fu6891787308814931657nteger: (num > num) > ((num > int) > num > code_integer) > (num > num > int) > num > num > code_integer).
% 25.35/7.41  thf(func_def_290, type, map_fu8638147718074629079nteger: (num > num) > (int > code_integer) > (num > int) > num > code_integer).
% 25.35/7.41  thf(func_def_291, type, map_fu4333342158222067775at_rat: (rat > product_prod_int_int) > ((product_prod_int_int > product_prod_int_int) > rat > rat) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > rat > rat > rat).
% 25.35/7.41  thf(func_def_292, type, map_fu898904425404107465nt_o_o: (rat > product_prod_int_int) > ($o > $o) > (product_prod_int_int > $o) > rat > $o).
% 25.35/7.41  thf(func_def_293, type, map_fu5673905371560938248nt_rat: (rat > product_prod_int_int) > (product_prod_int_int > rat) > (product_prod_int_int > product_prod_int_int) > rat > rat).
% 25.35/7.41  thf(func_def_294, type, fun_is_measure_int: (int > nat) > $o).
% 25.35/7.41  thf(func_def_295, type, fun_pair_leq: set_Pr8693737435421807431at_nat).
% 25.35/7.41  thf(func_def_296, type, fun_pair_less: set_Pr8693737435421807431at_nat).
% 25.35/7.41  thf(func_def_297, type, gcd_Gcd_int: set_int > int).
% 25.35/7.41  thf(func_def_298, type, gcd_Gcd_nat: set_nat > nat).
% 25.35/7.41  thf(func_def_299, type, bezw: nat > nat > product_prod_int_int).
% 25.35/7.41  thf(func_def_300, type, bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_301, type, gcd_gcd_Code_integer: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_302, type, gcd_gcd_int: int > int > int).
% 25.35/7.41  thf(func_def_303, type, gcd_gcd_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_304, type, gcd_lcm_Code_integer: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_305, type, gcd_lcm_int: int > int > int).
% 25.35/7.41  thf(func_def_306, type, gcd_lcm_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_307, type, gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_308, type, abs_abs_Code_integer: code_integer > code_integer).
% 25.35/7.41  thf(func_def_309, type, abs_abs_int: int > int).
% 25.35/7.41  thf(func_def_310, type, abs_abs_rat: rat > rat).
% 25.35/7.41  thf(func_def_311, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_312, type, minus_7197305767214868737atural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_313, type, minus_minus_int: int > int > int).
% 25.35/7.41  thf(func_def_314, type, minus_minus_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_315, type, minus_minus_rat: rat > rat > rat).
% 25.35/7.41  thf(func_def_316, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 25.35/7.41  thf(func_def_317, type, one_one_Code_integer: code_integer).
% 25.35/7.41  thf(func_def_318, type, one_one_Code_natural: code_natural).
% 25.35/7.41  thf(func_def_319, type, one_one_int: int).
% 25.35/7.41  thf(func_def_320, type, one_one_nat: nat).
% 25.35/7.41  thf(func_def_321, type, one_one_rat: rat).
% 25.35/7.41  thf(func_def_322, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_323, type, plus_p4538020629002901425atural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_324, type, plus_plus_int: int > int > int).
% 25.35/7.41  thf(func_def_325, type, plus_plus_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_326, type, plus_plus_num: num > num > num).
% 25.35/7.41  thf(func_def_327, type, plus_plus_rat: rat > rat > rat).
% 25.35/7.41  thf(func_def_328, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 25.35/7.41  thf(func_def_329, type, sgn_sgn_int: int > int).
% 25.35/7.41  thf(func_def_330, type, sgn_sgn_rat: rat > rat).
% 25.35/7.41  thf(func_def_331, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_332, type, times_2397367101498566445atural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_333, type, times_times_int: int > int > int).
% 25.35/7.41  thf(func_def_334, type, times_times_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_335, type, times_times_num: num > num > num).
% 25.35/7.41  thf(func_def_336, type, times_times_rat: rat > rat > rat).
% 25.35/7.41  thf(func_def_337, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 25.35/7.41  thf(func_def_338, type, uminus_uminus_int: int > int).
% 25.35/7.41  thf(func_def_339, type, uminus_uminus_rat: rat > rat).
% 25.35/7.41  thf(func_def_340, type, uminus5710092332889474511et_nat: set_nat > set_nat).
% 25.35/7.41  thf(func_def_341, type, zero_z3403309356797280102nteger: code_integer).
% 25.35/7.41  thf(func_def_342, type, zero_z2226904508553997617atural: code_natural).
% 25.35/7.41  thf(func_def_343, type, zero_zero_int: int).
% 25.35/7.41  thf(func_def_344, type, zero_zero_nat: nat).
% 25.35/7.41  thf(func_def_345, type, zero_zero_rat: rat).
% 25.35/7.41  thf(func_def_346, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 25.35/7.41  thf(func_def_347, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 25.35/7.41  thf(func_def_348, type, groups1705073143266064639nt_int: (int > int) > set_int > int).
% 25.35/7.41  thf(func_def_349, type, groups705719431365010083at_int: (nat > int) > set_nat > int).
% 25.35/7.41  thf(func_def_350, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 25.35/7.41  thf(func_def_351, type, groups9116527308978886569_o_int: ($o > int) > int > list_o > int).
% 25.35/7.41  thf(func_def_352, type, groups4561878855575611511st_nat: list_nat > nat).
% 25.35/7.41  thf(func_def_353, type, nO_MAT8252062027627875367nteger: code_integer > code_integer > $o).
% 25.35/7.41  thf(func_def_354, type, nO_MAT7795273704451493282er_rat: code_integer > rat > $o).
% 25.35/7.41  thf(func_def_355, type, nO_MAT9066612773553876470nteger: int > code_integer > $o).
% 25.35/7.41  thf(func_def_356, type, nO_MATCH_int_int: int > int > $o).
% 25.35/7.41  thf(func_def_357, type, nO_MATCH_int_nat: int > nat > $o).
% 25.35/7.41  thf(func_def_358, type, nO_MATCH_int_rat: int > rat > $o).
% 25.35/7.41  thf(func_def_359, type, nO_MAT8694959213317031834nteger: nat > code_integer > $o).
% 25.35/7.41  thf(func_def_360, type, nO_MATCH_nat_int: nat > int > $o).
% 25.35/7.41  thf(func_def_361, type, nO_MATCH_nat_nat: nat > nat > $o).
% 25.35/7.41  thf(func_def_362, type, nO_MATCH_nat_rat: nat > rat > $o).
% 25.35/7.41  thf(func_def_363, type, nO_MATCH_rat_rat: rat > rat > $o).
% 25.35/7.41  thf(func_def_364, type, the_int: (int > $o) > int).
% 25.35/7.41  thf(func_def_365, type, the_Pr4378521158711661632nt_int: (product_prod_int_int > $o) > product_prod_int_int).
% 25.35/7.41  thf(func_def_366, type, heap_T6183433275982383450t_unit: (heap_e7401611519738050253t_unit > option8956607266484857688it_nat) > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_367, type, heap_T2633723481742716231t_unit: heap_T5738788834812785303t_unit > (product_unit > heap_T5738788834812785303t_unit) > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_368, type, heap_T757603679106148408unit_a: heap_T5738788834812785303t_unit > (product_unit > heap_Time_Heap_a) > heap_Time_Heap_a).
% 25.35/7.41  thf(func_def_369, type, heap_T8685611227969916822t_unit: heap_Time_Heap_a > (a > heap_T5738788834812785303t_unit) > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_370, type, heap_Time_bind_a_a: heap_Time_Heap_a > (a > heap_Time_Heap_a) > heap_Time_Heap_a).
% 25.35/7.41  thf(func_def_371, type, heap_T875086893843062177t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > option8956607266484857688it_nat).
% 25.35/7.41  thf(func_def_372, type, heap_T7011250591035762645t_unit: (product_unit > product_unit) > product_unit > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_373, type, heap_T6901581777565460678unit_a: (product_unit > a) > product_unit > heap_Time_Heap_a).
% 25.35/7.41  thf(func_def_374, type, heap_Time_lift_a_a: (a > a) > a > heap_Time_Heap_a).
% 25.35/7.41  thf(func_def_375, type, heap_T2927564422264180874t_unit: list_char > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_376, type, heap_Time_raise_a: list_char > heap_Time_Heap_a).
% 25.35/7.41  thf(func_def_377, type, heap_T7507251653302230130t_unit: product_unit > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_378, type, heap_Time_return_a: a > heap_Time_Heap_a).
% 25.35/7.41  thf(func_def_379, type, heap_T4284346855313245393t_unit: product_unit > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_380, type, heap_Time_ureturn_a: a > heap_Time_Heap_a).
% 25.35/7.41  thf(func_def_381, type, heap_Time_wait: nat > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_382, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_383, type, if_Code_natural: $o > code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_384, type, if_Hea8138950348631371857t_unit: $o > heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_385, type, if_Heap_Time_Heap_a: $o > heap_Time_Heap_a > heap_Time_Heap_a > heap_Time_Heap_a).
% 25.35/7.41  thf(func_def_386, type, if_int: $o > int > int > int).
% 25.35/7.41  thf(func_def_387, type, if_list_int: $o > list_int > list_int > list_int).
% 25.35/7.41  thf(func_def_388, type, if_nat: $o > nat > nat > nat).
% 25.35/7.41  thf(func_def_389, type, if_num: $o > num > num > num).
% 25.35/7.41  thf(func_def_390, type, if_option_num: $o > option_num > option_num > option_num).
% 25.35/7.41  thf(func_def_391, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 25.35/7.41  thf(func_def_392, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_393, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 25.35/7.41  thf(func_def_394, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_395, type, if_rat: $o > rat > rat > rat).
% 25.35/7.41  thf(func_def_396, type, if_set_int: $o > set_int > set_int > set_int).
% 25.35/7.41  thf(func_def_397, type, infini8530281810654367211te_nat: set_nat > nat > nat).
% 25.35/7.41  thf(func_def_398, type, abs_Integ: product_prod_nat_nat > int).
% 25.35/7.41  thf(func_def_399, type, rep_Integ: int > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_400, type, cr_int: product_prod_nat_nat > int > $o).
% 25.35/7.41  thf(func_def_401, type, int_ge_less_than: int > set_Pr958786334691620121nt_int).
% 25.35/7.41  thf(func_def_402, type, int_ge_less_than2: int > set_Pr958786334691620121nt_int).
% 25.35/7.41  thf(func_def_403, type, intrel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_404, type, nat2: int > nat).
% 25.35/7.41  thf(func_def_405, type, pcr_int: product_prod_nat_nat > int > $o).
% 25.35/7.41  thf(func_def_406, type, power_int_rat: rat > int > rat).
% 25.35/7.41  thf(func_def_407, type, ring_11222124179247155820nteger: set_Code_integer).
% 25.35/7.41  thf(func_def_408, type, ring_1_Ints_int: set_int).
% 25.35/7.41  thf(func_def_409, type, ring_1_Ints_rat: set_rat).
% 25.35/7.41  thf(func_def_410, type, ring_18347121197199848620nteger: int > code_integer).
% 25.35/7.41  thf(func_def_411, type, ring_1_of_int_int: int > int).
% 25.35/7.41  thf(func_def_412, type, ring_1_of_int_rat: int > rat).
% 25.35/7.41  thf(func_def_413, type, inf_in3604695632404883862_int_o: (product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_414, type, inf_inf_int: int > int > int).
% 25.35/7.41  thf(func_def_415, type, inf_inf_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_416, type, semila1623282765462674594er_nat: (nat > nat > nat) > nat > (nat > nat > $o) > (nat > nat > $o) > $o).
% 25.35/7.41  thf(func_def_417, type, sup_sup_int: int > int > int).
% 25.35/7.41  thf(func_def_418, type, sup_sup_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_419, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 25.35/7.41  thf(func_def_420, type, lattic8263393255366662781ax_int: set_int > int).
% 25.35/7.41  thf(func_def_421, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 25.35/7.41  thf(func_def_422, type, quotie1194848508323700631at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int) > (int > product_prod_nat_nat) > (product_prod_nat_nat > int > $o) > $o).
% 25.35/7.41  thf(func_def_423, type, append_int: list_int > list_int > list_int).
% 25.35/7.41  thf(func_def_424, type, append_nat: list_nat > list_nat > list_nat).
% 25.35/7.41  thf(func_def_425, type, butlast_nat: list_nat > list_nat).
% 25.35/7.41  thf(func_def_426, type, drop_nat: nat > list_nat > list_nat).
% 25.35/7.41  thf(func_def_427, type, filter_nat2: (nat > $o) > list_nat > list_nat).
% 25.35/7.41  thf(func_def_428, type, fold_int_int: (int > int > int) > list_int > int > int).
% 25.35/7.41  thf(func_def_429, type, fold_nat_nat: (nat > nat > nat) > list_nat > nat > nat).
% 25.35/7.41  thf(func_def_430, type, foldr_o_nat: ($o > nat > nat) > list_o > nat > nat).
% 25.35/7.41  thf(func_def_431, type, foldr_int_nat: (int > nat > nat) > list_int > nat > nat).
% 25.35/7.41  thf(func_def_432, type, foldr_nat_nat: (nat > nat > nat) > list_nat > nat > nat).
% 25.35/7.41  thf(func_def_433, type, gen_length_o: nat > list_o > nat).
% 25.35/7.41  thf(func_def_434, type, gen_length_int: nat > list_int > nat).
% 25.35/7.41  thf(func_def_435, type, gen_length_nat: nat > list_nat > nat).
% 25.35/7.41  thf(func_def_436, type, last_nat: list_nat > nat).
% 25.35/7.41  thf(func_def_437, type, linord1735203802627413978nt_int: (int > int) > list_int > list_int).
% 25.35/7.41  thf(func_def_438, type, linord738340561235409698at_nat: (nat > nat) > list_nat > list_nat).
% 25.35/7.41  thf(func_def_439, type, linord2614967742042102400et_nat: set_nat > list_nat).
% 25.35/7.41  thf(func_def_440, type, cons_o: $o > list_o > list_o).
% 25.35/7.41  thf(func_def_441, type, cons_int: int > list_int > list_int).
% 25.35/7.41  thf(func_def_442, type, cons_nat: nat > list_nat > list_nat).
% 25.35/7.41  thf(func_def_443, type, cons_num: num > list_num > list_num).
% 25.35/7.41  thf(func_def_444, type, cons_rat: rat > list_rat > list_rat).
% 25.35/7.41  thf(func_def_445, type, cons_char: char > list_char > list_char).
% 25.35/7.41  thf(func_def_446, type, nil_o: list_o).
% 25.35/7.41  thf(func_def_447, type, nil_int: list_int).
% 25.35/7.41  thf(func_def_448, type, nil_nat: list_nat).
% 25.35/7.41  thf(func_def_449, type, nil_num: list_num).
% 25.35/7.41  thf(func_def_450, type, nil_rat: list_rat).
% 25.35/7.41  thf(func_def_451, type, nil_char: list_char).
% 25.35/7.41  thf(func_def_452, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 25.35/7.41  thf(func_def_453, type, set_int2: list_int > set_int).
% 25.35/7.41  thf(func_def_454, type, set_nat2: list_nat > set_nat).
% 25.35/7.41  thf(func_def_455, type, nth_o: list_o > nat > $o).
% 25.35/7.41  thf(func_def_456, type, nth_Code_integer: list_Code_integer > nat > code_integer).
% 25.35/7.41  thf(func_def_457, type, nth_int: list_int > nat > int).
% 25.35/7.41  thf(func_def_458, type, nth_nat: list_nat > nat > nat).
% 25.35/7.41  thf(func_def_459, type, nth_num: list_num > nat > num).
% 25.35/7.41  thf(func_def_460, type, nth_rat: list_rat > nat > rat).
% 25.35/7.41  thf(func_def_461, type, nth_char: list_char > nat > char).
% 25.35/7.41  thf(func_def_462, type, rotate1_o: list_o > list_o).
% 25.35/7.41  thf(func_def_463, type, rotate1_int: list_int > list_int).
% 25.35/7.41  thf(func_def_464, type, rotate1_nat: list_nat > list_nat).
% 25.35/7.41  thf(func_def_465, type, rotate_o: nat > list_o > list_o).
% 25.35/7.41  thf(func_def_466, type, rotate_int: nat > list_int > list_int).
% 25.35/7.41  thf(func_def_467, type, rotate_nat: nat > list_nat > list_nat).
% 25.35/7.41  thf(func_def_468, type, sorted_wrt_o: ($o > $o > $o) > list_o > $o).
% 25.35/7.41  thf(func_def_469, type, sorted710888440204495920nteger: (code_integer > code_integer > $o) > list_Code_integer > $o).
% 25.35/7.41  thf(func_def_470, type, sorted_wrt_int: (int > int > $o) > list_int > $o).
% 25.35/7.41  thf(func_def_471, type, sorted_wrt_nat: (nat > nat > $o) > list_nat > $o).
% 25.35/7.41  thf(func_def_472, type, sorted_wrt_num: (num > num > $o) > list_num > $o).
% 25.35/7.41  thf(func_def_473, type, sorted_wrt_rat: (rat > rat > $o) > list_rat > $o).
% 25.35/7.41  thf(func_def_474, type, take_nat: nat > list_nat > list_nat).
% 25.35/7.41  thf(func_def_475, type, upt: nat > nat > list_nat).
% 25.35/7.41  thf(func_def_476, type, upto: int > int > list_int).
% 25.35/7.41  thf(func_def_477, type, upto_aux: int > int > list_int > list_int).
% 25.35/7.41  thf(func_def_478, type, upto_rel: product_prod_int_int > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_479, type, slice_o: nat > nat > list_o > list_o).
% 25.35/7.41  thf(func_def_480, type, slice_int: nat > nat > list_int > list_int).
% 25.35/7.41  thf(func_def_481, type, slice_nat: nat > nat > list_nat > list_nat).
% 25.35/7.41  thf(func_def_482, type, slice_char: nat > nat > list_char > list_char).
% 25.35/7.41  thf(func_def_483, type, mset_nat: list_nat > multiset_nat).
% 25.35/7.41  thf(func_def_484, type, mset_set_nat: set_nat > multiset_nat).
% 25.35/7.41  thf(func_def_485, type, suc: nat > nat).
% 25.35/7.41  thf(func_def_486, type, compow_nat_nat: nat > (nat > nat) > nat > nat).
% 25.35/7.41  thf(func_def_487, type, case_nat_o: $o > (nat > $o) > nat > $o).
% 25.35/7.41  thf(func_def_488, type, case_nat_nat: nat > (nat > nat) > nat > nat).
% 25.35/7.41  thf(func_def_489, type, case_nat_option_num: option_num > (nat > option_num) > nat > option_num).
% 25.35/7.41  thf(func_def_490, type, pred: nat > nat).
% 25.35/7.41  thf(func_def_491, type, semiring_1_Nats_int: set_int).
% 25.35/7.41  thf(func_def_492, type, semiri4939895301339042750nteger: nat > code_integer).
% 25.35/7.41  thf(func_def_493, type, semiri3763490453095760265atural: nat > code_natural).
% 25.35/7.41  thf(func_def_494, type, semiri1314217659103216013at_int: nat > int).
% 25.35/7.41  thf(func_def_495, type, semiri1316708129612266289at_nat: nat > nat).
% 25.35/7.41  thf(func_def_496, type, semiri681578069525770553at_rat: nat > rat).
% 25.35/7.41  thf(func_def_497, type, semiri4055485073559036834nteger: (code_integer > code_integer) > nat > code_integer > code_integer).
% 25.35/7.41  thf(func_def_498, type, semiri2879080225315754349atural: (code_natural > code_natural) > nat > code_natural > code_natural).
% 25.35/7.41  thf(func_def_499, type, semiri8420488043553186161ux_int: (int > int) > nat > int > int).
% 25.35/7.41  thf(func_def_500, type, semiri8422978514062236437ux_nat: (nat > nat) > nat > nat > nat).
% 25.35/7.41  thf(func_def_501, type, semiri7787848453975740701ux_rat: (rat > rat) > nat > rat > rat).
% 25.35/7.41  thf(func_def_502, type, size_size_list_o: list_o > nat).
% 25.35/7.41  thf(func_def_503, type, size_s3445333598471063425nteger: list_Code_integer > nat).
% 25.35/7.41  thf(func_def_504, type, size_size_list_int: list_int > nat).
% 25.35/7.41  thf(func_def_505, type, size_size_list_nat: list_nat > nat).
% 25.35/7.41  thf(func_def_506, type, size_size_list_num: list_num > nat).
% 25.35/7.41  thf(func_def_507, type, size_size_list_rat: list_rat > nat).
% 25.35/7.41  thf(func_def_508, type, size_size_list_char: list_char > nat).
% 25.35/7.41  thf(func_def_509, type, size_size_num: num > nat).
% 25.35/7.41  thf(func_def_510, type, size_size_char: char > nat).
% 25.35/7.41  thf(func_def_511, type, nat_list_decode: nat > list_nat).
% 25.35/7.41  thf(func_def_512, type, nat_list_decode_rel: nat > nat > $o).
% 25.35/7.41  thf(func_def_513, type, nat_list_encode: list_nat > nat).
% 25.35/7.41  thf(func_def_514, type, nat_list_encode_rel: list_nat > list_nat > $o).
% 25.35/7.41  thf(func_def_515, type, nat_prod_decode: nat > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_516, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_517, type, nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_518, type, nat_prod_encode: product_prod_nat_nat > nat).
% 25.35/7.41  thf(func_def_519, type, nat_set_decode: nat > set_nat).
% 25.35/7.41  thf(func_def_520, type, nat_set_encode: set_nat > nat).
% 25.35/7.41  thf(func_def_521, type, nat_triangle: nat > nat).
% 25.35/7.41  thf(func_def_522, type, bitM: num > num).
% 25.35/7.41  thf(func_def_523, type, inc: num > num).
% 25.35/7.41  thf(func_def_524, type, neg_nu8804712462038260780nteger: code_integer > code_integer).
% 25.35/7.41  thf(func_def_525, type, neg_numeral_dbl_int: int > int).
% 25.35/7.41  thf(func_def_526, type, neg_numeral_dbl_rat: rat > rat).
% 25.35/7.41  thf(func_def_527, type, neg_nu7757733837767384882nteger: code_integer > code_integer).
% 25.35/7.41  thf(func_def_528, type, neg_nu3811975205180677377ec_int: int > int).
% 25.35/7.41  thf(func_def_529, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 25.35/7.41  thf(func_def_530, type, neg_nu5831290666863070958nteger: code_integer > code_integer).
% 25.35/7.41  thf(func_def_531, type, neg_nu5851722552734809277nc_int: int > int).
% 25.35/7.41  thf(func_def_532, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 25.35/7.41  thf(func_def_533, type, neg_nu5755505904847501662nteger: num > num > code_integer).
% 25.35/7.41  thf(func_def_534, type, neg_numeral_sub_int: num > num > int).
% 25.35/7.41  thf(func_def_535, type, bit0: num > num).
% 25.35/7.41  thf(func_def_536, type, bit1: num > num).
% 25.35/7.41  thf(func_def_537, type, one: num).
% 25.35/7.41  thf(func_def_538, type, case_num_option_num: option_num > (num > option_num) > (num > option_num) > num > option_num).
% 25.35/7.41  thf(func_def_539, type, size_num: num > nat).
% 25.35/7.41  thf(func_def_540, type, num_of_nat: nat > num).
% 25.35/7.41  thf(func_def_541, type, numera6620942414471956472nteger: num > code_integer).
% 25.35/7.41  thf(func_def_542, type, numera5444537566228673987atural: num > code_natural).
% 25.35/7.41  thf(func_def_543, type, numeral_numeral_int: num > int).
% 25.35/7.41  thf(func_def_544, type, numeral_numeral_nat: num > nat).
% 25.35/7.41  thf(func_def_545, type, numeral_numeral_rat: num > rat).
% 25.35/7.41  thf(func_def_546, type, pow: num > num > num).
% 25.35/7.41  thf(func_def_547, type, pred_numeral: num > nat).
% 25.35/7.41  thf(func_def_548, type, sqr: num > num).
% 25.35/7.41  thf(func_def_549, type, none_num: option_num).
% 25.35/7.41  thf(func_def_550, type, none_P9117596204409417319it_nat: option8956607266484857688it_nat).
% 25.35/7.41  thf(func_def_551, type, some_num: num > option_num).
% 25.35/7.41  thf(func_def_552, type, some_P1914260805536162275it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat).
% 25.35/7.41  thf(func_def_553, type, case_option_int_num: int > (num > int) > option_num > int).
% 25.35/7.41  thf(func_def_554, type, case_option_num_num: num > (num > num) > option_num > num).
% 25.35/7.41  thf(func_def_555, type, case_o6005452278849405969um_num: option_num > (num > option_num) > option_num > option_num).
% 25.35/7.41  thf(func_def_556, type, map_option_num_num: (num > num) > option_num > option_num).
% 25.35/7.41  thf(func_def_557, type, bot_bot_nat: nat).
% 25.35/7.41  thf(func_def_558, type, bot_bot_set_int: set_int).
% 25.35/7.41  thf(func_def_559, type, bot_bot_set_nat: set_nat).
% 25.35/7.41  thf(func_def_560, type, ord_Least_nat: (nat > $o) > nat).
% 25.35/7.41  thf(func_def_561, type, ord_less_o: $o > $o > $o).
% 25.35/7.41  thf(func_def_562, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 25.35/7.41  thf(func_def_563, type, ord_le5570908160329646204atural: code_natural > code_natural > $o).
% 25.35/7.41  thf(func_def_564, type, ord_less_int: int > int > $o).
% 25.35/7.41  thf(func_def_565, type, ord_less_nat: nat > nat > $o).
% 25.35/7.41  thf(func_def_566, type, ord_less_num: num > num > $o).
% 25.35/7.41  thf(func_def_567, type, ord_less_rat: rat > rat > $o).
% 25.35/7.41  thf(func_def_568, type, ord_less_set_nat: set_nat > set_nat > $o).
% 25.35/7.41  thf(func_def_569, type, ord_less_eq_o_int: ($o > int) > ($o > int) > $o).
% 25.35/7.41  thf(func_def_570, type, ord_less_eq_o_nat: ($o > nat) > ($o > nat) > $o).
% 25.35/7.41  thf(func_def_571, type, ord_less_eq_o_num: ($o > num) > ($o > num) > $o).
% 25.35/7.41  thf(func_def_572, type, ord_less_eq_o_rat: ($o > rat) > ($o > rat) > $o).
% 25.35/7.41  thf(func_def_573, type, ord_le7022414076629706543et_nat: ($o > set_nat) > ($o > set_nat) > $o).
% 25.35/7.41  thf(func_def_574, type, ord_less_eq_o: $o > $o > $o).
% 25.35/7.41  thf(func_def_575, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 25.35/7.41  thf(func_def_576, type, ord_le1926595141338095240atural: code_natural > code_natural > $o).
% 25.35/7.41  thf(func_def_577, type, ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o).
% 25.35/7.41  thf(func_def_578, type, ord_less_eq_int: int > int > $o).
% 25.35/7.41  thf(func_def_579, type, ord_less_eq_nat: nat > nat > $o).
% 25.35/7.41  thf(func_def_580, type, ord_less_eq_num: num > num > $o).
% 25.35/7.41  thf(func_def_581, type, ord_less_eq_rat: rat > rat > $o).
% 25.35/7.41  thf(func_def_582, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 25.35/7.41  thf(func_def_583, type, ord_max_Code_integer: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_584, type, ord_max_Code_natural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_585, type, ord_max_int: int > int > int).
% 25.35/7.41  thf(func_def_586, type, ord_max_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_587, type, ord_min_Code_integer: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_588, type, ord_min_Code_natural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_589, type, ord_min_int: int > int > int).
% 25.35/7.41  thf(func_def_590, type, ord_min_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_591, type, order_Greatest_int: (int > $o) > int).
% 25.35/7.41  thf(func_def_592, type, order_Greatest_nat: (nat > $o) > nat).
% 25.35/7.41  thf(func_def_593, type, order_Greatest_num: (num > $o) > num).
% 25.35/7.41  thf(func_def_594, type, order_Greatest_rat: (rat > $o) > rat).
% 25.35/7.41  thf(func_def_595, type, order_5724808138429204845et_nat: (set_nat > $o) > set_nat).
% 25.35/7.41  thf(func_def_596, type, order_mono_nat_nat: (nat > nat) > $o).
% 25.35/7.41  thf(func_def_597, type, ordering_top_nat: (nat > nat > $o) > (nat > nat > $o) > nat > $o).
% 25.35/7.41  thf(func_def_598, type, top_top_set_int: set_int).
% 25.35/7.41  thf(func_def_599, type, top_top_set_nat: set_nat).
% 25.35/7.41  thf(func_def_600, type, top_to1996260823553986621t_unit: set_Product_unit).
% 25.35/7.41  thf(func_def_601, type, top_top_set_char: set_char).
% 25.35/7.41  thf(func_def_602, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 25.35/7.41  thf(func_def_603, type, power_7079662738309270450atural: code_natural > nat > code_natural).
% 25.35/7.41  thf(func_def_604, type, power_power_int: int > nat > int).
% 25.35/7.41  thf(func_def_605, type, power_power_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_606, type, power_power_rat: rat > nat > rat).
% 25.35/7.41  thf(func_def_607, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 25.35/7.41  thf(func_def_608, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_609, type, produc3574140220909816553atural: code_natural > code_natural > produc7822875418678951345atural).
% 25.35/7.41  thf(func_def_610, type, produc6639722614265839536atural: code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 25.35/7.41  thf(func_def_611, type, produc584006145561248582it_nat: heap_e7401611519738050253t_unit > nat > produc6653097349344004940it_nat).
% 25.35/7.41  thf(func_def_612, type, product_Pair_int_int: int > int > product_prod_int_int).
% 25.35/7.41  thf(func_def_613, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_614, type, product_Pair_nat_num: nat > num > product_prod_nat_num).
% 25.35/7.41  thf(func_def_615, type, product_Pair_num_num: num > num > product_prod_num_num).
% 25.35/7.41  thf(func_def_616, type, produc4480994950612372183atural: produc7822875418678951345atural > produc7822875418678951345atural > produc6756470014200349799atural).
% 25.35/7.41  thf(func_def_617, type, produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat).
% 25.35/7.41  thf(func_def_618, type, produc7133225469290080770it_nat: product_unit > produc6653097349344004940it_nat > produc8664842809031399944it_nat).
% 25.35/7.41  thf(func_def_619, type, product_Unity: product_unit).
% 25.35/7.41  thf(func_def_620, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_621, type, produc4188289175737317920o_char: (code_integer > $o > char) > produc6271795597528267376eger_o > char).
% 25.35/7.41  thf(func_def_622, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 25.35/7.41  thf(func_def_623, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 25.35/7.41  thf(func_def_624, type, produc7336495610019696514er_num: (code_integer > code_integer > num) > produc8923325533196201883nteger > num).
% 25.35/7.41  thf(func_def_625, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 25.35/7.41  thf(func_def_626, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 25.35/7.41  thf(func_def_627, type, produc8282080750456430313atural: (code_natural > code_natural > produc6756470014200349799atural) > produc7822875418678951345atural > produc6756470014200349799atural).
% 25.35/7.41  thf(func_def_628, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_629, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 25.35/7.41  thf(func_def_630, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 25.35/7.41  thf(func_def_631, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_632, 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).
% 25.35/7.41  thf(func_def_633, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_634, type, produc2761476792215241774st_nat: (nat > nat > list_nat) > product_prod_nat_nat > list_nat).
% 25.35/7.41  thf(func_def_635, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 25.35/7.41  thf(func_def_636, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_637, type, produc478579273971653890on_num: (nat > num > option_num) > product_prod_nat_num > option_num).
% 25.35/7.41  thf(func_def_638, type, produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer).
% 25.35/7.41  thf(func_def_639, type, product_fst_int_int: product_prod_int_int > int).
% 25.35/7.41  thf(func_def_640, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 25.35/7.41  thf(func_def_641, type, produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer).
% 25.35/7.41  thf(func_def_642, type, produc6591912806276919810atural: produc5835291356934675326atural > produc7822875418678951345atural).
% 25.35/7.41  thf(func_def_643, type, product_snd_int_int: product_prod_int_int > int).
% 25.35/7.41  thf(func_def_644, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 25.35/7.41  thf(func_def_645, type, produc5538323210962509403atural: (produc7822875418678951345atural > produc5835291356934675326atural) > (code_natural > produc7822875418678951345atural > produc5835291356934675326atural) > produc7822875418678951345atural > produc5835291356934675326atural).
% 25.35/7.41  thf(func_def_646, type, inc_shift: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_647, type, iterat8892046348760725948atural: code_natural > (code_natural > produc7822875418678951345atural > produc5835291356934675326atural) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 25.35/7.41  thf(func_def_648, type, log: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_649, type, log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o).
% 25.35/7.41  thf(func_def_650, type, minus_shift: code_natural > code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_651, type, next: produc7822875418678951345atural > produc5835291356934675326atural).
% 25.35/7.41  thf(func_def_652, type, range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 25.35/7.41  thf(func_def_653, type, split_seed: produc7822875418678951345atural > produc6756470014200349799atural).
% 25.35/7.41  thf(func_def_654, type, abs_Rat: product_prod_int_int > rat).
% 25.35/7.41  thf(func_def_655, type, fract: int > int > rat).
% 25.35/7.41  thf(func_def_656, type, frct: product_prod_int_int > rat).
% 25.35/7.41  thf(func_def_657, type, rep_Rat: rat > product_prod_int_int).
% 25.35/7.41  thf(func_def_658, type, cr_rat: product_prod_int_int > rat > $o).
% 25.35/7.41  thf(func_def_659, type, normalize: product_prod_int_int > product_prod_int_int).
% 25.35/7.41  thf(func_def_660, type, of_int: int > rat).
% 25.35/7.41  thf(func_def_661, type, pcr_rat: product_prod_int_int > rat > $o).
% 25.35/7.41  thf(func_def_662, type, positive: rat > $o).
% 25.35/7.41  thf(func_def_663, type, quotient_of: rat > product_prod_int_int).
% 25.35/7.41  thf(func_def_664, type, abs_rat: set_Pr958786334691620121nt_int > rat).
% 25.35/7.41  thf(func_def_665, type, rep_rat: rat > set_Pr958786334691620121nt_int).
% 25.35/7.41  thf(func_def_666, type, ratrel: product_prod_int_int > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_667, type, ref_ch7259622376331601608t_unit: (product_unit > product_unit) > ref_Product_unit > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_668, type, ref_lo7930775386976318366t_unit: ref_Product_unit > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_669, type, ref_up627237114476368303t_unit: ref_Product_unit > product_unit > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_670, type, refine_Imp_assert: $o > heap_T5738788834812785303t_unit).
% 25.35/7.41  thf(func_def_671, type, refine451278484176762712t_unit: heap_T5738788834812785303t_unit > heap_T5738788834812785303t_unit > $o).
% 25.35/7.41  thf(func_def_672, type, refine_Imp_refines_a: heap_Time_Heap_a > heap_Time_Heap_a > $o).
% 25.35/7.41  thf(func_def_673, type, domain452967906960104687nteger: (int > code_integer > $o) > int > $o).
% 25.35/7.41  thf(func_def_674, type, domainp_int_int: (int > int > $o) > int > $o).
% 25.35/7.41  thf(func_def_675, type, domainp_nat_nat: (nat > nat > $o) > nat > $o).
% 25.35/7.41  thf(func_def_676, type, domain9213661015745956397nt_rat: (product_prod_int_int > rat > $o) > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_677, type, domain7287725470393535433at_int: (product_prod_nat_nat > int > $o) > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_678, type, relcom8911704206367525917at_int: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > int > $o) > product_prod_nat_nat > int > $o).
% 25.35/7.41  thf(func_def_679, type, algebr932160517623751201me_int: int > int > $o).
% 25.35/7.41  thf(func_def_680, type, algebr934650988132801477me_nat: nat > nat > $o).
% 25.35/7.41  thf(func_def_681, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_682, type, divide5121882707175180666atural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_683, type, divide_divide_int: int > int > int).
% 25.35/7.41  thf(func_def_684, type, divide_divide_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_685, type, divide_divide_rat: rat > rat > rat).
% 25.35/7.41  thf(func_def_686, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 25.35/7.41  thf(func_def_687, type, dvd_dvd_int: int > int > $o).
% 25.35/7.41  thf(func_def_688, type, dvd_dvd_nat: nat > nat > $o).
% 25.35/7.41  thf(func_def_689, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 25.35/7.41  thf(func_def_690, type, modulo8411746178871703098atural: code_natural > code_natural > code_natural).
% 25.35/7.41  thf(func_def_691, type, modulo_modulo_int: int > int > int).
% 25.35/7.41  thf(func_def_692, type, modulo_modulo_nat: nat > nat > nat).
% 25.35/7.41  thf(func_def_693, type, zero_n356916108424825756nteger: $o > code_integer).
% 25.35/7.41  thf(func_def_694, type, zero_n2684676970156552555ol_int: $o > int).
% 25.35/7.41  thf(func_def_695, type, zero_n2687167440665602831ol_nat: $o > nat).
% 25.35/7.41  thf(func_def_696, type, collect_int: (int > $o) > set_int).
% 25.35/7.41  thf(func_def_697, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 25.35/7.41  thf(func_def_698, type, collect_nat: (nat > $o) > set_nat).
% 25.35/7.41  thf(func_def_699, type, collec213857154873943460nt_int: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int).
% 25.35/7.41  thf(func_def_700, type, collec3392354462482085612at_nat: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 25.35/7.41  thf(func_def_701, type, collect_set_nat: (set_nat > $o) > set_set_nat).
% 25.35/7.41  thf(func_def_702, type, collec5210948495886036740nt_int: (set_Pr958786334691620121nt_int > $o) > set_se6260736226359567993nt_int).
% 25.35/7.41  thf(func_def_703, type, pow_nat: set_nat > set_set_nat).
% 25.35/7.41  thf(func_def_704, type, image_4470545334726330049nteger: (code_integer > code_integer) > set_Code_integer > set_Code_integer).
% 25.35/7.41  thf(func_def_705, type, image_int_int: (int > int) > set_int > set_int).
% 25.35/7.41  thf(func_def_706, type, image_int_nat: (int > nat) > set_int > set_nat).
% 25.35/7.41  thf(func_def_707, type, image_1215581382706833972nteger: (nat > code_integer) > set_nat > set_Code_integer).
% 25.35/7.41  thf(func_def_708, type, image_nat_int: (nat > int) > set_nat > set_int).
% 25.35/7.41  thf(func_def_709, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 25.35/7.41  thf(func_def_710, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 25.35/7.41  thf(func_def_711, type, image_nat_char: (nat > char) > set_nat > set_char).
% 25.35/7.41  thf(func_def_712, type, image_char_nat: (char > nat) > set_char > set_nat).
% 25.35/7.41  thf(func_def_713, type, insert_int: int > set_int > set_int).
% 25.35/7.41  thf(func_def_714, type, insert_nat: nat > set_nat > set_nat).
% 25.35/7.41  thf(func_def_715, type, vimage_nat_nat: (nat > nat) > set_nat > set_nat).
% 25.35/7.41  thf(func_def_716, type, set_fo1084959871951514735nteger: (nat > code_integer > code_integer) > nat > nat > code_integer > code_integer).
% 25.35/7.41  thf(func_def_717, type, set_fo9131927060563008058atural: (nat > code_natural > code_natural) > nat > nat > code_natural > code_natural).
% 25.35/7.41  thf(func_def_718, type, set_fo2581907887559384638at_int: (nat > int > int) > nat > nat > int > int).
% 25.35/7.41  thf(func_def_719, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 25.35/7.41  thf(func_def_720, type, set_fo1949268297981939178at_rat: (nat > rat > rat) > nat > nat > rat > rat).
% 25.35/7.41  thf(func_def_721, type, set_or189985376899183464nteger: code_integer > code_integer > set_Code_integer).
% 25.35/7.41  thf(func_def_722, type, set_or1266510415728281911st_int: int > int > set_int).
% 25.35/7.41  thf(func_def_723, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 25.35/7.41  thf(func_def_724, type, set_or8404916559141939852nteger: code_integer > code_integer > set_Code_integer).
% 25.35/7.41  thf(func_def_725, type, set_or4662586982721622107an_int: int > int > set_int).
% 25.35/7.41  thf(func_def_726, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 25.35/7.41  thf(func_def_727, type, set_ord_atLeast_nat: nat > set_nat).
% 25.35/7.41  thf(func_def_728, type, set_ord_atMost_nat: nat > set_nat).
% 25.35/7.41  thf(func_def_729, type, set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer).
% 25.35/7.41  thf(func_def_730, type, set_or6656581121297822940st_int: int > int > set_int).
% 25.35/7.41  thf(func_def_731, type, set_or6659071591806873216st_nat: nat > nat > set_nat).
% 25.35/7.41  thf(func_def_732, type, set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer).
% 25.35/7.41  thf(func_def_733, type, set_or5832277885323065728an_int: int > int > set_int).
% 25.35/7.41  thf(func_def_734, type, set_or5834768355832116004an_nat: nat > nat > set_nat).
% 25.35/7.41  thf(func_def_735, type, set_or1210151606488870762an_nat: nat > set_nat).
% 25.35/7.41  thf(func_def_736, type, set_ord_lessThan_nat: nat > set_nat).
% 25.35/7.41  thf(func_def_737, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 25.35/7.41  thf(func_def_738, type, size_char: char > nat).
% 25.35/7.41  thf(func_def_739, type, char_of_integer: code_integer > char).
% 25.35/7.41  thf(func_def_740, type, comm_s629917340098488124ar_nat: char > nat).
% 25.35/7.41  thf(func_def_741, type, integer_of_char: char > code_integer).
% 25.35/7.41  thf(func_def_742, type, unique3096191561947761185of_nat: nat > char).
% 25.35/7.41  thf(func_def_743, type, time_EQ_o: $o > $o > $o).
% 25.35/7.41  thf(func_def_744, type, time_T7469515765551943773t_unit: heap_T5738788834812785303t_unit > nat > $o).
% 25.35/7.41  thf(func_def_745, type, time_TBOUND_a: heap_Time_Heap_a > nat > $o).
% 25.35/7.41  thf(func_def_746, type, time_f8834461667527620124t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > $o).
% 25.35/7.41  thf(func_def_747, type, time_fails_a: heap_Time_Heap_a > heap_e7401611519738050253t_unit > $o).
% 25.35/7.41  thf(func_def_748, type, time_t3350536682685678164t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit).
% 25.35/7.41  thf(func_def_749, type, time_the_heap_a: heap_Time_Heap_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit).
% 25.35/7.41  thf(func_def_750, type, time_t2745601220510131320t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > product_unit).
% 25.35/7.41  thf(func_def_751, type, time_the_res_a: heap_Time_Heap_a > heap_e7401611519738050253t_unit > a).
% 25.35/7.41  thf(func_def_752, type, time_time_array_o: heap_T5660665574680485309rray_o > heap_e7401611519738050253t_unit > nat).
% 25.35/7.41  thf(func_def_753, type, time_time_array_int: heap_T1346037964561226099ay_int > heap_e7401611519738050253t_unit > nat).
% 25.35/7.41  thf(func_def_754, type, time_time_array_nat: heap_T3836121109492952855ay_nat > heap_e7401611519738050253t_unit > nat).
% 25.35/7.41  thf(func_def_755, type, time_t4224138285095624986t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > nat).
% 25.35/7.41  thf(func_def_756, type, time_time_a: heap_Time_Heap_a > heap_e7401611519738050253t_unit > nat).
% 25.35/7.41  thf(func_def_757, type, bi_tot1331153423839324337nteger: (int > code_integer > $o) > $o).
% 25.35/7.41  thf(func_def_758, type, bi_tot896582865486249351at_int: (product_prod_nat_nat > int > $o) > $o).
% 25.35/7.41  thf(func_def_759, type, bi_uni8663861020805155098nteger: (int > code_integer > $o) > $o).
% 25.35/7.41  thf(func_def_760, type, left_t3131394472396969446nt_int: (product_prod_int_int > product_prod_int_int > $o) > $o).
% 25.35/7.41  thf(func_def_761, type, left_u6795595883297946906nteger: (int > code_integer > $o) > $o).
% 25.35/7.41  thf(func_def_762, type, right_7281159819619925802nteger: (int > code_integer > $o) > $o).
% 25.35/7.41  thf(func_def_763, type, right_1157779049177982926at_int: (product_prod_nat_nat > int > $o) > $o).
% 25.35/7.41  thf(func_def_764, type, transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 25.35/7.41  thf(func_def_765, type, type_d8366093980585677751er_int: (code_integer > int) > (int > code_integer) > set_int > $o).
% 25.35/7.41  thf(func_def_766, type, type_d4410041424927559462al_nat: (code_natural > nat) > (nat > code_natural) > set_nat > $o).
% 25.35/7.41  thf(func_def_767, type, type_d8554052265237484179nt_int: (rat > set_Pr958786334691620121nt_int) > (set_Pr958786334691620121nt_int > rat) > set_se6260736226359567993nt_int > $o).
% 25.35/7.41  thf(func_def_768, type, accp_list_nat: (list_nat > list_nat > $o) > list_nat > $o).
% 25.35/7.41  thf(func_def_769, type, accp_nat: (nat > nat > $o) > nat > $o).
% 25.35/7.41  thf(func_def_770, type, accp_P8126237942716283194atural: (produc7822875418678951345atural > produc7822875418678951345atural > $o) > produc7822875418678951345atural > $o).
% 25.35/7.41  thf(func_def_771, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 25.35/7.41  thf(func_def_772, type, accp_P4275260045618599050at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 25.35/7.41  thf(func_def_773, type, accp_P3113834385874906142um_num: (product_prod_num_num > product_prod_num_num > $o) > product_prod_num_num > $o).
% 25.35/7.41  thf(func_def_774, type, pred_nat: set_Pr1261947904930325089at_nat).
% 25.35/7.41  thf(func_def_775, type, wf_int: set_Pr958786334691620121nt_int > $o).
% 25.35/7.41  thf(func_def_776, type, wf_nat: set_Pr1261947904930325089at_nat > $o).
% 25.35/7.41  thf(func_def_777, type, fChoice_int: (int > $o) > int).
% 25.35/7.41  thf(func_def_778, type, fChoice_nat: (nat > $o) > nat).
% 25.35/7.41  thf(func_def_779, type, fChoic6978938873391328853at_nat: (product_prod_nat_nat > $o) > product_prod_nat_nat).
% 25.35/7.41  thf(func_def_780, type, fChoice_set_nat: (set_nat > $o) > set_nat).
% 25.35/7.41  thf(func_def_781, type, fChoic2749331249758569069nt_int: (set_Pr958786334691620121nt_int > $o) > set_Pr958786334691620121nt_int).
% 25.35/7.41  thf(func_def_782, type, member_Code_integer: code_integer > set_Code_integer > $o).
% 25.35/7.41  thf(func_def_783, type, member_int: int > set_int > $o).
% 25.35/7.41  thf(func_def_784, type, member_list_nat: list_nat > set_list_nat > $o).
% 25.35/7.41  thf(func_def_785, type, member_nat: nat > set_nat > $o).
% 25.35/7.41  thf(func_def_786, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 25.35/7.41  thf(func_def_787, type, member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o).
% 25.35/7.41  thf(func_def_788, type, member_rat: rat > set_rat > $o).
% 25.35/7.41  thf(func_def_789, type, member_set_nat: set_nat > set_set_nat > $o).
% 25.35/7.41  thf(func_def_790, type, member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o).
% 25.35/7.41  thf(func_def_792, type, h: heap_e7401611519738050253t_unit).
% 25.35/7.41  thf(func_def_793, type, m: heap_Time_Heap_a).
% 25.35/7.41  thf(func_def_794, type, t: nat).
% 25.35/7.41  thf(func_def_817, type, sP0: nat > nat > nat > $o).
% 25.35/7.41  thf(func_def_818, type, sP1: nat > nat > nat > $o).
% 25.35/7.41  thf(func_def_819, type, sP2: nat > nat > nat > $o).
% 25.35/7.41  thf(func_def_820, type, sK3: heap_T5738788834812785303t_unit > nat > (product_unit > heap_Time_Heap_a) > product_unit).
% 25.35/7.41  thf(func_def_821, type, sK4: heap_T5738788834812785303t_unit > nat > (product_unit > heap_Time_Heap_a) > heap_e7401611519738050253t_unit).
% 25.35/7.41  thf(func_def_822, type, sK5: nat > nat).
% 25.35/7.41  thf(func_def_823, type, sK6: (nat > $o) > nat).
% 25.35/7.41  thf(func_def_824, type, sK7: nat > (nat > $o) > nat).
% 25.35/7.41  thf(func_def_825, type, sK8: heap_Time_Heap_a > nat > heap_e7401611519738050253t_unit).
% 25.35/7.41  thf(func_def_826, type, sK9: (nat > $o) > nat > nat).
% 25.35/7.41  thf(func_def_827, type, sK10: (nat > $o) > nat > nat).
% 25.35/7.41  thf(func_def_828, type, sK11: heap_Time_Heap_a > nat > heap_e7401611519738050253t_unit).
% 25.35/7.41  thf(func_def_829, type, sK12: nat > nat).
% 25.35/7.41  thf(func_def_830, type, sK13: (nat > $o) > nat).
% 25.35/7.41  thf(func_def_831, type, sK14: (nat > $o) > nat > nat).
% 25.35/7.41  thf(func_def_832, type, sK15: (nat > nat) > nat).
% 25.35/7.41  thf(func_def_833, type, sK16: (nat > nat) > nat).
% 25.35/7.41  thf(func_def_834, type, sK17: nat > nat).
% 25.35/7.41  thf(func_def_835, type, sK18: (nat > nat > $o) > nat).
% 25.35/7.41  thf(func_def_836, type, sK19: (nat > nat > $o) > nat).
% 25.35/7.41  thf(func_def_837, type, sK20: (nat > nat > $o) > nat).
% 25.35/7.41  thf(func_def_838, type, sK21: (nat > nat > $o) > nat).
% 25.35/7.41  thf(func_def_839, type, sK22: nat > nat).
% 25.35/7.41  thf(func_def_840, type, sK23: nat > (nat > $o) > nat).
% 25.35/7.41  thf(func_def_841, type, sK24: nat > (nat > $o) > nat).
% 25.35/7.41  thf(func_def_842, type, sK25: (nat > $o) > nat > nat > nat).
% 25.35/7.41  thf(func_def_843, type, sK26: nat > (nat > $o) > nat > nat).
% 25.35/7.41  thf(func_def_844, type, sK27: (product_unit > heap_Time_Heap_a) > (product_unit > heap_Time_Heap_a) > product_unit).
% 25.35/7.41  thf(func_def_846, type, ph29: !>[X0: $tType]:(X0)).
% 25.35/7.41  thf(func_def_847, type, sK30: heap_e7401611519738050253t_unit).
% 25.35/7.41  thf(f14711,plain,(
% 25.35/7.41    $false),
% 25.35/7.41    inference(subsumption_resolution,[status(thm)],[f14710,f14141])).
% 25.35/7.41  thf(f14141,plain,(
% 25.35/7.41    ( ! [X0 : nat] : (($true = (ord_less_eq_nat @ zero_zero_nat @ X0))) )),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f6122])).
% 25.35/7.41  thf(f6122,plain,(
% 25.35/7.41    ! [X0 : nat] : ($true = (ord_less_eq_nat @ zero_zero_nat @ X0))),
% 25.35/7.41    inference(fool_elimination,[status(thm)],[f6121])).
% 25.35/7.41  thf(f6121,plain,(
% 25.35/7.41    ! [X0 : nat] : (ord_less_eq_nat @ zero_zero_nat @ X0)),
% 25.35/7.41    inference(rectify,[status(thm)],[f229])).
% 25.35/7.41  thf(f229,axiom,(
% 25.35/7.41    ! [X16 : nat] : (ord_less_eq_nat @ zero_zero_nat @ X16)),
% 25.35/7.41    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_228_less__eq__nat_Osimps_I1_J)).
% 25.35/7.41  thf(f14710,plain,(
% 25.35/7.41    ($true != (ord_less_eq_nat @ zero_zero_nat @ t))),
% 25.35/7.41    inference(forward_demodulation,[status(thm)],[f14709,f14099])).
% 25.35/7.41  thf(f14099,plain,(
% 25.35/7.41    ( ! [X0 : list_char,X1 : heap_e7401611519738050253t_unit] : ((zero_zero_nat = (time_time_a @ (heap_Time_raise_a @ X0) @ X1))) )),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f13897])).
% 25.35/7.41  thf(f13897,plain,(
% 25.35/7.41    ! [X0 : list_char,X1 : heap_e7401611519738050253t_unit] : (zero_zero_nat = (time_time_a @ (heap_Time_raise_a @ X0) @ X1))),
% 25.35/7.41    inference(rectify,[status(thm)],[f224])).
% 25.35/7.41  thf(f224,axiom,(
% 25.35/7.41    ! [X47 : list_char,X0 : heap_e7401611519738050253t_unit] : (zero_zero_nat = (time_time_a @ (heap_Time_raise_a @ X47) @ X0))),
% 25.35/7.41    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_223_time__raise)).
% 25.35/7.41  thf(f14709,plain,(
% 25.35/7.41    ((ord_less_eq_nat @ (time_time_a @ (heap_Time_raise_a @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char))))))) @ h) @ t) != $true)),
% 25.35/7.41    inference(forward_demodulation,[status(thm)],[f14708,f14090])).
% 25.35/7.41  thf(f14090,plain,(
% 25.35/7.41    ( ! [X0 : list_char,X1 : product_unit > heap_Time_Heap_a] : (((heap_T757603679106148408unit_a @ (heap_T2927564422264180874t_unit @ X0) @ X1) = (heap_Time_raise_a @ X0))) )),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f13877])).
% 25.35/7.41  thf(f13877,plain,(
% 25.35/7.41    ! [X0 : list_char,X1 : product_unit > heap_Time_Heap_a] : ((heap_T757603679106148408unit_a @ (heap_T2927564422264180874t_unit @ X0) @ X1) = (heap_Time_raise_a @ X0))),
% 25.35/7.41    inference(rectify,[status(thm)],[f164])).
% 25.35/7.41  thf(f164,axiom,(
% 25.35/7.41    ! [X33 : list_char,X1 : product_unit > heap_Time_Heap_a] : ((heap_Time_raise_a @ X33) = (heap_T757603679106148408unit_a @ (heap_T2927564422264180874t_unit @ X33) @ X1))),
% 25.35/7.41    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_163_raise__bind)).
% 25.35/7.41  thf(f14708,plain,(
% 25.35/7.41    ($true != (ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char))))))) @ (^[Y0 : product_unit]: (m))) @ h) @ t))),
% 25.35/7.41    inference(subsumption_resolution,[status(thm)],[f14292,f14640])).
% 25.35/7.41  thf(f14640,plain,(
% 25.35/7.41    (p != $true)),
% 25.35/7.41    inference(subsumption_resolution,[status(thm)],[f14639,f14194])).
% 25.35/7.41  thf(f14194,plain,(
% 25.35/7.41    ( ! [X0 : heap_e7401611519738050253t_unit] : (((ord_less_eq_nat @ (time_time_a @ m @ X0) @ t) = $true) | (p != $true)) )),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f13964])).
% 25.35/7.41  thf(f13964,plain,(
% 25.35/7.41    ! [X0 : heap_e7401611519738050253t_unit] : ((p != $true) | ((ord_less_eq_nat @ (time_time_a @ m @ X0) @ t) = $true))),
% 25.35/7.41    inference(ennf_transformation,[status(thm)],[f8210])).
% 25.35/7.41  thf(f8210,plain,(
% 25.35/7.41    ! [X0 : heap_e7401611519738050253t_unit] : ((p = $true) => ((ord_less_eq_nat @ (time_time_a @ m @ X0) @ t) = $true))),
% 25.35/7.41    inference(fool_elimination,[status(thm)],[f8209])).
% 25.35/7.41  thf(f8209,plain,(
% 25.35/7.41    ! [X0 : heap_e7401611519738050253t_unit] : (p => (ord_less_eq_nat @ (time_time_a @ m @ X0) @ t))),
% 25.35/7.41    inference(rectify,[status(thm)],[f1])).
% 25.35/7.41  thf(f1,axiom,(
% 25.35/7.41    ! [X0 : heap_e7401611519738050253t_unit] : (p => (ord_less_eq_nat @ (time_time_a @ m @ X0) @ t))),
% 25.35/7.41    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_0__092_060open_062_092_060And_062h_O_AP_A_092_060Longrightarrow_062_Atime_Am_Ah_A_092_060le_062_At_092_060close_062)).
% 25.35/7.41  thf(f14639,plain,(
% 25.35/7.41    ($true != (ord_less_eq_nat @ (time_time_a @ m @ h) @ t)) | (p != $true)),
% 25.35/7.41    inference(beta_eta_normalization,[status(thm)],[f14638])).
% 25.35/7.41  thf(f14638,plain,(
% 25.35/7.41    (p != $true) | ((ord_less_eq_nat @ (time_time_a @ ((^[Y0 : product_unit]: (m)) @ product_Unity) @ h) @ t) != $true)),
% 25.35/7.41    inference(forward_demodulation,[status(thm)],[f14637,f14136])).
% 25.35/7.41  thf(f14136,plain,(
% 25.35/7.41    ( ! [X0 : product_unit,X1 : product_unit > heap_Time_Heap_a] : (((heap_T757603679106148408unit_a @ (heap_T4284346855313245393t_unit @ X0) @ X1) = (X1 @ X0))) )),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f13876])).
% 25.35/7.41  thf(f13876,plain,(
% 25.35/7.41    ! [X0 : product_unit,X1 : product_unit > heap_Time_Heap_a] : ((heap_T757603679106148408unit_a @ (heap_T4284346855313245393t_unit @ X0) @ X1) = (X1 @ X0))),
% 25.35/7.41    inference(rectify,[status(thm)],[f218])).
% 25.35/7.41  thf(f218,axiom,(
% 25.35/7.41    ! [X5 : product_unit,X1 : product_unit > heap_Time_Heap_a] : ((heap_T757603679106148408unit_a @ (heap_T4284346855313245393t_unit @ X5) @ X1) = (X1 @ X5))),
% 25.35/7.41    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_217_ureturn__bind)).
% 25.35/7.41  thf(f14637,plain,(
% 25.35/7.41    (p != $true) | ($true != (ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (heap_T4284346855313245393t_unit @ product_Unity) @ (^[Y0 : product_unit]: (m))) @ h) @ t))),
% 25.35/7.41    inference(forward_demodulation,[status(thm)],[f14619,f14225])).
% 25.35/7.41  thf(f14225,plain,(
% 25.35/7.41    ( ! [X2 : heap_T5738788834812785303t_unit,X3 : product_unit > heap_Time_Heap_a,X1 : heap_T5738788834812785303t_unit] : (((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ $true @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X2 @ X3))) )),
% 25.35/7.41    inference(equality_resolution,[status(thm)],[f14152])).
% 25.35/7.41  thf(f14152,plain,(
% 25.35/7.41    ( ! [X2 : heap_T5738788834812785303t_unit,X3 : product_unit > heap_Time_Heap_a,X0 : $o,X1 : heap_T5738788834812785303t_unit] : (($true != X0) | ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X2 @ X3))) )),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f13905])).
% 25.35/7.41  thf(f13905,plain,(
% 25.35/7.41    ! [X0 : $o,X1 : heap_T5738788834812785303t_unit,X2 : heap_T5738788834812785303t_unit,X3 : product_unit > heap_Time_Heap_a] : ((($true != X0) | ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X2 @ X3))) & (((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X1 @ X3)) | ($true = X0)))),
% 25.35/7.41    inference(ennf_transformation,[status(thm)],[f13874])).
% 25.35/7.41  thf(f13874,plain,(
% 25.35/7.41    ! [X0 : $o,X1 : heap_T5738788834812785303t_unit,X2 : heap_T5738788834812785303t_unit,X3 : product_unit > heap_Time_Heap_a] : ((($true = X0) => ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X2 @ X3))) & (($true != X0) => ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X1 @ X3))))),
% 25.35/7.41    inference(flattening,[status(thm)],[f12872])).
% 25.35/7.41  thf(f12872,plain,(
% 25.35/7.41    ! [X0 : $o,X1 : heap_T5738788834812785303t_unit,X2 : heap_T5738788834812785303t_unit,X3 : product_unit > heap_Time_Heap_a] : ((($true = X0) => ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X2 @ X3))) & (~($true = X0) => ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X1 @ X3))))),
% 25.35/7.41    inference(fool_elimination,[status(thm)],[f12871])).
% 25.35/7.41  thf(f12871,plain,(
% 25.35/7.41    ! [X0 : $o,X1 : heap_T5738788834812785303t_unit,X2 : heap_T5738788834812785303t_unit,X3 : product_unit > heap_Time_Heap_a] : ((X0 => ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X2 @ X3))) & (~X0 => ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X1 @ X3))))),
% 25.35/7.41    inference(rectify,[status(thm)],[f21])).
% 25.35/7.41  thf(f21,axiom,(
% 25.35/7.41    ! [X7 : $o,X9 : heap_T5738788834812785303t_unit,X8 : heap_T5738788834812785303t_unit,X1 : product_unit > heap_Time_Heap_a] : ((X7 => ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X7 @ X8 @ X9) @ X1) = (heap_T757603679106148408unit_a @ X8 @ X1))) & (~X7 => ((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X7 @ X8 @ X9) @ X1) = (heap_T757603679106148408unit_a @ X9 @ X1))))),
% 25.35/7.41    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_20_distrib__if__bind)).
% 25.35/7.41  thf(f14619,plain,(
% 25.35/7.41    (p != $true) | ((ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ $true @ (heap_T4284346855313245393t_unit @ product_Unity) @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char)))))))) @ (^[Y0 : product_unit]: (m))) @ h) @ t) != $true)),
% 25.35/7.41    inference(beta_eta_normalization,[status(thm)],[f14265])).
% 25.35/7.41  thf(f14265,plain,(
% 25.35/7.41    ( ! [X0 : nat] : (((ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ $true @ (heap_T4284346855313245393t_unit @ product_Unity) @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char)))))))) @ (^[Y0 : product_unit]: (m))) @ h) @ t) != $true) | ($true != ((^[Y0 : nat]: (p)) @ X0))) )),
% 25.35/7.41    inference(superposition,[status(thm)],[f14251,f14081])).
% 25.35/7.41  thf(f14081,plain,(
% 25.35/7.41    ( ! [X0 : nat,X1 : nat > $o] : (((X1 @ (sK10 @ X1 @ X0)) = $true) | ((X1 @ X0) != $true)) )),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f14018])).
% 25.35/7.41  thf(f14018,plain,(
% 25.35/7.41    ! [X0 : nat,X1 : nat > $o] : ((((X1 @ (sK10 @ X1 @ X0)) = $true) & ((ord_less_eq_nat @ (sK10 @ X1 @ X0) @ X0) = $true)) | (((X1 @ X0) != $true) & ! [X3 : nat] : (((ord_less_nat @ X3 @ X0) != $true) | ($true != (X1 @ X3)))))),
% 25.35/7.41    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f14016,f14017])).
% 25.35/7.41  thf(f14017,plain,(
% 25.35/7.41    ! [X0 : nat,X1 : nat > $o] : (? [X2 : nat] : (($true = (X1 @ X2)) & ($true = (ord_less_eq_nat @ X2 @ X0))) => (((X1 @ (sK10 @ X1 @ X0)) = $true) & ((ord_less_eq_nat @ (sK10 @ X1 @ X0) @ X0) = $true)))),
% 25.35/7.41    introduced(definition,[],[choice_axiom])).
% 25.35/7.41  thf(f14016,plain,(
% 25.35/7.41    ! [X0 : nat,X1 : nat > $o] : (? [X2 : nat] : (($true = (X1 @ X2)) & ($true = (ord_less_eq_nat @ X2 @ X0))) | (((X1 @ X0) != $true) & ! [X3 : nat] : (((ord_less_nat @ X3 @ X0) != $true) | ($true != (X1 @ X3)))))),
% 25.35/7.41    inference(rectify,[status(thm)],[f13909])).
% 25.35/7.41  thf(f13909,plain,(
% 25.35/7.41    ! [X0 : nat,X1 : nat > $o] : (? [X3 : nat] : (($true = (X1 @ X3)) & ($true = (ord_less_eq_nat @ X3 @ X0))) | (((X1 @ X0) != $true) & ! [X2 : nat] : (($true != (ord_less_nat @ X2 @ X0)) | ($true != (X1 @ X2)))))),
% 25.35/7.41    inference(ennf_transformation,[status(thm)],[f13883])).
% 25.35/7.41  thf(f13883,plain,(
% 25.35/7.41    ! [X0 : nat,X1 : nat > $o] : ((! [X2 : nat] : (($true = (ord_less_nat @ X2 @ X0)) => ($true != (X1 @ X2))) => ((X1 @ X0) = $true)) => ? [X3 : nat] : (($true = (X1 @ X3)) & ($true = (ord_less_eq_nat @ X3 @ X0))))),
% 25.35/7.41    inference(flattening,[status(thm)],[f10860])).
% 25.35/7.41  thf(f10860,plain,(
% 25.35/7.41    ! [X0 : nat,X1 : nat > $o] : ((! [X2 : nat] : (($true = (ord_less_nat @ X2 @ X0)) => ~($true = (X1 @ X2))) => ((X1 @ X0) = $true)) => ? [X3 : nat] : (($true = (X1 @ X3)) & ($true = (ord_less_eq_nat @ X3 @ X0))))),
% 25.35/7.41    inference(fool_elimination,[status(thm)],[f10859])).
% 25.35/7.41  thf(f10859,plain,(
% 25.35/7.41    ! [X0 : nat,X1 : nat > $o] : ((! [X2 : nat] : ((ord_less_nat @ X2 @ X0) => ~(X1 @ X2)) => (X1 @ X0)) => ? [X3 : nat] : ((ord_less_eq_nat @ X3 @ X0) & (X1 @ X3)))),
% 25.35/7.41    inference(rectify,[status(thm)],[f1402])).
% 25.35/7.41  thf(f1402,axiom,(
% 25.35/7.41    ! [X16 : nat,X27 : nat > $o] : ((! [X86 : nat] : ((ord_less_nat @ X86 @ X16) => ~(X27 @ X86)) => (X27 @ X16)) => ? [X87 : nat] : ((ord_less_eq_nat @ X87 @ X16) & (X27 @ X87)))),
% 25.35/7.41    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_1401_exists__leI)).
% 25.35/7.41  thf(f14251,plain,(
% 25.35/7.41    ($true != (ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ p @ (heap_T4284346855313245393t_unit @ product_Unity) @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char)))))))) @ (^[Y0 : product_unit]: (m))) @ h) @ t))),
% 25.35/7.41    inference(beta_eta_normalization,[status(thm)],[f14203])).
% 25.35/7.41  thf(f14203,plain,(
% 25.35/7.41    ($true != (ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ ((^[Y0 : $o]: (if_Hea8138950348631371857t_unit @ Y0 @ (heap_T4284346855313245393t_unit @ product_Unity) @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char))))))))) @ p) @ (^[Y0 : product_unit]: (m))) @ h) @ t))),
% 25.35/7.41    inference(definition_unfolding,[status(thm)],[f14051,f14140])).
% 25.35/7.41  thf(f14140,plain,(
% 25.35/7.41    (refine_Imp_assert = (^[Y0 : $o]: (if_Hea8138950348631371857t_unit @ Y0 @ (heap_T4284346855313245393t_unit @ product_Unity) @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char))))))))))),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f7010])).
% 25.35/7.41  thf(f7010,plain,(
% 25.35/7.41    (refine_Imp_assert = (^[Y0 : $o]: (if_Hea8138950348631371857t_unit @ Y0 @ (heap_T4284346855313245393t_unit @ product_Unity) @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char))))))))))),
% 25.35/7.41    inference(fool_elimination,[status(thm)],[f7009])).
% 25.35/7.41  thf(f7009,plain,(
% 25.35/7.41    (refine_Imp_assert = (^[X0 : $o] : (if_Hea8138950348631371857t_unit @ X0 @ (heap_T4284346855313245393t_unit @ product_Unity) @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char))))))))))),
% 25.35/7.41    inference(rectify,[status(thm)],[f5899])).
% 25.35/7.41  thf(f5899,axiom,(
% 25.35/7.41    (refine_Imp_assert = (^[X81 : $o] : (if_Hea8138950348631371857t_unit @ X81 @ (heap_T4284346855313245393t_unit @ product_Unity) @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char))))))))))),
% 25.35/7.41    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',fact_5898_assert_H__def)).
% 25.35/7.41  thf(f14051,plain,(
% 25.35/7.41    ($true != (ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (refine_Imp_assert @ p) @ (^[Y0 : product_unit]: (m))) @ h) @ t))),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f13873])).
% 25.35/7.41  thf(f13873,plain,(
% 25.35/7.41    ($true != (ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (refine_Imp_assert @ p) @ (^[Y0 : product_unit]: (m))) @ h) @ t))),
% 25.35/7.41    inference(flattening,[status(thm)],[f11690])).
% 25.35/7.41  thf(f11690,plain,(
% 25.35/7.41    ~($true = (ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (refine_Imp_assert @ p) @ (^[Y0 : product_unit]: (m))) @ h) @ t))),
% 25.35/7.41    inference(fool_elimination,[status(thm)],[f11689])).
% 25.35/7.41  thf(f11689,plain,(
% 25.35/7.41    ~(ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (refine_Imp_assert @ p) @ (^[X0 : product_unit] : (m))) @ h) @ t)),
% 25.35/7.41    inference(rectify,[status(thm)],[f6109])).
% 25.35/7.41  thf(f6109,negated_conjecture,(
% 25.35/7.41    ~(ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (refine_Imp_assert @ p) @ (^[X37 : product_unit] : (m))) @ h) @ t)),
% 25.35/7.41    inference(negated_conjecture,[status(cth)],[f6108])).
% 25.35/7.41  thf(f6108,conjecture,(
% 25.35/7.41    (ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (refine_Imp_assert @ p) @ (^[X37 : product_unit] : (m))) @ h) @ t)),
% 25.35/7.41    file('/export/starexec/sandbox/tmp/tmp.3RAdJfyPae/DTF2THF_31173.p',conj_0)).
% 25.35/7.41  thf(f14292,plain,(
% 25.35/7.41    ($true != (ord_less_eq_nat @ (time_time_a @ (heap_T757603679106148408unit_a @ (heap_T2927564422264180874t_unit @ (cons_char @ (char2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ $false) @ (cons_char @ (char2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ $false) @ nil_char))))))) @ (^[Y0 : product_unit]: (m))) @ h) @ t)) | (p = $true)),
% 25.35/7.41    inference(superposition,[status(thm)],[f14251,f14151])).
% 25.35/7.41  thf(f14151,plain,(
% 25.35/7.41    ( ! [X2 : heap_T5738788834812785303t_unit,X3 : product_unit > heap_Time_Heap_a,X0 : $o,X1 : heap_T5738788834812785303t_unit] : (((heap_T757603679106148408unit_a @ (if_Hea8138950348631371857t_unit @ X0 @ X2 @ X1) @ X3) = (heap_T757603679106148408unit_a @ X1 @ X3)) | ($true = X0)) )),
% 25.35/7.41    inference(cnf_transformation,[status(thm)],[f13905])).
% 25.35/7.41  % SZS output end Proof for DTF2THF_31173
% 25.35/7.41  % (31394)------------------------------
% 25.35/7.41  % (31394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.35/7.41  % (31394)Termination reason: Refutation
% 25.35/7.41  
% 25.35/7.41  % (31394)Memory used [KB]: 20084
% 25.35/7.41  % (31394)Time elapsed: 0.588 s
% 25.35/7.41  % (31394)Instructions burned: 1150 (million)
% 25.35/7.41  % (31394)------------------------------
% 25.35/7.41  % (31394)------------------------------
% 25.35/7.41  % (31293)Success in time 2.8 s
%------------------------------------------------------------------------------